ADELAIDE by yaofenji

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									ADELAIDE
CASINO




GAMING
MANUAL
CONTENT OVERVIEW

PREFACE

CHAPTER 1 PLAYER RATING ………………………………………………...1
 1.0   Terminology ……………………………………………………………………. 3
 1.1   Introduction (background) ……………………………………………………. 3
 1.2   The Current Adelaide Casino Complimentary Policy ………………………5
 1.3   System walkthrough ………………………………………………………….. 6
 1.4   Premium player marketing …………………………………………………… 7
 1.5   The Adelaide Casino’s Competitors ………………………………………… 7
 1.6   Complimentary Policy Profitability ……………………………………………10
 1.7   Hard Versus Soft Comps …………………………………………………….. 11
 1.8   Rating Efficiency Levels ……………………………………………………… 12
 1.9   Conclusion …………………………………………………………………….. 12
 1.10 A Commentary On Casino Player Rating Systems ……………………….. 13
 1.11 Promotional Chips and Tokens ……………………………………………… 28


CHAPTER 2 JUNKET PROGRAM …………………………………………….33
 2.1   Junket Fact Sheet …………………………………………………………….. 35
 2.2   Overview of Junkets …………………………………………………………...36
 2.3   Extract From Junket Manual …………………………………………………. 36
 2.4   Cash Chip System Analysis …………………………………………………..49
 2.5   Non Negotiable Chip System Non Negotiable Chip Program ……………. 62
 2.6   Premium Player 0.5% (Splinter Policy) ……………………………………... 81
 2.7   Player Loss …………………………………………………………………….. 84


CHAPTER 3 CARD COUNTING ……………………………………………….93
 3.1   Brief Overview …………………………………………………………………. 95
 3.2   Legalities (Precedents) ……………………………………………………….. 96
 3.3   Counter Measures …………………………………………………………….. 97
 3.4   Profit Analysis …………………………………………………………………. 99
 3.5   Blackjack Simulation Experiment ……………………………………………. 104


CHAPTER 4 KEY CONCEPTS …………………………………………………109
 4.1   Sub Optimisation …………….………………………………………………... 111
 4.2   Hold Percentage ………………………………………………………………. 111
 4.3   Law of Averages ………………………………………………………………. 112
 4.4   Money Management ………………………………………………………….. 114
 4.5   Psychology Of Gamblers ……………………………………………….……. 115
 4.6   Mathematical Expectation ……………………………………………………. 115
 4.7   Standard Deviation (Repeated Trials) ………………………………………. 117
 4.8   Optimal Betting …………………………………………………………………117
 4.9   House Advantage ……………………………………………………………... 118
 4.10 Throwing Out Ties (Absolute Versus Relative Probability) ……………….. 119
 4.11 Blackjack Win Percentage …………………………………………………… 120
 4.12 Blackjack Formula …………………………………………………………….. 121
 4.13 Various Numbers of Decks (Blackjack) …………………………………….. 123
 4.14 Baiting the Hook ………………………………………………………………. 123
 4.15 Baccarat and Chemin De Fer ………………………………………………... 124
 4.16 Why People Gamble ………………………………………………………….. 125
 4.17 Customers Expectations of Staff ……………………………………………..126


CHAPTER 5 INSPECTOR’S DUTIES …………………………………………127
 5.1   Inspector Job Specification ………………………………………………..                129
 5.2   Inspectors Manual …………………………………………………………                        131
 5.3   Blackjack Game Protection ………………………………………………                    136
 5.4   Roulette Game Protection …………………………………………………                    137
 5.5   Building Extraordinary Casino Patron Service …………………………… 141
 5.6   Casino Supervision – A Basic Guide ……………………………………… 147
 5.7   I am Your Guest ……………………………………………………………                         148
 5.8   Extract from the Pit Boss Training Manual ……………………………….         148


CHAPTER 6 SETTING TABLE MAXIMUM BET LIMITS ……………………151
 6.1   Background ………………………………………………………………                             153
 6.2   Key Principles ……………………………………………………………                          153
 6.3   Setting proper table limits ………………………………………………..                154
 6.4   Maximum Loss Point …………………………………………………….                        158
 6.5   Effect of Variable Bet Distributions ………………………………………            159
 6.6   Non High-End Casino Operation …………………………………………                  162
 6.7   Conclusion ………………………………………………………………..                           166


INDEX ………………………………………………………………………………167
PREFACE

The information contained within the following text is intended to provide an interesting insight to the
reader on general Casino information and is issued as a basic reference guide.

This has been collated from analyses written by myself and extracts have also been taken from various
books and articles.

Whilst a plethora of documentation exists on various Casino games and gaming, very little of this is
truly useful. It would seem that generally anyone can write a book on gaming and more particularly on
“winning” systems. Texts which I would highly recommend to any Casino staff are as follows:

               “The Casino Gamblers‟ Guide” by Alan N Wilson
               “Card Counting for the Casino Executive” by Bill Zender
               “Playing Blackjack in Atlantic City” by Chambliss and Roginski
               “The Mathematics of Gambling” by E O Thorp
               Any works by Peter Griffin
               Any works by Jim Kilby

Any reading on the subject is obviously worthwhile but I believe these books will assist you in
questioning or accepting some of the statements which are made elsewhere.

In closing, I would like to thank Sara Wegener for her painstaking assistance in putting this manual
together.

I trust you will find it both interesting and useful as you progress through the Casino industry.

Regards,




Andrew MacDonald
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Chapter 1     Player Rating




    “We are in the gambling business not
    in the business of gambling”
Chapter 1       Player Rating

1.0      Terminology ……………………………………………………………….                                  3

1.1      Introduction (background) …………………………………………………                           3
1.1.1    What is player rating? ……………………………………………………...                          3
1.1.2    Why rate players? ………………………………………………………….                               3
1.1.4    How much of a “high rollers” theoretical loss is extended to him/her in
         complimentaries? ………………………………………………………….                                4
1.1.5    How do the Casinos generally define “high rollers”? ……………………. 4
1.1.6    How much revenue is contributed on a yearly basis by rated players? ……4
1.1.7    Why rebate complimentaries and not cash? ………………………………. 4

1.2      The Current Adelaide Casino Complimentary Policy …………………….. 5
1.2.1    Formulae and system standards (as at 10.10.1991) ……………………….. 5
1.2.2    General policy requirements ……………………………………………….              5

1.3      System walkthrough ……………………………………………………….                              6

1.4      Premium player marketing …………………………………………………                           7

1.5      The Adelaide Casino’s Competitors ……………………………………….                     7
1.5.1    Wrest Point Casino complimentary policy (extract) Wrest Point .………..   7
1.5.2    Wrest Point Casino system standards ……………………………………..                   8
1.5.3    Jupiters Casino Complimentary policy (extract) Jupiters …………………        8
1.5.4    Jupiter’s Casino system standards …………………………………………                     8
1.5.5    Sheraton Breakwater (Townsville) complimentary policy ………………..         9
1.5.6    Sheraton Breakwater system standards ……………………………………                    10

1.6      Complimentary Policy Profitability ………………………………………..                   10
1.6.1    System Weaknesses ………………………………………………………..                              10

1.7      Hard Versus Soft Comps ………………………………………………….                            11
1.7.1    Definitions …………………………………………………………………                                  11
1.7.2    Implications ………………………………………………………………..                                11

1.8      Rating Efficiency Levels …………………………………………………..                         12

1.9      Conclusion …………………………………………………………………                                   12

1.10     A Commentary On Casino Player Rating Systems ………………………..               13
1.10.1   Introduction ……………………………………………………………….                                 13
1.10.1   Four Most Common Player Rating System Weaknesses …………………               13
1.10.2   System Development ……………………………………………………...                             18
1.10.3   Criteria Development ………………………………………………………                             18
1.10.3   Summary and Conclusions ………………………………………………..                           26

1.11     Promotional Chips and Tokens …………………………………………..                        28
1.0             Terminology
The following Casino terminology/abbreviations are used extensively throughout this report:

Comps.                     Complimentaries (eg. room, food, beverage etc.) extended to a third party at
                           partial or no cost.
Bottom line                Net profit after all costs have been deducted.
Bev.                       Beverage
Av. Bet                    Average bet
BJ                         Blackjack
AR                         American Roulette
MB                         Mini Baccarat
BA                         Baccarat
B&S                        Big and Small
PRS                        Player Rating System – Computerised database used to maintain player
                           information.
VIP                        Very Important Person
Line                       Credit line/facility


1.1             Introduction (background)
1.1.1           What is player rating?

Player rating is a system by which a player‟s worth/value to the profitability of the Casino Operation is
approximated.

1.1.2           Why rate players?

Once a player‟s value is determined, complimentaries such as room, food and beverage, airfare
reimbursement etc. may be offered to that player as an enticement for a return visit to the Casino. This
is a valuable marketing tool used to penetrate the premium or “high roller” market both interstate and
overseas.

1.1.3           How is a player rated?

Various rating systems exist however the systems in Australian Casinos at present rely on gaming
personnel to provide the following information on individual players:

               buy in
               average bet (bet range)
               time played
               win/loss
               game played (decision rates)
               location


This source information is collated and utilised to calculate a theoretical win by applying the following
formula.

Theoretical win = average bet x time played x hands/hour x game edge.
The game edge is the mathematical expectation based on game odds, probabilities, and distribution of
play.

The hands/hour information may be based on average decision rates from gaming surveys of individual
games or may be provided by the gaming personnel at time of rating.

1.1.4        How much of a “high rollers” theoretical loss is extended to
him/her in complimentaries?

This may vary from player to player and Casino to Casino. Other Australian Casinos offer between 25
and 50 percent return based on theoretical win and other conditions.

1.1.5            How do the Casinos generally define “high rollers”?

Some Casinos require a minimum bankroll (deposit) to qualify and/or minimum average bet
requirements, these may vary by player‟s state or origin and game played etc. In Tasmania for example
the minimum bankroll required is $10,000 for Victorian players with an average bet of $150. The
Adelaide Casino policy at present is to require a minimum wager amount to qualify. Whilst this may
seem low by comparison the complimentaries offered to a player playing the minimum required are also
much lower.

Bankroll requirements are generally meaningless when turnover is utilised and comps. provided based
of play levels.

1.1.6            How much revenue is contributed on a yearly basis by rated
players?

While this is not greatly significant in itself for an operation of this size, given that the general Casino
infrastructure would already exist this is an important potential increment to bottom line profit.

1.1.7            Why rebate complimentaries and not cash?

Complimentaries are often “soft” costs to the Casino operator. For example in-house food and beverage
complimentaries may really only cost the operator the cost of the ingredients and the preparation time.
Therefore the real cost differs from the retail cost of the complimentary. This is also true of room costs
if the Casino is part of a hotel/Casino complex. In this case the real cost depends on percentage
occupancy and possibly the real cost during off season periods may be as low as the cost of cleaning the
room. This means that the Casino operators rebate based on theoretical win can really be non existent
until such time as external costs are incurred, as soon as this happens bottom line is affected. The other
obvious problem with cash rebates is the fact that generally with high level premiums the players
expenses do not meet the complimentary value, however with a cash rebate the maximum would always
be paid out. Another problem is the inherent inaccuracy of player rating in this manner (ie totally
accurate turnover and game edge information is often not available), therefore costs incurred could be
greater than the potential revenue achieved in some cases.

Thus complimentaries such as room, food and beverage may be easier comps. to provide and can be in
some cases a cost free marketing tool.


1.2              The Current Adelaide Casino Complimentary Policy
1.2.1            Formulae and system standards (as at 10.10.1994)

The current policy is based on the following formula, decision rates and game edges.
Complimentary value = complimentary % x (theoretical win – tax – staff costs)
Complimentary % = 50% standard
Theoretical win = av. bet x time played x hands/hr x edge
Tax % = 20%
Staff costs = $10 / hour of recorded play



SYSTEM STANDARDS

GAME                     LOCATION                   SYSTEM                SYSTEM
                                                    DECISION              HOUSE
                                                    RATE/HR               ADVANTAGE

BJ                       CGA                        63                    1.30%
BJ                       IR                         76                    1.30%
AR                       CGA                        36                    2.70%
AR                       IR                         33                    2.70%
MB                       CGA                        58                    1.26%
MB                       IR                         53                    1.26%
BA                       IR                         41                    1.26%
TWO UP                   CGA                        45                    3.13%
CRAPS                    CGA                        50                    1.50%
BIG WHEEL                CGA                        42                    7.69%
B&S                      CGA                        46                    2.78%
KENO                     CGA                        1                     23.00%
Keno decision rate 1 as turnover figures utilised
CGA = Common Gaming Area
IR = International Room

1.2.2           General policy requirements

COMPLIMENTARY                                       AVERAGE BET REQUIREMENT
2 nights at Hyatt                                   $50 per hand/spin*
Regency Adelaide
* based on 12 hours playing time


Airfare reimbursements are based on the formula provided in 3.1, therefore depending on the cost of the
ticket average bet details may vary. The Casino‟s Melbourne policies are based on 12 hours play during
a visit and 15 hours play for players from other locations.


1.3             System walkthrough
a.      An interstate or overseas player having either identified themselves or having been identified by
        a member of the Casino staff is provided with the general policy details.

b.      The players name and other details are taken with a file being opened on that player in the
        Player Rating System. This file maintains player details and individual transaction details.
c.     Prior to a player‟s arrival their name, flight/arrival details, accommodation and special
       requirements (if any) are placed on a VIP list which is distributed to various Casino personnel.

d.     On arrival at the Casino the player receives a package containing an identifying rating card and
       vouchers to allow dining in the Pullman Restaurant (these are now provided only if authorised
       by the Player Development Manager).

e.     The player on arriving at a gaming table is to present their rating card to the table Inspector.
       This identifies the player to the Inspector and makes him/her aware that the player is to be rated.
       The inspector then transcribes information from the rating card to a worksheet also noting the
       time of commencement and initial buy in details.

f.     The Inspector‟s worksheet is updated for the duration of the player‟s play at that table.

g.     On the player leaving the table, the Inspector finalises details for that player on his/her
       worksheet. The following information is then transcribed to a rating sheet:-

               Players full name and number
               Game played
               Location
               Buy in
               Average bet
               Win/loss
               Time played
               Date
               Inspectors name
               Pit Boss name

h.     This data is then entered into the Casino‟s computer system (AS/400 Player Rating System) by
       another member of staff.

i.     Having been entered, the system automatically updates the player‟s transaction file for that visit
       and a complimentary value is calculated and displayed on the player‟s visit/totals file.

j.     The player‟s file is continually updated with gaming transactions for the duration of the stay
       with the expenses incurred by that player being entered against the complimentary value.
       Generally speaking all reimbursements are made after the players current comp. value has been
       referred to.

k.     On the player leaving, their comp. value is reviewed with reimbursement of the players
       expenses made accordingly.

l.     Each player‟s visit is treated separately however on occasions practical business decisions may
       be based on previous play levels. Also should the player suffer a substantial “premature” loss
       without accruing turnover and therefore comp. value, 10% of the loss may be extended to the
       player in complimentaries.


1.4             Premium player marketing
The Adelaide Casino penetrates the premium player market by the following means:-
a.     interstate and overseas offices (offices are located in Melbourne and Singapore)
b.     promotions and tournaments (eg High Stakes, Blackjack)
c.     special events (Grand Prix)
d.     telemarketing
e.     direct marketing
f.      advertising (magazines etc)

1.5             The Adelaide Casino’s Competitors
Obviously given that a premium player‟s contribution is an important potential increment to bottom line
profitability, fierce competition exists between Casinos in an attempt to gain a larger market share.
Therefore each Casino tends to offer slightly different policies to entice players as well as offering
various combinations of the aforementioned marketing packages.

As far as the Australian premium player market is concerned the main competitors to the Adelaide
Casino are Jupiter‟s Casino on the Gold Coast and the two Tasmanian Casinos operated by Federal
Hotels. The primary reason that these Casinos are competitors is basically proximity to the large
Eastern seaboard markets of Melbourne and Sydney. The Tasmanian Casinos success may be due in
some degree to player loyalty established through a long association both with the Casino and individual
staff members (West Point Casino in Hobart opened in 1972 and held a virtual monopoly until the major
Australian Casinos developments of 1985).

The Jupiters Casino on the Gold Coast has only recently moved into the premium player market with
their Club Conrad opening in 1989. The success of this operation may rely on proximity to the Sydney
market, the resort facilities offered, climate and general Gold Coast facilities. Both operators would
also suggest excellence of service plays a role.

In terms of competition for the overseas premium player it is first necessary to establish that due to
proximity the Asian market is the most lucrative and has the greatest potential for Australian Casino
operators.

The Adelaide Casino‟s Australian competitors for this market are Burswood Resort Casino (Perth),
Diamond Beach Casino (Darwin) and Jupiter‟s Casino (Gold Coast). Due to the immense population
base and wealth (albeit of a small percentage) of this area makes this a very competitive market. The
proximity and resort facilities provide our competitors with some advantages, however, the Adelaide
Casino‟s service levels still provide an acceptable market share. Still in dollar terms the local premium
market, due to a greater total volume of players, is the Adelaide Casino‟s primary market.


1.5.2           Wrest Point Casino complimentary policy (extract) Wrest Point

STATE OF ORIGIN                  AMOUNT                   AVE BET

Victoria                         10 000                   $150
NSW, SA & ACT                    15 000                   $200
Queensland                       15 000                   $250
WA & NT                          20 000                   $300

“To qualify for Premium Player Status, the following conditions must be observed. Playing time per
day has to be a minimum of four hours duration but not necessary at one sitting, in order to qualify for
one economy airfare and two nights in house accommodation. Upon arrival at the Casino you must
exchange cash or bank cheques for cheque credits at the Casino Cash Desk. The amount to be lodged,
and the average bet per hand or spin varies depending on the player‟s state of origin. The table above
should assist you.

Premium players are requested to wear a VIP pin at all times, to enable our staff to provide you with the
attention you deserve”.


1.5.3           Wrest Point Casino system standards
Complimentary value (max) = 30% x theoretical win


GAME              DECISION RATE                    EDGE

BJ                                80                       2.0%
AR                                60                       2.7%
BA                                40                       1.0%

Also 20% payable on substantial loss greater than 3500.

1.5.3             Jupiters Casino Complimentary policy (extract) Jupiters


PLAYER DEPOSIT/LINE               MIN. AVE         IN HOUSE                         MAX
REIMBURSEMENT                     BET              COMPLIMENTARY                    AIRFARE

$3 000                            $50               Room only                       0
$5 000                            $50               Room only                       0
                                  $100              R,F,B                           0
$ 7 500                           $100              R,F,B                           0
                                  $150              R,F,B                           $250
$10 000                           $125              R,F,B                           0
                                  $150              R,F,B                           $250
                                  $175              R,F,B                           $400
$15 000                           $150              R,F,B                           $250
                                  $175              R,F,B                           $400
                                  $200              R,F,B                           $550

1.        Complimentaries are based on playing requirements of four hours per day.

2.        Maximum guest trips shall be three nights/four days.

3.        In house complimentaries of room, food and beverage are extended to the player and one guest.
          All other charges are the responsibility of the player and shall be settled on check out.

4.        Airfare reimbursements are based on a minimum of 12 hours playing time.

5.        A player‟s complimentary level may be reduced if his average bet size falls below the expected
          level as indicated by his deposit/line.

6.        A player who loses a significant portion of his deposit/line shall be entitled to the maximum
          level of complimentaries available to him, regardless of his average bet size.


1.5.4             Jupiter’s Casino system standards

GAME         DECISION RATE             EDGE
__________________________________________________

BJ                                60                       2.0%
AR                                60                       2.0%
BA                                45                       1.27%
CR                                40                       2.5%
TU                                35                       3.1%
BS                                45                       4.0%
BW                               40                       4.0%
MB                               60                       1.27%
KE                               10                       27.0%

1.5.5           Sheraton Breakwater (Townsville) complimentary policy

A player should begin by establishing a credit line with the Casino, or by depositing front money at the
Casino cage commensurate with the playing levels described below.

All complimentary room, food, beverage and airfare reimbursement are based on a minimum of four
hours of play per day or multiples thereof. Complimentary privileges are extended for a maximum of
four nights (16 hours of play). A minimum of 12 hours of play is required for airfare reimbursements
(see 5 to 10 over).


Sunday through Thursday package average wagers


CREDIT LINE BLACK DICE            BACC- ROULETTE COMP. DESCRIPTION**
FRONT         JACK     SPREAD ARAT        “0”/”00”
MONEY                  *
__________________________________________________________________________________

$1000-1500       $35         $35          $35       $35/25        Deluxe rm ***
$1500-2500       $50         $50          $50       $50/25        Deluxe rm, $20 per day food & bev.
$2500-5000       $75         $75          $75       $75/50        Deluxe rm, $65 per day food & bev.
$5000-7500       $100        $100         $100      $100/50       Deluxe rm, $110 per day food & bev.
$7500-10000      $150        $150         $150      $150/75       Deluxe $100 per day food and bev.
                                                                  limited coach airfare max $300
$10000-12500     $225        $225         $225      $225/125      Deluxe $150 per day food and bev.
                                                                  limited coach/airfare max. $600
$12500–15000     $250        $250         $250      $250/125      Mini $175 per day food and bev.
                                                                  limited coach airfare max. $600
$15000-20000     $300        $300         $300      $300/150      Corner $175 per day food and bev.
                                                                  limited coach airfare max $600
$20000-2500      $400        $400         $400      $400/200      Theme suite, $200 per day food &
                                                                  bev. Limited coach airfare max $800


Sunday through Thursday package average wagers


CREDIT LINE Blackjack Dice        Baccarat   Roulette COMP. DESCRIPTION**
FRONT                   Spread*              “0/00”
MONEY
___________________________________________________________________________________

$25000           $500         $500        $500          $500        Theme suite, $250 per day food and
                                                                    bev. Limited coach airfare max.
                                                                    $1200

         *      Odds do not count in determining spread
         **     All complimentaries are given at the discretion of management and
               can be changed without notice
         ***    Average room rate is $225
General

AVERAGE             HOURS PLAYED PER                VALUE OF COMPS PER
BET                 DAY                             DAY
________________________________________________________________________

50                       5                                                  170
75                       5                                                  225
100                      5                                                  340
200                      5                                                  680


We always take into account in-house costs before reimbursing airfares.

1.5.6           Sheraton Breakwater system standards


GAME                     DECISION                 EDGE
                         RATE

BJ                               80                        1.7%
AR                               60                        2.7%
MB                               70                        1.1%
TWO UP                           40                        3.25%
BIG WHEEL                        60                        4.4%
CRAPS                            45                        1.5%

Complimentary % = 50%


1.6             Complimentary Policy Profitability
The basic rationale behind the Adelaide Casino Complimentary Policy should ensure the profitability of
the program. This is because 50% of theoretical win after tax and staff costs is returned to the player,
thus theoretically leaving a balance of around 30 – 40% in Casino net profit. The criteria for
determining theoretical win is unambiguous as it is based on average bet, time played, hands/hours and
game edges etc.

Therefore if these values are determined correctly and the staff/operational cost is also correct the
program is ensured of operating at a net profit over time, if other general operating costs are also
constrained.

1.6.1           System Weaknesses

The major problem with a system of this type is that whilst overall it is an adequate guide to providing
the value of complimentaries which may be reimbursed, it is a system based on standards which are
averages. Thus the player who does not meet the average criteria may be disadvantaged or conversely
advantaged. For example let us examine the following table of decision rates at the game of Blackjack.
ANALYSIS OF ROUNDS PER HOUR ON BLACKJACK

                 Cards per 7 decks dealt 6 decks dealt 5 decks dealt       4 decks dealt    3 decks dealt
                 hand ave


1 player           2.6        70             60            50               40              30
2 player           2.6        47             40            33               27              20
3 player           2.6        35             30            25               20              15
4 player           2.6        28             24            20               16              12
5 player           2.6        23             20            17               13              10
6 player           2.6        20             17            14               11              9
7 player           2.6        18             15            13               10              8

shuffle time                  2.5            2.5           2.5              2.5             2.5
playing time                  17.6           15.1          12.6             10.1            7.5
total shoe                    20.1           17.6          15.1             12.6            10.0

PER HOUR (per player/box)

1 player                      209            205           199              191             179
2 player                      139            137           133              127             120
3 player                      105            102           100              96              90
4 player                      84             82            80               76              72
5 player                      70             68            66               64              60
6 player                      60             59            57               55              51
7 player                      52             51            50               48              45

This shows the number of variables which exist in determining an average decision rate. The speed of
the dealer, the number of boxes played, the player‟s decision time, deck penetration etc. may all play a
role.

Then we have the situation of variable Blackjack edges depending on skill levels. The combination of
these factors may seriously distort comp. value calculations for individual players. Whilst this should
average out overall, individual players who are disadvantaged will be left with a negative impression of
the Adelaide Casino. This is true for all games where decision rates are variable depending on the
volume of play at the time and various bets with different edges are available on the same game. The
ultimate complimentary system would be based on absolute knowledge of turnover levels, skill levels
and bets placed. No such system for Casino table games currently exists, thus the most appropriate
system is an average system with override capabilities.


1.7                Hard Versus Soft Comps
1.7.1              Definitions

a.         Hard comps: A complimentary which is extended where the actual cost to the company of the
           reimbursement is equal to the retail cost due to a payment being made to a non affiliated third
           party.

b.         Soft comp: A complimentary which is extended where the actual cost to the company of the
           reimbursement is not equal to the retail cost but equals a wholesale cost or partial cost plus
           labour component. Soft comps may vary from being a 100% soft comp. (no real cost) to a hard
           comp in situations where 100% utilisation of the facility occurs.
1.7.2           Implications

The real profitability of operating a premium play program can be distorted by the manner in which
complimentary costs are handled in accounting terms. If the retail cost of every complimentary is
accrued against the program then that process may negatively impact on the program if the provision of
some of these soft comps. is a marketing tool.

For example, if a premium player visits this facility and is provided Pullman meals at her/her request at
full retail cost against their comp. value then the value of other complimentaries which may be extended
will be reduced. This may alter a player‟s perception of the Adelaide Casino if their play levels have
not altered, yet the perceived level of service has declined by reduced comps. This is more true of the
marginal premium player whose average bet level is between $50 to $100 per decision.

The obverse to these scenarios is that during peak periods (Grand Prix etc.) all complimentaries must be
considered at retail value.

This duplicity of costs suggests that the optimal scenario would be to offer distinct programs based on
seasonality/special events with greater soft comps being offered in the off season as an incentive to
attract gaming activity, thus potentially increasing the total complex profit.


1.8             Rating Efficiency Levels
The ability of Gaming personnel to provide reasonably accurate estimates of average bet levels is
questionable given the current sampling criteria and method of rating. The sampling criteria for rated
players is generally by observation and estimate only with no written record to cross reference. Also the
rating is generally completed at the completion of a patron‟s playing time and changing bet levels within
that time may complicate the issue. Given that an Inspector may be required to individually rate a
number of players in a shift, ratings will possibly vary by +/- 10-20%. Other issues that become
involved in this analysis would be staff awareness of game speeds and player skill levels.

There may also be a real tendency towards over-estimating average bet levels when progressive betting
systems are used. This may be because the larger bets are often viewed more closely even though the
actual percentage of these bets is small which when the rating is completed skews the staff members
guess-estimate of an average upwards. Another tendency is for the rated players themselves to attempt
to increase their rating. This can be done by placing larger bets when the Inspector is watching, making
larger than normal bets before leaving the table, missing hands/spins occasionally, making odd wagers
which may be rounded up etc.

Some of these scenarios are not important if the patron‟s play is not in the marginal range. That is if the
patron‟s average bet and time played is sufficiently large to ensure full complimentary privileges and a
Casino net profit then verifying the average bet will have little effect as comp. expense will not meet
comp. value.

It is nevertheless essential that ongoing training of gaming Inspectors occurs to ensure that they are fully
aware both of their duties and the implications of those tasks.


1.9             Conclusion
Effective player rating service and control is a paradox of individual elements. The conundrums of soft
and hard comps., true bottom line profit, value of marketing expenditure, cost accounting etc., all raise
questions which may be answered differently based on a relative perspective.

In essence, however, the only perspective which is of real importance is the premium players. That
view will not be distorted by the Adelaide Casino‟s own internal problems, rather it is a view focussed
on levels of service. To compete successfully for a market share with Jupiters Casino, Wrest Point
Casino and so on, the excellence of service which has been a hallmark at this facility must not be seen to
falter.

Petty items such at the general provision of Pullman meals (which is an internal buffet) to Premium
Players may be the small attention to detail which gains a player‟s return visit. Knowing people‟s
names, greeting preferred premiums at the airport, ensuring ratings are as accurate as possible, sending
these players birthday cards etc, will possibly gain more than attempting to buy their custom. For the
Asian market this may mean changing some of our ways of thinking if we are to seriously endeavour to
successfully penetrate this rich market.

In conclusion the optimisation of Casino profitability will only occur if management recognises the
complex interplay between the service or support functions of the facility and the primary revenue-
generating function of the Casino. If this process is successful then the important potential contribution
of the premium play segment will be attained.


1.10            A Commentary On Casino Player Rating Systems
By Dennis C. Gomes

1.10.1          Introduction

Each year Nevada Casinos payout millions of dollars in complimentaries for their “premium” or “high
line” customers. In fact, such expenditures represent the second largest cost category listed on the
income statements of most major Casino operations. The only expense larger than complimentaries is
payroll.

Obviously, Casino operators are not incurring such heavy expenditures without the expectations of a
significant benefit in return. More specifically, payment of these complimentaries represents a major
Casino marketing tool which is intended to increase

Casino profits and simultaneously strengthen the bond between the Casino and its preferred customers.
In short, the basic business theory behind this widely utilised marketing device is that the cost of the
room, food, beverage and travel expense provided to the “high line” customers is far less than the
gaming revenues generated by them.

However, in far too many cases this theory is frustrated by those customers who do not gamble to a
sufficient degree to justify the complimentary costs incurred by them. Unfortunately, this undesirable
state of affairs is often compounded by failure of the Casino to recognise the existence of the problem.
Many major Casino operators do not have systems available that can generate sufficient information to
determine whether customers are providing adequate gambling action. In some of these cases, the
systems necessary to accomplish this task just don‟t exist. However, in most instances the systems do
exist but are ineffective because they contain one or more basic flaws. The first section of this article
will identify and expand on the four most common and serious of these flaws or weaknesses and the
second section will demonstrate the development of a system that is free from such weaknesses.

1.10.2          Four Most Common Player Rating System Weaknesses

1. Lack of correlation between the customer play criteria and the customer rating output

The basic components of any effective player monitoring system are essentially twofold. First, the
Casino must establish the amount of gambling action that a customer must provide in order to qualify
for the various possible levels of complimentary expenditures. This component shall be referred to as
the “player action criteria”. Second, the Casino must be able to precisely and objectively measure
whether the customer has, in fact, met the stated play requirements. This quantification component shall
be referred to as the “player rating system”. In more elemental terms, the first component merely
specifies the amount of gambling required from customers and the second measures the amount of
gambling provided by them.

Since these two system elements are so basic and fundamental, it is difficult to imagine that when
combined as components of a player monitoring system, confusion could result. Nevertheless, many
Casinos are currently burdened with systems made ineffective because the player rating output is
basically incompatible with the player action requirements. The following examples amply illustrate
such incompatibility.

COMPS                           PLAYER ACTION                            ACTUAL PLAYER
AVAILABLE                       RQMENTS OR CRITERIA                      RATING RESULTS

EXAMPLE #1

RFB                             $5 000 line -
                                “must play to line”                      “B” player
RFB & $300 airfare              $10 000 line –
                                “must play to line                       “A” player
RFB & $600 airfare              $20 000 line –
                                “must play to line”                      “C” player

EXAMPLE # 2

RFB                             4 hours per day @
                                $50 bets                                 “Good” player
RFB and $300 Airfare            4 hour per day
                                @ $100 bets                              “Excellent” player
RFB and $600 airfare            4 hours per day @
                                $150 bets                                “Average” player

EXAMPLE #3

RFB                             $5000 line –                             $10 000 marker
                                “must play to line”                      issues

RFB and $300 airfare            $10000 line –                            $20 000 marker
                                “must play to line”                      issues

RFB and $600 airfare            $20000 line –                            $30 000 marker
                                “must play to line”                      issues


As can be seen, in all of the above examples, the first component or Player Criteria is stated in
different terms than the second component of player rating. Given this lack of consistency, it is often
difficult to determine, on a consistent basis, whether the customer has or has not qualified for the
available complimentaries. For instance, in Example #2, in order for a customer to qualify for RFB and
$300 in airfare reimbursement, he would be required to play four (4) hours per day at $100 per hand.
However, when the customer‟s play is actually quantified in order to determine whether he merits such
complimentaries his play is labelled as “excellent”. Because of this immediate lack of connection
between the two system components, the pit executive is forced to take an additional and unnecessary
step in the rating process. He must determine whether an “excellent” rated player actually meets the
play requirements for RFB and $300 in airfare. In reviewing the definition, of an “excellent” rating, he
will probably find that the complimentary determination, for an “excellent” rating is dependent on one
or more other factors. For example, an “excellent” rating with a low amount of playing time may not
qualify, while one with a high amount of time may. This situation may further be complicated by the
fact that the “excellent” designation may be the end product of a multitude of factors, some subjective
and other objective in nature, that may bear little direct relationship to the customer‟s play criteria.
Consequently, because of the lack of correlation between the criteria and the rating results, costly
executive time is unnecessarily wasted and inconsistent decision making is fostered in the Casino.

2.      Ambiguity of customer action criteria

As indicated, play action criteria are the gambling parameters established by the Casino to determine
whether a customer qualifies for receipt of the various available levels of complimentaries. A common
problem associated with these criteria is that they are often too vague or ambiguous to function
effectively. This condition not only makes it difficult for the customer to know what levels of play are
expected of him, but it also makes it impossible for the Casino to determine, on a consistent basis,
whether the customer has actually met the criteria.

An example of such vague play criteria would be that of the system referenced earlier that states action
criteria in the following terms:-

COMPLIMENTARIES AVAILABLE                                            PLAY CRITERIA

RFB                                                                  $5000 line –
                                                                     “Must play to line”

RFB and $300 airfare                                                 $10 000 line –
                                                                     “Must play to line”

RFB and $600 airfare                                                 $20 000 line -
                                                                     “Must play to line”

This particular play criteria has been used extensively over the years and is still utilised in some
Casinos. The primary problem, however, is that it is non-specific and as such, tends to generate much
confusion and misunderstanding among both customers and Casino personnel. From the customer
standpoint, the determination of what “play to line” means is essentially left up to him. If he guesses
right, he qualifies for the specified complimentaries and if he guesses wrong, he receives less than he
might be expecting. To compound the problem, Casino executives may have diverse understandings of
what the phrase means that customers are required to draw marker issues equivalent to their lines.
While this interpretation is common, it is, of course, ridiculous. For example, a credit customer with a
$20000 line could conceivably play Blackjack for 12 hours at $250 per hand and have marker issues of
only $1000 or less. To be more specific, the customer could have won $15,000 dollars on the first
$1000 marker during a six hour period and lost the $15000 back to the house during the next six hour
period. However, under the referenced Casino executive‟s definition of “play to line” this man, who
provided 12 hours of play at $250 per hand, would not qualify. Likewise, a credit customer with a $20
000 line and $50 000 in issues might have provided very little good play but would still, under the
referenced definition, more than qualify for complimentaries. In other words, the customer could be
merely repeatedly drawing markers, playing for small amounts, and then paying the markers at the cage.

Another Casino executive, employed by the same Casino as the first, provided an entirely different and
even more ambiguous definition of the “play to line” phrase. He stated that it meant that the customer
had to provide gambling action consistent with his credit line. When asked specifically what that
meant, he stated that determination of whether a customer‟s play was consistent with his line was
basically left up to the judgement of each Casino executive who was engaged in rating players. The
problem with this interpretation is that is engenders inconsistency because what might be considered
“good” gambling action by one Casino executive might be viewed as wholly inadequate by another.

3.      Subjective determination of play criteria

Ideally, minimum player betting levels or action criteria should be set sufficiently high to generate
enough revenues (on an expected value basis over a theoretically long term period) to cover the
complimentaries provided to the customer plus an added profit considered reasonable by the Casino.
Obviously, the fact that a Casino operation establishes specific play criteria indicates that its executives
are confident that such requirements will produce sufficient revenues to meet these complimentary and
profit costs. However, because of the subjective methods by which most play criteria are derived, they
are often set too low and consequently produce net losses after consideration of direct complimentary
costs. This is particularly the case at the lower betting levels.

Examples of subjective criteria development are numerous. For instance, a common method of
determining play criteria involves the use of drop/win percentages to calculate the expected revenues at
each betting level. One such method consists of the multiplication of the customers credit line by the pit
drop/win percentage. For example, a $10000 credit card holder would be expected to generate a $2100
in Blackjack revenue ($10000 credit line x 21% - BJ drop/win percentage and a $20000 card holder $4
200 in Blackjack revenue ($20000 credit line x 21% - BJ drop/win percentage). The complimentaries
available to players in each of these categories would then be calculated on the basis of the expected win
estimates. Thus, complimentary availability would be based on customer credit lines plus the
previously referenced stipulation that the customer play to his line.

Another common method of incorporating drop/win percentages to develop customer play criteria is
very similar to the first. The difference is that rather than multiply the drop/win percentage by the
customer‟s credit line, it is multiplied by his marker issues. As a result, marker issues, in the Blackjack
pit, of $10000 would be expected to produce $2100 in revenue and issues of $20000 would produce
$4200 in revenue. Thus, in this case, the customer play criteria would take the form of marker issue
requirements and the complimentaries available at each criteria level would be dependant on the amount
of expected revenue calculated from the issues.

Although, at first glance, use of drop/win percentages to derive customer play criteria appears analytical
and thus objective, it is, in reality, as subjective as pulling the criteria out of thin air. More specifically,
calculation of expected revenues based on customer credit lines bears no mathematical or logical
relationship to the actual play provided by the customer. Any Casino executive who has dealt with
credit knows that the size of a customers credit line has little bearing on the quality of his play. For
example, a wealthy customer with a $100000 credit line may gamble very conservatively whereas a
customer with a $7500 credit line may lose his entire line in 10 bets. Differences in the quality of
players at each credit line category vary as greatly as do the personalities of the individuals themselves.
Consequently, how can a meaningful credit play criteria be developed from expected revenue
calculations that are based on meaningless credit line categories? The simple answer is that they cannot.

Likewise, the similar derivation of credit play criteria, based on marker issues, is also without an
objective foundation and will result in meaningless parameters. For example, marker issues of $20000
might qualify a customer for full RFB complimentaries and $600 in airfare reimbursement. However,
like the previously cited examples of the customer playing under the “play to line” criteria, this
customer, in reality, may have merely drawn markers in the pit, played very little and subsequently paid
the markers at the cage. Thus, the application of pit win percentages against this customer‟s marker
issues would produce erroneous expected revenues.

On the other hand, as indicated in a previous example, another customer with only $1000 in marker
issues could have provided sufficient pit action to rightfully qualify for maximum RFB complimentaries
and airfare. However, because he had only $1000 in marker issues, he probably wouldn‟t qualify under
the marker issue criteria for even a reduced room rate. Consequently, because of reliance on the
subjectively conceived marker issue criteria, one customer who had high marker issues, and actually
deserves little consideration, would be provided maximum complimentaries and another customer who
was a quality gambler would receive nothing and would probably be lost by the Casino.

In summary, use of drop/win percentages in conjunction with credit lines or marker issues, to develop
customer action criteria, has no valid basis. Therefore results are subjective and consequently
ineffective.
Another common method utilised to develop customer action criteria is reliance on the experience
of Casino personnel to subjectively determine play requirements. For example, one Casino executive
may decide that $50 bets for four hours per day are sufficient to generate expected revenues large
enough to qualify a customer for RFB complimentaries and airfare reimbursement of $400. The
problem is that another Casino executive might feel that $50 bets are not enough and that $100 bets are
necessary to qualify for such complimentaries. On the other hand, a third executive might feel that a
$50 betting requirement is too stringent and that $25 bets are more than sufficient. Which answer is
correct? Each executive feels that his criteria is effective but non can explain the process utilised to
derive the numbers. This diversity of opinion is precisely why such wide variation exists from one
Casino to another in betting requirements.

Again, like use of drop/win percentages to derive betting requirements, reliance on the opinions of
Casino executives for such derivations will result in a purely subjective and therefore probably
ineffective set of gambling criteria.

In summary, subjectively derived play criteria are unreliable and often generate unprofitable results.
Unfortunately, however, because of the Casino‟s inability to measure theoretical Casino win against
actual costs, at the various criteria betting levels, this negative situation most often goes undetected. As
a result, Casino profits decline and either no one knows why or the declines are erroneously attributed to
other factors (ie complimentary abuse, economy etc).

4.       Failure to Accurately Record Customer Play

Assuming that an effective set of customer action criteria has been developed and that such criteria are
compatible with the player rating output, the system may still be dysfunctional if the pit rating
procedure are ill conceived or are not properly enforced.

A prime example of ineffective rating systems are those that rate customers on the basis of their first
bets only. Such systems incorporate an implied assumption that the quality of the customer‟s gaming
activity remains constant throughout his play. In reality, however, player betting patterns vary greatly.
Some customers initiate their play with small bets and will later increase or parlay their bets if they are
winning. Others begin small and may increase their bets when losing. Consequently, a rating system
based on initial betting patterns may produce ratings that are not representative of a customers overall
play. As a result, regardless of how well designed the play criteria and how compatible the rating
output, the system will not function effectively because actual ratings will not be consistently accurate.

Although not an inherent system weakness, another problem occasionally associated with the rating
process is a failure on the part of floor personnel to conscientiously rate customer play. For example,
rather than expend the energy to accurately rate a player‟s betting action, a lazy floorman might merely
record fictitious information that, in his estimation, appears reasonable. Similarly, a dishonest floorman
might record fictitious rating information in an effort to assist an outside accomplice in establishing a
good record of play preparatory to a large credit fraud.

Both of these problem areas can have serious repercussions to the Casino if not properly handled.
However, an effective method of eliminating them is available through the use of eye monitoring
procedures. More specifically, it is both feasible and practical to have eye personnel randomly rate
customer‟s play concurrently with pit personnel. These ratings, along with marker numbers, rating slip
numbers (if appropriate) and customer names, can easily be recorded on a report form and later
compared to pit ratings. Consequently, the psychological impact on floor personnel of knowing that
their ratings are randomly monitored with encourage them to take great care in accurately rating
customers.

1.10.3           System Development
As indicated, many of the player rating systems in use today are severely hampered by certain
common weaknesses. The purposes of this section of the article will be to demonstrate a method of
constructing a player evaluation system that will eliminate these weaknesses and thereby create a system
that will:-

1.       enable ease of comparison between the customer play criteria and the rating results.

2.       embody a set of unambiguous play criteria that are clearly understandable by customers.

3.       Incorporate objectively conceived play criteria that will, over the long-term, provide assurance
         that minimum required play at each betting level will result in an expected minimum profit after
         direct expenses.

4.       Enable accurate and consistent rating of customer play.

Before outlining the system design, however several important points must be clarified. First, the
procedures that will be detailed herein should not be considered as constituting a complete system.
Rather, they should be regarded merely as guidelines intended to demonstrate the steps necessary in the
development of an effective player rating system. Second, it must be kept in mind that such evaluation
systems while essential in monitoring the play of those customers that bet at lower and mid levels are
not necessary regarding premium players. The reason for this is that the expected revenue from
premium players is so large that it does not take a sophisticated rating system to ascertain the degree to
which these customers qualify for airfare and complimentaries.Furthermore, the revenue generated by
their play is so disproportionately larger than the cost incurred by them that decisions, concerning
exactly how much they qualify for, become meaningless. In short, these are the high profit margin
customers and as such, do not require close monitoring.

On the other hand, the dollar amount of RFB complimentaries and airfares that are available for lower
and mid level players represents a significant portion of the gaming revenues expected from them.
Consequently, airfare and RFB decisions can often make the difference between a profit or a loss on
their play. In short if these customers are monitored properly their play, after complimentaries and
airfare, can produce marginal profits. However, if not monitored or monitored improperly, their play
can generate losses that, when combined with other Casino operating data, are virtually undetectable.

1.10.4           Criteria Development

The first step necessary in the development of a player monitoring system is the selection of the
parameters that will be utilised in the establishment of customer play requirements or criteria. As
indicated earlier, such criteria must be clear, concise, and not subject to diverse interpretation. Such
qualifications are readily met by measurements of the size of a player‟s average bet and the hours of his
play. Consequently, these parameters have been selected as the means of expressing the play criteria for
purposes of this system.

The next step is to decide the amount of minimum profit (after direct expenses) that the Casino wishes
to make per customer at each criteria betting level. Since this minimum figure is arbitrarily established,
it can be set at any amount desired and can be varied for each betting category. However, if set too
high, it will cause the gaming criteria to materially exceed the play requirements of competing Casinos.
Therefore, reasonableness must be exercised in determining this minimum profit level. In order to
facilitate construction of this system, it will be assumed that the minimum desired profit per player is set
as follows:

         BETTING CATEGORY                 MINIMUM EXPECTED PROFIT PER PLAYER
              $25 - $50                                  $200
              $75 - $100                                 $300
              $125 - $150                                $400
              $175 - $200                                $500
                 $250 - $300                                        $600

The most important and most complex of the steps necessary in the development of the customer play
criteria is the determination of the amount of complimentaries and airfares that can be provided to
customers at each betting level. Completion of this step actually involves three developmental stages.
First and most importantly, the amount of expected revenue that will be derived from customers at each
betting category must be calculated. Next, the amount of direct costs, other than complimentaries and
airfare, (ie representative commissions, gaming taxes, etc) must be determined and subtracted from
expected revenues at each betting level. The resulting balances constitute the amount of funds available
for player complimentaries and airfares at each betting level. Finally, a comprehensive set of play
criteria can be prepared from the data developed.

Because these three developmental stages are so critical to the subsequent effectiveness of the customer
play criteria, the methodology of their construction is outlined in detail following:-

1.      Derivation of expected revenues at each betting level

Many executives employed in the gaming industry take the position that it is not possible to determine
the outcome of a customer‟s gambling activity in advance. While such position is correct regarding an
individual customer‟s play during a specific gambling occasion, it is not accurate concerning the
predictability of the long term results of that same customers play. More specifically, given the size of a
customers average bet and the nature of his betting pattern the results of his play over a theoretically
extended period of time can be reasonably forecast.

It is precisely this long term concept that must be applied to determine the gaming revenue expected
from a specific customer even though his play occurs over a short period of time. The reasons for this is
simple. Even though the players losses may deviate from the theoretical on specific occasion, his
average loss per visit, over a long term period, will equal the theoretically calculated loss per trip.
Likewise, while one member of a large group of gamblers may experience gambling wins or losses on a
single occasion, that vary from the theoretically expected result, given a large enough group, the average
loss per member of the group will equal the theoretically expected loss per person.

Consequently, when deriving expected theoretical win, at the various betting levels of the customer play
criteria, the theoretical or long term basis of calculation should be employed. The first step necessary in
the derivation of such theoretical or expected win, for the various betting categories, is the calculation of
the house advantage or “edge” for each table game. In order to simplify this example, “edge”
calculations will be confined to the two most popular Casino games – Craps and Blackjack.

Calculation of Craps “edge”

There are numerous types of bets available in the game of Craps, each having a different house
advantage or “edge”. Consequently, because the play criteria are calculated on the basis of each game‟s
edge, this multi “edge” aspect of Craps raises an important question relative to establishment of the play
criteria. It is desirable to have a multitude of separate play criteria for Craps, each depending on the
customers bet selections or is it preferable to have one single set of play criteria for Craps?

Obviously, if a set of play criteria was established for each type of betting “edge” available on the crap
table, then, for Craps alone, approximately 21 sets of criteria would be necessary. Such a system would
be ridiculously confusing to the player and thus impractical. In addition, under a multi criteria system
for Craps, rating of players by pit personnel would become unusually cumbersome and time consuming
because of the necessity of specifying not only the amount bet but also the nature of every bet.
Consequently, from both the customers standpoint and the Casinos, computation of a multitude of play
criteria for Craps is impractical. Thus, expected revenues, at each betting level of the Craps criteria
must be calculated on the basis of a single Craps “edge”.

In order to calculate a single “edge” the average “edge” for all Craps bets must be determined. This
would prove a simple task if all players made a habit of spreading their dollars evenly among all of the
bets available on the layout. In that case, a simple average of the various Craps bet “edges” would
suffice. However, it is well known that Craps players are as varied as 21 players in their skill, style and
volume of play. Consequently, the only reasonable method of calculating an average Craps “edge” is to
weight each of the bet “edges” in accordance with the estimated or actual average of the betting
volumes placed on each type of bet.

These average volumes or mix of bets can either be estimated by experienced personnel or can be
determined by recording and averaging the actual mix of Craps bets over a given period of time. Both
methods are demonstrated below:-

Imperical Determination

Discussion with various experienced Casino personnel resulted in the following as an estimate of the
average long-term mix of Craps bets at a particular Casino:

Percent of Total

Pass line – with odds                             40%
Come bets – with odds                             30%
Place bets                                        20%
Don‟t pass; Don‟t come – lay odds                 5%
Proposition bets & one roll bets                  5%
                                                  100%

Based on this estimated average mix of bets at the crap table, the average Craps edge can be computed
as follows:-

                                   (A)            (B)              (A) & (B)

Type of wager (2)                  Edge           Weight           Weighted average Craps edge

Pass line/odds                     .85%           40%              .340%
Come bets/odds          .85%              30%              .255%
Place bets                         3.43% (1)      20%              .690%
Don‟t pass & dot
come/lay odds                      .69%           5%               .035%
Propositioned one roll bets        13.5%          5%               .675%

TOTAL                                             100%             1.995% average Craps

(1)     This percentage consists of the average “edge” for all place bets excluding four and ten. In the
        case of four and ten, the “edge” for a buy on four and ten was substituted in the calculation.‟

(2)     Field bets and big 6 and 8 bets were not calculated into the mix as their volume was considered
        by experienced personnel to be negligible.

Sample determination of average Craps edge

An alternative and more reliable method of estimating the average Craps “edge” is to observed and
record the actual mix of bets on the crap table during a selected representative period of time. The
actual mix recorded during this test period could then be used to calculate a sample Craps “edge”. Such
“edge” would be considered as representative of Craps play in general and would serve as the average
Craps “edge” for purposes of deriving the Craps play criteria.
This sampling procedure was utilised at a major Strip Casino during a randomly selected period of
heavy Craps play and resulted in the following derivation of the average Craps edge.

TYPE OF WAGER             AMOUNT                 % OF              HOUSE           EXPECTED
                          WAGERED                TOTAL             EDGE            WIN
                          DURING SAMPLE
                          PERIOD

Pass/line odds            120 895                45%               0.85%           1 027
Come bets/odds            89 680                 34%               0.85%             762
Place bets                35 290                 14%               3.43%           1 210
Don‟t pass and don‟t      2 985                  1%                0.69%              21
Come/lay odds
Proposition and one       15 165                 6%                13.5%           2 047
roll bets
TOTAL                     264015                 100%                              5 067

Expected win $5 067 = 1.92% average Craps edge

Amount wagered $264 015

As can be seen, both the empirical or “experience” based method and the sampling technique of
calculating the average Craps “edge” resulted in similar finds of 1.99% and 1.92% respectively. For
purposes of deriving the Craps play criteria, these “edges” will be rounded to 2%.

Calculation of Blackjack “edge”

As illustrated above, one of the difficulties in calculating the average “edge” for the game of Craps is
that there are approximately 21 different bets available on the layout, many of which carry different
house advantages. Consequently this necessitates the determination of an average mix of bets in order
to mathematically derive the average Craps “edge”.

This multi-edge problem is even more severe when considered with respect to the game of Blackjack.
For example, if a customer is a perfect basic strategy player, the house “edge”, regarding his play, is
reduced to approximately .6% on a six deck shoe. On the other hand, the house “edge” derived from the
play of a customer who knows nothing about play strategy can rise to above 6%. Obviously, then the
house “edge” in 21 can vary as widely as the customers ability to play the game. Consequently, the
number of separate resultant “edges” in 21 are unlimited. Thus, because of this multi-variate aspect in
the quality of Blackjack customers play, it is virtually impossible to estimate an average mix, by skill
levels, of Blackjack betting volumes. Therefore, since each skill level generates a separate house
“edge”, it is not feasible to calculate an average “edge” for Blackjack in the same manner as was
accomplished for Craps. However, an alternative method utilising the Craps “edge”, is available for
calculation of an average Blackjack “edge”. More specifically, once the craps “edge”, is available for
calculation of an average Blackjack “edge”. More specifically, once the raps “edge” has been
determined it can be utilised as part of a mathematical proportion to accurately calculate the actual
average Blackjack “edge”. The logic underlying the proportion is as follows:

If it is assumed that:-

A.      The same number of hands are dealt per hour in Blackjack as in Craps and
B.      The drop/win percentage is the same in Blackjack as in Craps

then the house “edge” in Blackjack would be the same as the house “edge” in Craps. Thus, based on
these relationships, given historical data regarding average number of hands dealt per hour and the
actual drop/win percentages for Craps and Blackjack, the actual average Blackjack “edge” for the
Casino can be calculated as follows:

Historical data
                                                  CRAPS                    Blackjack

Drop/win percentage for the most
recent 12 month period                            19%                      21%

Average number of hands dealt per
hour (per survey results)                         50*                      65

Proportion

The Craps drop/win percentage of 19% and the number of Craps hands dealt per hour of 50 is to the
average Craps “edge” of 2% what the Blackjack drop/win percentage of 21% and the number of
Blackjack hands dealt per hour of 65 is to the average Blackjack “edge” which is unknown.

Proportion equation

19% (or .0038) is to 2% what 21% (or .00323) is to X %
50                             65

.0038   = .00323
.02        X

.0038X = .00065

X       =.017

X       =1.7%

therefore, the average Blackjack edge” is 1.7%.

Calculation of expected revenues for Craps and Blackjack at betting levels ranging from $25 to
$300

Once the average house “edge” for Craps and Blackjack are known, the amount of expected revenue per
hour can be determined for each betting category by use of the following formula:

Average bet per hand X average hands (decision in Craps) per hour X average house “edge” = Average
expected revenue per hour

Assuming that the criteria are to be stated in terms of an average three day stay, this hourly revenue rate
can then be converted to expected revenues for 12 hours.

* For Craps this represents decisions per hour of play (three days at an average of four hours per day).

The tables below provide the results of these calculations, for Craps and for Blackjack:

  CRAPS 12 HRS                   EXPCTD CAS. WIN PER                       EXPCTD CAS. WIN FOR
PLAYERS AVG BET                  HR @ 50 DECISIONS/HR &                    12 HRS OR AN AVG OF 4
                                 AVG CRAPS “EDGE” OF 2%                    PER DAY FOR 3 DAYS

        $25                               $25                              $300
        $50                               $50                              $600
        $75                              $75                              $900
        $100                             $100                             $1200
        $125                             $125                             $1500
        $150                             $150                             $1800
        $175                             $175                             $2100
        $200                             $200                             $2400
        $250                             $250                             $3000
        $300                             $300                             $3600


BLACKJACK 12 HRS                EXPCTD CAS. WIN PER    EXPCTD CAS. WIN OR AN
PLAYERS AVG BET                 HR @ 65 HANDS/HR & AN AVG OF 4 HRS PER DAY
                                AVG. BJ “EDGE” OF 1.7% FOR 3 DAYS

        $25                              $28                              $336
        $50                              $55                              $660
        $75                              $83                              $996
        $100                             $110                             $1320
        $125                             $138                             $1656
        $150                             $166                             $1992
        $175                             $193                             $2316
        $200                             $221                             $2652
        $250                             $276                             $3312
        $300                             $331                             $3972

As can be seen from a comparison of the expected revenue tables for Craps and Blackjack, the amounts
earned, from both games over a three day period of four hours of play per day, are fairly similar. Thus,
if management so desires the two tables can be combined permitting subsequent development of one
play criteria for both games as opposed to a separate set each for Craps and Blackjack. This would have
the effect of streamlining the play criteria thereby facilitating ease of customer understanding. For the
purposes of this article, the two tables have been combined as follows:

Combined Expected revenue tables – Craps and Blackjack


     PLAYERS AVG HTS            CRAPS & BLACKJACK                EXPCTD CAS. WIN 12 OR
        BET                     AVERAGE CASINO WIN               AVG OF 4 HRS PER DAY
                                PER HOUR                         FOR 3 DAYS

        $25                              $26                              $312
        $50                              $52                              $624
        $75                              $79                              $948
        $100                             $105                             $1260
        $125                             $131                             $1572
        $150                             $158                             $1896
        $175                             $184                             $2208
        $200                             $210                             $2520
        $250                             $263                             $3156
        $300                             $315                             $3780

2.      Determination of expected revenue – balances available for complimentaries and airfare

The final step necessary in the development of the customer play criteria is the calculation of the
amount of expected revenue, at each betting level, that will be available for the payment of
complimentaries and airfares. This can be accomplished by deducting all non complimentary direct
costs (taxes, bad debts etc) plus the pre determined minimum profit, from expected revenues at each
betting level. The remaining balances can then be utilised as parameters for the establishment of
complimentary and airfare packages available for customers at each betting category. Any balances
remaining after deduction of these complimentary allocations can be added back to profits. The
following table illustrates the procedures necessary to determine the amount of expected revenues, at
each betting category, that are available for complimentaries and airfares.

        DEDUCT DIRECT NON COMPLIMENTARY EXPENSES

MIN REQD                EXPECTED        BAD      REP             GAMING MIN                BALANCES
BET($) HOURS            WIN             DEBTS(1) COMM(2)         TAX(3) PROFIT(4)          AVAIL FOR
                                                                                           COMPS &
                                                                                           AIRFARES

25      12              312              19        --             20       200            75
50      12              624              37        50             39       200            298
75      12              948              57        100            60       300            431
100     12              1260             76        125            80       300            679
125     12              1572             94        150            100      400            828
150     12              1896             114       150            120      400            1112
175     12              2208             132       200            140      500            1236
200     12              2520             151       250            160      500            1459
250     12              3156             189       300            200      600            1869
300     12              3780             227       350            240      600            2363

Footnotes:-

        (1)     Expresses as a percentage of credit play win.

        (2)     This expense would not apply if customers were not sent to the Casino by a
                commissioned outside representative of the Casino.

        (3)     Based on 6-1/2% gaming tax rate on gross income.

        (4)     This represents an arbitrarily established minimum profit and as such can be set at any
                level that management desires.

3.      Preparation of customer play criteria

Once the balances available for complimentaries and airfares, at each betting level, have been
determined as illustrated above, the necessary allocation of gratuities can then be accomplished as
shown below:-

Complimentary and Airfare Allocation (1)

MIN     COMP            ROOM            F&B         A/FARE      TOTAL         EXPCTD       PROFIT/
        VALUE           BALNC OR         (3)        PERSON      REMAIN        REV          BET
                        (DEFICIT)(2)                            ING

25      73               *CR90          --           --          90           (17)         183
50      298              200            --           --          200          98           298
75      431              200            250          --          450          (19)         281
100     679              200            250          200         650          29           329
125     828              200            250          350         800          28           428
150     1112             200            250          450         900          212          612
175     1236             200            250

Footnotes:-
(1)     Room costs are shown at retail value. This means that if the hotel is running at capacity, the
        room complimentary costs shown would be a true reflection of lost cash and thus an accurate
        depiction of cost. However, if the hotel is not operating at capacity, the true cost of the room
        complimentary would be the actual cost of providing the room (maid costs, front desk cost, etc)
        and thus would result in actual profits being higher than indicated above.

(2)     Represents average rack rate for three nights.

(3)     Represents average food and beverage consumption for 3 days per complimentary customer.

** Represents “Casino Rate”

Player Action Criteria

PLAY REQUIREMENTS                                 GRATUITIES
(see note below)                                  COMPLIMENTARIES                   AIRFARE

$25 bets – 4 hours per day                        Casino room rate                  none
$50 bets – 4 hours per day                        complimentary room                none
$75 bets – 4 hours per day                        complimentary RFB                 none
$100 bets – 4 hours per day                       complimentary RFB                 $200
$125 bets – 4 hours per day                       complimentary RFB                 $350
$150 bets – 4 hours per day                       complimentary RFB                 $450
$175 bets – 4 hours per day                       complimentary RFB                 $600
$200 bets – 4 hours per day                       complimentary RFB                 $800
$250 bets – 4 hours per day                       complimentary RFB                 $1000
$300 bets – 4 hours per day                       complimentary RFB                 $1200

Note: These requirements are based on four hours of play per day. Playing time exceeding that
amount reduces the average bet requirements and larger average bets reduce the playing time
requirements.

For example: 8 hours of play per day at an average bet of $50 is equal to four hours of play at $100 per
hand. Likewise, two hours of play per day at $200 per hand is equivalent to four hours of play per day
at $100 per hand.

Airfare reimbursements are based on at least 12 hours for playing time at a minimum bet of $100 per
hand.

Once the above criteria have been finalised, development of the actual monitoring and rating system is a
relatively simple matter. An outline of the steps necessary in such development is presented below:-

1.      Develop a credit playing rating slip that will preferably be included as a tear-off stub of the
        marker and will incorporate space for the following information:-

        A.      Player name
        B.      Table number
        C.      Average bet
        D.      Time played
        E.      Result
        F.      Amount walked with
        G.      Rated by
        H.      Comments
        I.      Marker number
2.       Develop a cash player rating slip that includes all but items F and I above.

3.       Establish either through manual or electronic data processing means, a method of accumulating
         and summarising the rating information on a daily basis. This information must be available on
         a timely basis in order to insure its usage for RFB and airfare decisions.

4.       Develop a rating information reporting format that simplifies comparison of the rating results
         with the play criteria. For example, in addition to stating rating results in terms of actual
         average bets and time played, such information can also be stated in terms of the average bet for
         the required hours of play. More specifically, since the criteria playing time requirements are
         stated in terms of 12 hours (four hours per day for three days) a players actual bets can be
         adjusted to reflect equivalent dollars amount for the required playing time. For example, if a
         customer bets $300 per hand for eight hours of play over a three day stay, then his average bet
         could be restated to $200 per hand for 12 hours ($300 x 8/12 = $200). This simple conversion
         of actual bets to bets stated in terms of the required playing time enables an easier comparison
         of rating results with criteria requirements.

1.10.3           Summary and Conclusions

In summary, implementation of a player rating system similar to that illustrated herein will insure
against the weaknesses inherent in many of the rating systems being utilised in the gambling industry
today. In addition, such A system will provide management with a relatively precise method of
measuring the revenue producing potential of players at each betting level. Consequently, Casino
executives will then be able to determine in advance the exact amount of such revenues that can be
expended for complimentaries, airfares, and other costs (ie special event costs).

In addition to the above, many subsidiary benefits will accrue to those Casinos that utilise player
evaluation systems that have similar characteristics to the system illustrated. The following are
examples of a few of such benefits:-

1.       The actual win generated by a particular junket or other Casino groups (ie special event guest)
         may fluctuate significantly from trip to trip. Therefore, a meaningful evaluation of each trips
         outcome is only possible if expected or theoretical revenues, rather than actual revenues, are
         considered when calculating the profit produced by the group. A player rating system having
         the properties of the system recommended herein will automatically provide comparisons of this
         nature.

2.       Monthly Casino host evaluations can be made more useful and equitable by basing them on the
         expected or theoretical win produced by the hosts players. Since the concept of expected win
         takes into consideration “action” only and does not consider the player‟s actual win or loss, it
         will naturally generate a more comparable and meaningful basis for measuring Casino host
         performance. In addition, when coupled with cost data, it will provide a vehicle for calculating,
         on a monthly basis, the long-term net profit produced by each host.

3.       Casino customers can be categorised by the size of their average bets (adjusted by required
         playing time) instead of the size of their credit lines. This permits a more valid determination of
         customer quality for purposes of “special event” invitation selection.

4.       Given knowledge of the betting levels of “special event” invitees, the revenue expected from
         such events can be more accurately forecast. This enables preparation of a more meaningful
         projection of the expected profits to be produced by the proposal event.

In summary, the system detailed herein is intended to serve as an example of a possible alternative to
the traditional methods of monitoring and evaluating Casino customers. However, it must be stressed
that the system advocated is not a panacea and, if not properly implemented, can be as ineffective as
many existing evaluation methodologies. For this reason, the following and final paragraphs of this
article will serve to communicate various admonitions to operators contemplating installation of
systems modelled after that suggested in this article.

1.      Although previously stated, it is important to reiterate that the system described herein is not
        necessary for the monitoring of premium quality players. Such customers produce profits
        regardless of the level of their complimentary privileges and airfares (assuming that such
        expenditures are kept within reasonable limits) and thus, do not require exact evaluation.
        Furthermore, since the individual action generated by these players is significant they can be
        easily monitored, on an informal basis, by pit personnel.

        However, the lower to intermediate betting level players, who generally account for the
        numerical majority of a Casino‟s customer mix, will produce only marginal profits.
        Consequently completion of an accurate and quantifiable determination of the playing quality of
        such customers, before complimentary and airfare decisions are made, can often make the
        difference between a profit and a loss relative to their play.

2.      The values assigned for “edge” determination purposes, to the variables of “Craps betting mix”
        and “the number of hands dealt per hour” were not intended to be representative of any specific
        Casino or category of Casino in general. Consequently, any operator wishing to implement the
        system illustrated must determine the value of these variables through independent observation
        within his specific Casino operation. Reliance on the variable amounts utilised herein could
        result in a defective system.

3.      Once the play criteria have been established there is a danger that Casino executives may make
        RFB and airfare decisions strictly in accordance with the betting and time parameters specified
        by the criteria. In other words, in the absence of instructions to the contrary, Casino executives
        may tend to become “programmed” by the system and consequently may make decisions that
        are consistent with such system and contrary to good judgement. A typical example would be
        the situation wherein a customer who has always qualified in the past, is denied airfare because
        his play did not meet the criteria requirements during his current trip. This certainly represents
        a situation in which good judgement would dictate that an exception to the system be made and
        that the customer be granted the airfare. Another example would be that of a customer that
        loses his entire $7000 line after only one hour of play. Although strictly speaking, such
        customer would not have met the time and betting requirements, good judgement would
        mandate that the customer receive full complimentaries and airfare.

        In brief, the point being stressed here is that prior to implementation of a player monitoring and
        rating system, similar to that detailed herein, pit personnel should be instructed that good
        judgement must always take precedence over system requirements.

4.      Some readers, upon reviewing the system detailed, may conclude that the “expected Casino
        win” per hour is too low. Their experience may seem to tell them that a $100 Craps bettor will
        lose much more than $100 per hour and therefore, that the stated criteria are too stringent.
        However, when analysed closely it can be seen that the real danger is not that the Craps betting
        requirements are too high, but that in some cases they may be too low.

        More specifically, as seen from the calculations presented in this article, the overall “edge”
        established for Craps was 2% per hand. Although this may seem somewhat low to some, when
        considered in light of the “edge” inherent in the very common pass line only bets and pass line
        with odds bets, the 2% does not seem high at all. For example, if a customer makes pass line
        bets, the house edge will only amount to 1.4%; thus, producing approximately $70 win per hour
        on $100 bets as opposed to the $100 per hour calculated at the 2% average “edge”.
        Furthermore, if the customer divides the bet between pass line and single odds, then the house
        “edge” is reduced to .85% and the $100 bets then only produce approximately $43 per hour.

        In essence, the admonition intended here is that the house “edges” utilised in the criteria
        calculations are based on the average betting mix and may be either too low or occasionally too
        high relative to the play of specific individuals. However, relative to large groups of
        bettors, the average betting mix used should hold true. The negative side effect of this is that
        the customer that does consistently make the pass line with odds bets will receive more
        complimentaries and airfare than warranted by his expected revenue.

        As indicated earlier in this article, the only way to overcome this problem would be to establish
        separate Craps criteria for each category of Craps bettors. However, as stated, this approach
        would not be practical. Furthermore, with respect to Blackjack, the problem would be even
        more severe since the number of possible “edge” percentages for individual players is almost
        limitless.


1.11             Promotional Chips and Tokens
                 (and the use thereof)
By Andrew McDonald
Senior Executive Casino Operators – The Adelaide Casino


The issuance of promotional chips and tokens to attract play is a widespread practice within the Casino
industry. The objective of this is obviously to increase profits by inducing the public to gamble at that
particular facility. Therefore such a mechanic is often externally focussed and packaged with internal
retail offers. That is, the promotional chips are utilised to effectively discount the standard retail price
of items offered by the facility. These generally include room, food and beverage services where,
depending upon occupancy or utilisation levels, the retail cost differs from the marginal cost to the
company.

As an example if, and only if, occupancy is low during a particular period then the cost of providing a
room to a customer is effectively the cost of cleaning and servicing that room. If occupancy is high,
however, the cost, is that of the potentially displaced revenue from a normal sale.

In the Casino industry it is particularly useful to apply this logic during non-peak periods where
packaging an attractive offer is used to attract players to gamble.

One highly marketable method by which this can be achieved is to provide package customers with a
room at the standard retail rate but include promotional chips to add value to the product. If they were
merely cash chips, no incentive exists for the customer to play in the Casino as they could easily cash
these out. Thus, the provision of cash chips to discount the room rate may only attract customers
interested in a cheap room which would be of little value to the overall operation.

A more effective technique is to utilise match play token or non negotiation chips. Match play tokens
require a player to match the value of the token played with an equal or greater value of cash chips.
This practice marginally reduces the cost to the company of providing match play tokens. Of greater
value, is the fact that this ensures people attracted by the package have a propensity to gamble as they
must also place at risk their own money.

To increase the amount of match play tokens which may be provided and thus enhance the market
perception of added value, these tokens are often used on a “with exchange” basis. In such
circumstances each token can be used once only, that is, if the bet wins the token is removed. Simply
speaking, on an even chance game, if the player bets a $5 cash chip and a $5 match play and the bet
wins then the player is paid $10 and the match play token removed. A total return to the player of $15
being bet and payout, therefore the match play could be described as having a $2.50 betting value. If
this is the case and we wish to discount a room by $50 we could provide the customer with $100 in
match play tokens as part of the room package.
If the purchaser of the package doesn‟t gamble then they pay full price as match play tokens have
no value except in play. Only by gambling the full amount does the customer receive the discounting
value. An added advantage of this is that there is no need to rate (record) play for this player as all
calculations on discount have been made prior to the sale and thus no requirement exists to monitor how
much and how long the player gambles.

Such a simplistic analysis is however fraught with danger and more detailed calculations are required to
determine the potential cost to the company of the unrestricted use of match play tokens.

In any game the cost of providing a chip to a player is the probability of the player winning multiplied
by the total return to the player (bet plus payout). In the case of match play tokens (with exchange) the
cost is the probability of the player winning multiplied by the payout only (ie the bet component is not
returned). In an even chance game with a 1.5% house advantage the cost of a token is 49.25% of its
face value. As the token must at least be matched with an equivalent cash chip bet, then the cost of the
token may be reduced by the potential loss from this required bet, in this example that reduces the
49.25% by 1.5% to 47.75%.

At the Adelaide Casino all tokens at their face dollar value will be treated as drop, therefore a tax
implication exists which in Adelaide is 20% of net win. This increases the cost to 58.2% of the value of
the tokens provided.

What if, however, the tokens could be utilised on non even payoff games such as Roulette?

In this example, if the player bets only on straight ups the initial cost of the token is 94.59% of its value.
The benefits derived from matching the token is 2.7% thus reducing the cost to 91.89%.

After tax the cost is increased to 93.51%.

Details of the above calculations are shown below.

MATCH PLAY TOKENS (with exchange)

Cost assessment

Terms = pw = probability of player winning
R = standard returns (payout + bet)
$ = value of match play token
Match Play Cost = $ pw (r-1)


Example One
For even chance game where pw = 0.4925
Cost    = $.0.4925 x (2-1)
        = $0.4925 x 1


Example Two
For single zero Roulette where pw = 1/37
Playing straight ups
Cost    = $0.027 x (36-1)
        = $0.027 x 35
        = $0.945945

Benefit due to requirement to match the value of the token with an equal or greater value of cash chip.

Benefit = $ - $ pwr
        = $ (1 – pwr)

Therefore sub total cost = $pw (r – 1) - $ (1 – pwr)
        = $ (2pw r – pw – 1) or $ {{pw(2r-1)}-1}

Example One expanded
        = $0.4925 - $0.015
        = $0.4775


Example Two extended
        = $0.945945 - $0.027027
        = $0.918918

A tax implication exists due to the fact that all tokens (face $ value) will be treated as drop. Tax in
South Australia at 20% of net win.

Tax     =        20% (1 – Sub Total Cost)
        =        0.2 – 0.2 Subtotal Cost

Therefore Grand Total Cost = Sub Total Cost + (0.2 – 0.2. Sub Total Cost)

        = 0.8 Sub Total Cost + 0.2

Therefore Grand Total Cost = $ (0.8 (2pwr – pw – 1) + 0.2)

Example One Continued
Grand Total Cost         = $(0.8 x 0.4775 + 0.2)
                         = $0.582

Example Two Continued
Grand Total Cost         = $(0.8 x 0.918918 + 0.2)
                         = $0.9351344

It is important to note this detailed analysis does highlight some areas of concern if the tokens are used
on non even payoff games. In such a case the implied cost of the token can rise from 58.2% of the
dollar value of the token to 93.5% of the value if played on single numbers on Roulette.

This may potentially cause problems in that the discounting value of the match play when associated
with a retail purchase is not then constant, which if the upper value is used, limits the marketability of
the product.

To overcome these concerns it is possible to implement one of the following:-
             Restrict usage to even money bets only
             Restrict usage to Blackjack and Baccarat
             Accept varying percentage cost as commercial risk and assume a weighted 75% cost
              element
             Pay only even money for the match play component of a bet even if placed on higher
              payout bet or,
             State on the token that they pay at 50% of the marked value.

The simplest alternative and the one generally adopted is to restrict usage to even money bets only.

Having done this, it is now possible to structure an off peak package which includes match play tokens
using a 60% cost element on the value of the tokens provided.

A multitude of options exist to package not only room, food and beverage items but these could be
extended to incorporate a travel component.

It must be remembered, however, that the primary objective is to increase profits not just revenue or
headcount but PROFIT. Therefore, any package should be structured to attain at minimum play levels
a breakeven result after all costs are considered, or preferably a level of profit which does not impinge
upon the marketability of the service given that is already impeded by off peak restrictions etc.

An example of a breakeven package is the following:-
One nights accommodation (mid week only)
Cost      $300 normal rack rate $270
Includes $300 in match play tokens plus dinner for one in the buffet restaurant.
Cost assessment:-
Revenue = $300
Costs = $180 Match play at 60%
                  + $60 room marginal cost
                  + $10 marginal meal cost
                  + $20 advertising/marketing allocation
                  + $20 labour/administration allocation
                  + $10 sales commission
Net = 0

The difficulty here is that the advertising and labour allocations are volume based which means that if
the package is unsuccessful, the advertising allocation will increase dramatically, whereas the labour
allocation may only reduce to zero. It is therefore important to structure the package so that it is
appealing to the potential market. To accomplish this it may be necessary to conduct market research
prior to advertising the package.

In conclusion, when structuring any promotional package the following should be considered essential
elements:-

             The objective is to increase profits therefore set the objective.
             Conduct detailed analysis and identify all cost elements prior to staging.
           Minimum breakeven structure.
           Market research and follow up to identify appeal and/or success.
           Analyse results and consider whether this is the best way to achieve the result.

If the business cannot be operated in this manner then the Casino may be gambling itself and often it
would be better not to do the promotion at all.

As the saying goes

“We are in the gambling business not in the business of gambling”
(This page is intentionally left blank)
Chapter 2        Junket Program




“Junkets have the potential to contribute
 significantly to the Casino’s revenue”
CHAPTER 2 Junket Program

2.1      Junket Fact Sheet …………………………………………………………………                                35

2.2      Overview of Junkets ………………………………………………………………                               36

2.3      Extract From the Adelaide Casino Internal Junket Manual ……………… ……… 36
2.3.1    The Adelaide Casino Junket Program Rebate and Premium Policy Players……… 37
2.3.2    The Adelaide Casino Junket Program Policies …………………………………… 38
2.3.3    Schedule of Programs ……………………………………………………………..                          39
2.3.4    Rebate Player Program Non-Negotiable and Cash Chip …………………………. 45
2.3.5    The Adelaide Casino Complimentary Program for Premium Players ……………. 46

2.4      Cash Chip System Analysis ……………………………………………………….                           49
2.4.1    Live Chips …………………………………………………………………………                                    49
2.4.2    Profit Analysis Utilising Baccarat Edge…………………………………………..                  52
2.4.3    Profit Analysis Utilising Budgeted Edge (89/90) …………………………………              52
2.4.4    Profit Analysis Utilising Budgeted Edge Based on Initial Program
         Assumptions ………………………………………………………………………                                    53
2.4.5    Profit Analysis Utilising Budgeted Edge Based on Initial Program
         Assumptions & Average Turnover ………………………………………………                          54
2.4.6    Casino Net Analysis Utilising Budgeted Edge (90/91). Based on
         Varied Program Assumptions Given ……………………………………………..                       54
2.4.7    Casino Net To Commission percentage Comparisons (Initial
         Assumptions to “Actual”) For 20 Turns………………………………….……….                    56
2.4.8    Breakdown of Expenses for Various Front Monies Given Frequency
         Of Front Monies ………………………………………………………………….                                 57
2.4.9    Casino Net Calculations (Revised Expenses) 20 Turns (Edge 1.33%) …………..    58
2.4.10   Casino Net Comparisons (Cash Chip to Non Negotiable) at Cash Chip
         Breakeven Levels …………………………………………………………………                                 59
2.4.11   Junket Operator’s Expenses Per Person …………………………………………...                  59
2.4.12   Operator’s Costs (Approximate) ………………………………………………….                        60
2.4.13   Casino Net to Operator’s Net Comparison (Revised Expenses)
         20 Turns, Edge 1.33 ……………………………………………………………….                              60
2.4.14   Possible Junket Programme Modifications ……………………………………….                   61
2.4.15   Comparison of Required Turns (Existing to Modified) …………………………..           61
2.4.16   Conclusion ………………………………………………………………………...                                  62

2.5      Non Negotiable Chip System ……………………………………………………..                          62
2.5.1    Introduction ……………………………………………………………………….                                  62
2.5.2    Games Available …………………………………………………………………..63
2.5.3    Deposits And Number of Players …………………………………………………                         63
2.5.4    Commission Structure …………………………………………………………….                              63
2.5.5    Operators’ Responsibilities ……………………………………………………….                         64
2.5.6    Commission Calculation Example ………………………………………………..                        64
2.5.7    Revenue Calculations ……………………………………………………………..                             65
2.5.8    Other Information ………………………………………………………………...                              65
2.5.9    Splinter Program …………………………………………………………………..                               65
2.5.10   Commission Calculations Analysis ……………………………………………….                       65
2.5.11   Revenue Calculations ……………………………………………………………..                             77
2.5.12   Conclusion …………………………………………………………………………81

2.6      Premium Player 0.5% (Splinter Policy) ………………………………………….                    81
2.6.2    Commission Agents Program …………………………………………………….                            82
2.6.2    Banking Details …………………………………………………………………..                                84

2.7      Player Loss (How to Deal with Actual Loss in the Casino Industry) …………….   84
2.1            Junket Fact Sheet
Table Limits

Baccarat

Table differential = $100K TO $200K
Maximum bet = unlimited

Blackjack

Per player per box maximum = $10K

Roulette

$500 flat on numbers
$10K on even chances

Tables Available in International Room

Blackjack
Roulette
Baccarat

Programs

1.     Individual Player.
       Minimum front money = $100K
       Rebate/commission = 0.5% on turnover
       Room, food and beverage (no airfare)

2.     Program Two.
       Minimum front money = $250K
       Rebate/commission = 0.45% on turnover
                             = up to 17.5% on loss

3.     Program Three.
       Minimum front money = $1.5M
       Rebate/commission = up to 35.5% on loss
       Room, food and beverage + one first class airfare

4.     Program 1A.
       Minimum front money = $400K
       Minimum players = 3
       Rebate/commission = 0.6% on turnover
                             plus 0.05% expense subsidy
                             plus 0.125% bonus on turnover > $30M

5.     Commission Agent.
       Minimum front money = 5K
       Commission = 0.2% on turnover
       Room, food and beverage and airfare rebate at 0.4% on turnover
2.2             Overview of Junkets
(The following information may be outdated, however, is provided as it analyses the various chip
systems available. The previous fact sheet is more up to date although it would be beneficial to check
with VIP Services as to the actual policy in operation).

Possibly the first question to answer regarding junkets is, “what is a junket”?

A junket may simply be defined as a group of people (4 or more) from overseas or interstate who come
to a Casino for the purpose of gambling and who meet specified criteria set by the Casino.

The criteria set by the Casino are the minimum deposit amount per group or per member, minimum
number of players, etc.

Why do they come to a Casino?

Firstly these people are what are referred to as high rollers, people with large amounts of money who
enjoy leading the “high life”, this of course includes gambling. Also, the Casino markets to these
peoples needs and offers group incentives to an organiser or junket operator, for bringing these people
to the Casino.

What sort of incentives are offered?

The junket operator receives a commission based on the level of play of the players they bring in. The
commission structures vary from Casino to Casino in an attempt to tap this lucrative market.

Where are the players from?

As far as the Adelaide Casino is concerned the players generally are from Asian countries, especially
those countries where Casino gambling is illegal.

When do they come to the Casino?

Junkets arrive all year around, however the predominant time is around Chinese New Year or other
Asian festival times such as Hary Raya Puasa, etc.

What games do the players play?

Predominantly these players play the game of Baccarat, however this is a personal preference and some
players will play the other Casino games.

How much money is involved?

The minimum front monies per junket at the Adelaide Casino are $400,000. The maximum front
monies deposited to date by any one junket was $6,255,000.
What sort of turnover is involved?

Turnover varies from player to player, however turnovers up to $173,000,000 have been recorded in one
stay.

Having answered these basic questions let us now look at the programs themselves and the Casino‟s
policies and thoughts on the junket program.

2.3             Extract from Junket Manual
“Junkets have become an intrinsic part of the Casino‟s operation and a marketing tool that has been used
to identify and develop good player markets.

Junkets have the potential to contribute significantly to the Casino‟s revenue. The volatility of these
groups is such that it is important to maintain a continuous flow of play so that the fluctuations that can
be experienced are substantially flattened.

There are a number of programs offered by the Casino and they are designed to cater to the needs of the
market. The policies are designed to benefit the Casino and it must be remembered that junkets and
players come to the Adelaide Casino on our terms and conditions.

These terms and conditions can change, however, before any changes take place, it is important to let
the operator or player know of such changes prior to their visit to Adelaide.

The following sections provide details of each program. The programs have been put together using a
model based on calculations the Statistics Department of the Adelaide University has provided to us.

All of the calculations for junket play are based on the Baccarat edge of 1.26%. Any play other than
Baccarat is a bonus to the program. The American Roulette edge is 2.7% and the Blackjack edge is
1.6% - 2.0%. All the minor Games are usually higher than 2.5% although there are exceptions.

The hold the Casino looks for is approximately 1.35%. This is because junkets do not only play
Baccarat. They also play other Games such as Roulette and Blackjack and Big and Small is also
popular. By taking into account the edges of these other games this lifts the overall edge.

Although the Baccarat edge is 1.26% our observations over many shoes and with different groups, has
indicated that this edge is in fact, higher. An example of this is the tie bet; $100 on the “Tie” is
equivalent to $1000 on the “Bank” or the “Player”. Even though the tie bet is not played that often, it
still has quite an effect on the game‟s edge.

There is a perceived belief that junket players are skilled players. Regardless of this perception, the
edge built into all our games will eventually win over, and provided our costs are kept well under
control and monitored closely, junket play will be very profitable for the Casino.

One area to monitor closely is Blackjack. Clients who are basic strategy players are not worth bringing
in. Most Blackjack strategies are under 1% and can go as low as 0.6%. This type of play is of no
benefit to the Casino and must be monitored carefully. There are players the Casino has asked the
operators not to bring back.

Blackjack players are definitely a minority and most play that occurs is usually between Baccarat
shuffles.

The key to the success of junkets, apart from the commission, is service. This area has the potential to
make or break a junket program.
Staff must be made aware when dealing with these people that there are culture differences and
what may appear humorous to us may, in fact, be the opposite to these people. “Face” is important to
Asian players and any “loss of fact” can be both embarrassing and humiliating to them and must be
avoided. Age and respect is held in high regard, and when dealing with Asian players older than
oneself, it is important to remember this point.

2.3.1           The Adelaide Casino Junket Program
                Rebate Players and Premium Policy Players

It is with pleasure that we forward to you documentation outlining the various incentive programs
currently available at the Adelaide Casino.

Mr. Craig Ashton, Director of International Marketing – Asia, is available at our office to answer any
enquiries and assist with Visa applications.

In order to ensure that we retain our fine reputation, we also have V.I.P. Hosts in Adelaide whose sole
duties are to service the needs of our V.I.P. clients.

Adelaide

Mr. Andrew MacDonald
Senior Executive Casino Operations
Tel: 61-8-2184178, Fax: 61-8-2124047

Mr. Craig Ashton
Director International Marketing – Asia
Tel: 61-8-218-4292, Mobile 61-8-041-9800-698 Fax:          61-8-231-0260

Ms. Christine Giam VIP Services Secretary
Tel: 61-8-2184254

Singapore

Ms. Loh Pek Lim
Marketing Assistant
Tel: 65-2554850, Mobile: 65-7216797, Fax: 65-2532598

For further enquiries please do not hesitate to contact the numbers listed.
The attached documents consist of the following:-

1.      General Conditions
2.      Program 1
3.      Program 2
4.      Program 3
5.      Individual Rebate Player Program
6.      Complimentary Program
7.      Banking Details
8.      Tables

2.3.2           The Adelaide Casino Junket Program Policies

1.      The Casino will provide hotel accommodation for all qualified players, subject to the minimum
        turnover requirements of the individual programs.

2.      All hotel accounts to be settled by the operator/player before the group/player‟s department
        excluding qualifying accommodation cost.

3.      The Casino may provided one tour for the group/player during the stay if requested.

4.      Cash, bank drafts and travellers cheques are acceptable. However, if a draft is to be used a copy
        must be forwarded by facsimile 48 hours before arrival, to enable our Finance Department to
        approve clearance.

5.      We also have bank accounts in Hong Kong, Singapore and Adelaide which can be used for
        deposits. If overseas deposits are made the bank will issue a receipt which should be faxed 48
        hours before arrival.

6.      All group members names are to be faxed 48 hours before arrival.

7.      Rebate may be withheld if all bank drafts and/or bank deposits have not been cleared through
        our bank account.

8.      An operator bringing in a large group may find it difficult to secure his/her clients on the same
        flight and therefore unable to deposit their funds together. The Casino acknowledges that this
        situation occurs, so operators may deposit their front monies as their groups arrive, provided
        that in the case of split arrival all members of the group were in the original schedule of arrival.

9.      If this is not the case the additional members must qualify as a new junket group as per these
        terms and conditions or be placed on the premium or complimentary programs as applicable.

10.     A junket will only be deemed to continue if the operator or an authorised representative (who
        must also be an approved Junket Operator) is present. That is, rebate will only be paid on play
        where the operator/representative is present with the group. Should the operator/representative
        arrive subsequent to the junket group‟s arrival or depart prior to the groups departure, rebate
        will only be payable on play during the period where the stays coincide. The Chief Executive
        may consider allowing the junket to continue without the operator‟s presence.

11.     Should an operator find his/her group has lost all their front money or can prove an individual
        has lost his/her front monies, the Chief Executive may consider allowing the operator to deposit
        further funds to allow his/her client to continue playing.

12.     The junket operator/player shall be required to designate which junket program (from the
        following schedule) they wish to utilise prior to arrival.
13.     A minimum deposit of 1.5 million dollars in front money is required to utilise a $100,000 table
        differential at the game of Baccarat or Mini Baccarat.

2.3.3             Schedule of Programs

Program One (Rebate on turnover and contingency bonus)

1.      Front money

        Minimum front money per group AUD$400,000.
        Minimum front monies per qualifying players/room AUD$50,000
        Maximum front money unlimited.

2.      Players

        Minimum number of players per group is four

3.      Rebate %

i)      Cash chip system

        a.        A rebate of 0.60% on turnover shall be payable to the junket operator.
        b.        All play will be tracked and monitored to give the Casino the required information on
                  qualification.
        c.        Rebate, shall only be paid on play on the games of Baccarat, Mini Baccarat, Blackjack
                  and Roulette except where otherwise authorised by the Chief Executive.

ii)     Non Negotiable chip system

        a.        A rebate of 1.20% of the recorded loss of non negotiable chips shall be payable to the
                  junket operator.
        b.        Non negotiable chips can only be played on the games of Baccarat, Mini Baccarat and
                  Blackjack in the International Room and other such areas as designed. Where players
                  wish to play games not available on the non negotiable system the Chief Executive may
                  authorise that the play of other games with cash chips be recorded as per the cash chip
                  system and rebate paid at 0.6% of turnover.
4.      Bonus payments

A bonus rebate shall be payable at 0.05% of cash chip turnover (0.1% non negotiable) for all turnover
greater than the negotiated level (as per section 9).

5.      Contingency Bonus

Should the group lose, a bonus shall be payable based on the recorded loss of the group. The rebate %
on loss shall be payable at the following rates up to a maximum of 4%.


                NUMBER OF HANDS AT                                REBATE ON
                PLAYERS (group) MAX.                              LOSS %
                BET (examples)

                        10                                                 -
                        100                                               1.0%
                        500                                               2.5%
                        1000                                              3.0%
                        5000                                              4.0%


The above table details the rebate percentages at each number of hands. Should the groups number of
hands fall between two values on the table it shall be the lower value on which the rebate % shall be
calculated.

The number of hands at players (group) maximum bet shall be calculated by dividing the total turnover
for the visit by the players (group) maximum bet recorded during the visit.

6.      Room, Food and Beverage

The Casino will pay all room, food and beverage requirements for the group up to the negotiated level
(section 9). Any costs incurred beyond those amounts shall be the responsibility of the junket operator.
If the operator so requests he/she may re-negotiate with Casino management the level of
complimentaries to be provided. In such instances the bonus/penalty turnover requirements may be
altered during the groups stay.

7.      Operator’s Airfare

The Casino will reimburse the operator AUD $2000 towards his/her personal travelling expenses.

8.      Expense Contribution

An expense contribution may be deductible from commission should the group not reach the pre-
negotiated turnover level. The expense contribution shall be calculated at 0.05% of cash chip turnover
(0.1% non negotiable) for all turnover less than the negotiated level (as per section 9). A loss of 75% or
greater of front money may negate any contribution which may otherwise be required.
Example                   Actual turnover =       $15 million (cash)
                          Required turnover       =       $ 20 million
                          Commission              =       $90,000
                          Expense contribution    =       $2,500
                          Net                     =       $87,500

All expenses paid pre any bonus payable on group loss and prior to payment of operator‟s airfare.

9.      Negotiations

Bonus and expense contribution levels shall be set for each individual junket following discussions
between the junket operator and Casino management regarding the following:-

i)      number of persons
ii)     length of stay
iii)    room requirements
iv)     food and beverage requirements
v)      table requirements and hours of operation

Program One (Rebate on turnover and bonus)

1.      Front money

        Minimum front money per group AUD$400,000.
        Maximum front money unlimited.

2.      Players

        Minimum number of players per group is four.

3.      Rebate %

i)      Cash chip system

        a.        A rebate of 0.60% on turnover shall be payable to the junket operator, on the games of
                  Baccarat, Mini Baccarat and Blackjack. A rebate of 1.30% on turnover shall be payable
                  on the game of Roulette.

        b.        All play will be tracked and monitored to give the Casino the required information on
                  qualification.

        c.        Rebate shall only be paid on play on the games of Baccarat, Mini Baccarat, Blackjack
                  and Roulette except where otherwise authorised by the Chief Executive.

ii)     Non Negotiable chip system

        a.        A rebate of 1.20% of the recorded loss of non negotiable chips shall be payable to the
                  junket operator.

        b.        Non negotiable chips can only be played on the games of Baccarat, Mini Baccarat and
                  Blackjack in the International Room and other such areas as designated. Where players
                  wish to play games not available on the non negotiable system the Chief Executive may
                  authorise that the play of other games with cash chips be recorded as per the cash chip
                  system and rebate paid at 0.6% of turnover.
4.     Expense Subsidy

i)     Cash Chip System

       An expense subsidy of 0.05% of cash chip turnover shall be payable to the operator.

ii)    Non Negotiable Chip System

       An expense subsidy of 0.1% on the recorded loss of non negotiable chips shall be payable to the
       junket operator.

5.     Bonus payments

i)     Cash Chip System

       A bonus of 0.125% of cash chip turnover shall be payable to the operator on all turnover greater
       than AUD$30 million in a single visit.

ii)    Non Negotiable Chip System

       A bonus of 0.25% on the recorded loss of non negotiable chips shall be payable to the operator
       on all recorded losses (turnover) greater than AUD $15 million in a single visit.

6.     Expenses

       All expenses incurred during a visit shall be the responsibility of the junket operator.

Program Two (Rebate on turnover and loss)

1.     Front money

       Minimum front money is AUD$250,000 per player
       Maximum front money unlimited.

2.     Players

       Minimum number of players is one.
3.        Rebate %

i)        refer to the following table for full details

                  NUMBER OF HANDS AT                        REBATE ON LOSS
                  PLAYERS MAX.                                 %
                  BET (examples)

                           10                               1.5%
                           100                              5.0%
                           500                              10.0%
                           1000                             12.5%
                           5000                             17.5%

The above table details the rebate percentages at each number of hands. Should the player/groups
number of hands fall between two values on the table it shall be the lower value on which the rebate %
shall be calculated.

The number of hands at players maximum bet shall be calculated by dividing the total turnover for the
visit by the group/player‟s maximum bet recorded during the visit.

Should the number of hands at the player‟s maximum bet be less than ten no rebate on loss will be
payable.

ii)       A commission on turnover shall also be payable at 0.45% for all turnover.

iii)      Rebates will only be payable on the total group position, unless an individual player is utilising
          the program.

iv)       The group/player must utilise the designated rebate chips.

4.        Games available

Baccarat and Mini Baccarat only.

5.        Wagers

Minimum = $2000 on “Player” in units of $100
$2000 on “Bank” in units of $2000
$200 on “Tie” in units of $100

Maximum = $150,000 - $200,000 subject to Management approval
“Player” and “Bank”
Tie = one eighth maximum limit

Program Three (Rebate on loss only)

1. Front money

       Minimum front money is AUD$1.5 million
       Minimum front money per qualifying player/room AUD $500,000
       Maximum front money unlimited.
2. Players

3. Rebate %

i)      refer to the following table for full details

                NUMBER OF HANDS AT                       REBATE ON LOSS
                PLAYERS MAX.                                %
                BET (examples)

                         10                              3.5%
                         100                             10.0%
                         500                             20.0%
                         1000                            25.5%
                         5000                            35.5%

The above table details the rebate percentages at each number of hands. Should the player/groups
number of hands fall between two values on the table it shall be the lower value on which the rebate %
shall be calculated.

Should the number of hands at the player‟s maximum bet be less than ten no rebate on loss will be
payable.

The number of hands at players maximum bet shall be calculated by dividing the total turnover for the
visit by the group/player‟s maximum bet recorded during the visit.

ii)     Rebates will only be payable on the total group win/loss not individuals win/loss, unless an
        individual player on the program.

iii)    The group/player must utilise the designated rebate chips.

4. Games available

Baccarat and Mini Baccarat only.

5. Wagers

Minimum = $2000 on “Player” in units of $100
$2000 on “Bank” in units of $2000
$200 on “Tie” in units of $100

Maximum = $100,000 Table Differential
“Player” and “Bank”
$12,500 “Tie”

6. Airfare

The Casino will provide one (1) first class airfare, Adelaide – destination – Adelaide, to the junket
operator/individual player provided the group player turns over at least $30 million dollars or loses 75%
of front money.
7. Room, Food and Beverage

The Casino will provide to bonafide players room, food and beverage for the duration of the group‟s
stay, provided the group/player turns at least one turn of front money per days stay. Room, food and
beverage may be allocated on the following basis:-


    FRONT                                  ROOM              F&B
MONEY/PLAYER                                                 ALLOWANCE/DAY

          $500,000                         Exec. Suite             200
          $750,000                         Deluxe Suite            200
          $1,000,000 +                     Dip./Pres Suite         300

Program Four (Private Jet)

1. Front money

       Minimum front money per group AUD$3 million
       Minimum front money per qualifying player AUD $1 million
       Maximum front money unlimited.

2. Players

       Minimum number of players per group is one.

3. Rebate %

i)        Rebate on loss of up to 15% at maximum. Rebate percentage calculated at 1% for each full
          shoe of Baccarat played. A full show being 70 (non tie) coups. Should the number of shoes fall
          between two values it shall be the lesser value on which the rebate percentage shall be
          calculated (Table Four).

ii)       Rebates will only be payable on the total group win/loss not individuals win/loss, unless an
          individual player on the program.

iii)      The group/player must utilise the designated rebate chips.

4. Games available

Baccarat and Mini Baccarat only.

5. Wagers

Minimum = $2000 on “Player” in units of $100
$2000 on “Bank” in units of $2000
$200 on “Tie” in units of $100

Maximum = $200,000 Table Differential “Player” and “Bank”
$20,000 “Tie”
6. Airfare

The Casino will provide a private jet to players on this program to facilitate travel to and from the
Casino. The Casino shall be responsible for all bookings and payments for the jet.

7.   Room, Food and Beverage

The Casino will provide suite accommodation, food, beverage and all incidental payments for the player
during the course of their visit.

8. Up Front Commission Payment

A payment of AUD $100,000 will be made to the group/player on arrival in the form of chip purchase
vouchers.

9. Cheque Cashing Facilities

Cheque cashing facilities may be provided subject to review and sufficient time allowed for any
application to be processed.

10. Availability

This program is only available to established players of high repute with a propensity to turnover a
minimum of AUD$60 million cash chip.


        NUMBER OF HANDS                            SHOES                    REBATE %

                 70                                1                        1%
                 140                               2                        2%
                 210                               3                        3%
                 280                               4                        4%
                 350                               5                        5%
                 420                               6                        6%
                 490                               7                        7%
                 560                               8                        8%
                 630                               9                        9%
                 700                               10                       10%
                 770                               11                       11%
                 840                               12                       12%
                 910                               13                       13%
                 980                               14                       14%
                 1050                              15                       15%

2.3.4            Rebate Player Program
                 Non-Negotiable and Cash Chip

This program is offered to clients of high repute in terms of their betting action.

A minimum bankroll of AUD$100,000 is required to utilise this program.
To qualify for this program the client must turn over their monies a minimum of four times (cash chip
system) and two times (non-negotiable system) during their stay.

1.      a. All reasonable food and beverage at the Casino‟s outlets will be complimentary. Each night
        the Casino will provide an evening supper in the International Room for the player.

        b. If a meal is taken outside the Casino facility at one of the Casino‟s preferred restaurants, a
        complimentary voucher will be extended to the player (value of such to be at Casino
        Management‟s discretion).

        c. Total reasonable expenses (including accommodation, food and beverage) are defined so as
        not to exceed 0.05% of turnover. This condition may be overridden by the Casino
        Management.

2. All hotel incidental expenses such as telephone, laundry, etc, are to be settled by the player prior to
   departure.

3. Cash, bank drafts and travellers cheques are acceptable. However, if a draft is to be used a copy
   must be forwarded by facsimile 48 hours before arrival to enable our Finance Department to
   approve clearance.

4. We have bank accounts in Hong Kong, Singapore and Adelaide which can be used for deposits.
   The bank will issue a receipt which should be presented when checking in at the Casino Cash Desk.

5. The rebate may be withheld if all bank drafts and/or bank deposits have not been cleared through
   our bank account.

6. The Casino will provide transportation – airport-hotel-airport.

7. Terms and conditions may be re-negotiated with the client in accordance with this policy document
   where the client wishes to stay for greater than a seven (7) day period.

Non negotiable chip system

A rebate of 1% on turnover will be paid to the client, subject to qualification, for all non negotiable chip
losses.

Non negotiable chips may only be played on the games of Baccarat, Minim Baccarat and Blackjack in
the International Room and other designated areas.

Where players wish to play games not available on the non negotiable system the Chief Executive may
authorise that the play of other games with cash chips be recorded as per the cash chip system and
rebate paid at 0.5% of turnover.
Cash chip system

A rebate of 0.5% of turnover will be paid to the client subject to qualification, on the games of Baccarat,
Mini Baccarat and Blackjack. A rebate of 1.1% of turnover shall be payable on the game of Roulette.

Rebate will only be paid on play on the games of Baccarat, Mini Baccarat, Blackjack and Roulette
except where otherwise authorised by the Chief Executive.

2.3.5             The Adelaide Casino Complimentary Program
                  Complimentary Program for Premium Players

This program is for clients coming to the Adelaide Casino from overseas, wishing to play for
complimentary airfare, room, food and beverage costs.

The following bankrolls and levels of play are required to receive the listed complimentaries and
rebates.

AUD$              TURNS           COMPLIMENTARY
BANKROLL          REQ’D

20,000             18             3 nights accom Hyatt Regency (Deluxe Room) Airfare rebate
                                  AUD $1000 Food & Beverage (Casino) Limousine transfers
                                  airport-hotel-airport

50,000             14             3 nights accom Hyatt Regency (Exec Suite) Airfare rebate
                                  AUD $2000 Food & Beverage (Casino) Limousine transfers
                                  airport-hotel-airport

70,000              13            3 nights accom Hyatt Regency (Exec Suite) Airfare rebate
                                  AUD $3000 Food & Beverage (Casino) Limousine transfers
                                  airport-hotel-airport

100,000             12            3 nights accom Hyatt Regency (Exec Suite) Airfare rebate
                                  AUD$4500 Food & Beverage (Casino) Limousine transfers
                                  Airport-hotel-airport

Should a player not reach the required turnover level then all complimentaries and rebates will be
reduced proportionately.

Poker play does not attract complimentaries.

In order to ensure that all turnover is recorded, the client will be issued with a VIP identification rating
card, which must be shown at each table played to the gaming staff member.

Banking Details

Accounts are provided at the following locations for your convenience:
SINGAPORE          Aitco Pty,. Ltd.
                   (Trading as Adelaide Casino)
                   Singapore Dollar Account Number:  141-278036-001
                   Malaysian Ringgit Account Number: 260 350079-186
                   Hong Kong & Shanghai Banking Corp
                   01-01 Collyer Quay
                   Singapore 0104

HONG KONG Aitco Pty. Ltd.
                  (Trading as Adelaide Casino)
                  Hong Kong Dollar Account Number:         567-343827-001
                  Hong Kong & Shanghai Banking Corp.
                  1 Queens Road
                  Central
                  Hong Kong

ADELAIDE           Aitco Pty. Ltd.
                   Trading as Adelaide Casino)
                   Australian Dollar Account Number:       931-556-640
                   State Bank of South Australia
                   97 King William Street
                   ADELAIDE 5000

TABLE ONE

NUMBER OF          REBATE %              NUMBER OF REBATE %
HANDS                                        HANDS

10                        -                     2500              3.5%
50                        -                     2600              4.0%
100                       1.0%                  2700              4.0%
200                       1.5%                  2800              4.0%
300                       2.0%                  2900              4.0%
400                       2.0%                  3000              4.0%
500                       2.5%                  3100              4.0%
600                       2.5%                  3200              4.0%
700                       2.5%                  3300              4.0%
800                       2.5%                  3400              4.0%
900                       3.0%                  3500              4.0%
1000                      3.0%                  3600              4.0%
1100                      3.0%                  3700              4.0%
1200                      3.0%                  3800              4.0%
1300                      3.0%                  3900              4.0%
1400                      3.0%                  4000              4.0%
1500                      3.5%                  4100              4.0%
1600                      3.5%                  4200              4.0%
1700                      3.5%                  4300              4.0%
1800                      3.5%                  4400              4.0%
1900                      3.5%                  4500              4.0%
2000                      3.5%                  4600              4.0%
2100                      3.5%                  4700              4.0%
2200              3.5%        4800             4.0%
2300              3.5%        4900             4.0%
2400              3.5%        5000             4.0%


TABLE TWO

NUMBER OF     REBATE %    NUMBER OF REBATE %
HANDS                         HANDS

10                1.5%        2500             15.5%
50                4.0%        2600             16.0%
100               5.0%        2700             16.0%
200               7.0%        2800             16.0%
300               8.0%        2900             16.0%
400               9.0%        3000             16.5%
500               10.0%       3100             16.5%
600               10.5%       3200             16.5%
700               11.0%       3300             16.5%
800               11.5%       3400             16.5%
900               12.0%       3500             16.5%
1000              12.5%       3600             17.0%
1100              13.0%       3700             17.0%
1200              13.0%       3800             17.0%
1300              13.5%       3900             17.0%
1400              13.5%       4000             17.0%
1500              14.0%       4100             17.0%
1600              14.0%       4200             17.5%
1700              14.5%       4300             17.5%
1800              14.5%       4400             17.5%
1900              15.0%       4500             17.5%
2000              15.0%       4600             17.5%
2100              15.0%       4700             17.5%
2200              15.5%       4800             17.5%
2300              15.5%       4900             17.5%
2400              15.5%       5000             17.5%


TABLE THREE

NUMBER OF     REBATE %    NUMBER OF REBATE %
HANDS                         HANDS

10                3.5%        2500             31.5%
50                8.0%        2600             32.0%
100               10.5%       2700             32.0%
200               14.0%       2800             32.5%
300               16.5%       2900             32.5%
400               18.5%       3000             33.0%
500               20.0%       3100             33.0%
600               21.5%       3200             33.0%
700                             22.5%                    3300                    33.5%
800                             23.5%                    3400                    33.5%
900                             24.5%                    3500                    33.5%
1000                            25.0%                    3600                    34.0%
1100                            26.0%                    3700                    34.0%
1200                            26.5%                    3800                    34.0%
1300                            27.0%                    3900                    34.0%
1400                            27.5%                    4000                    34.5%
1500                            28.0%                    4100                    34.5%
1600                            28.5%                    4200                    35.0%
1700                            29.0%                    4300                    35.0%
1800                            29.5%                    4400                    35.0%
1900                            30.0%                    4500                    35.0%
2000                            30.0%                    4600                    35.0%
2100                            30.5%                    4700                    35.5%
2200                            31.0%                    4800                    35.5%
2300                            31.0%                    4900                    35.5%
2400                            31.5%                    5000                    35.5%

2.4             Cash Chip System Analysis
2.4.1           Live Chips

This program is becoming one of the most popular systems and allows the players the flexibility to play
any game they choose. The system itself involves the recording of individual betting transactions made
by junket players. This is achieved by having a Casino staff member record the total of all bets made
where a result occurs for that wager on a rating/turnover sheet. The information is recorded by the
individual game and, in the case of Baccarat and mini Baccarat played in the International Room, this
information is collated at the end of every shoe. For other games the information is collated at the end
of each shift. Once collated, all information regarding win/loss and turnover for the junket group is
entered into the Casino computer system, known as the player rating system (P.R.S.), which collates the
information for the total period of the group‟s stay. This turnover information is then utilised to
calculate the commission payable to the junket operator. The advantage of this system is that actual
turnover is being recorded (given reasonable levels of tolerance for human error) and therefore
reasonably accurate expected revenue calculations may be derived from this information. Also, all
games are available in any location of the Casino. From the junket operator‟s point of view this system
of calculating commission provides a number of advantages over the non negotiable chip system.
Firstly, the operator is not responsible for the continuous changing of cash chips to cheque credits.
Secondly, the commission calculation is independent of win/loss. Thirdly, individual‟s turnover may be
recorded on the rating sheets if desired. This information is useful in determining bona fide players.
Fourthly, the system provides an up to date method of calculating commission.

This system is utilised by the Adelaide Casino in the following manner:

GAMES AVAILABLE

Any Casino game may be played in any area of the Casino. Standard chips will be used in the playing
of the games available and individual transactions will be recorded by the Casino or his/her agent.
DEPOSITS AND NUMBER OF PLAYERS

The minimum deposit is $400,000. The minimum bankroll for an “individual” is $20,000. “Individual”
may also refer to a room booked at the Hyatt as this is considered a standard cost against which
expenses may be accounted. For example two persons with individual bankrolls of $10,000 each who
share a room still meet the minimum bankroll amount.

COMMISSION STRUCTURE

Commission structure = 9%, 6%, 6% unlimited (that is the 6% figure is used thereafter). This is based
on the amount of the actual turnover in relation to the required turnover. The required turnover as
shown below is based on the “individual” bankroll (front monies). Commission is calculated as a
percentage of front monies, 9% of front monies or a percentage thereof based on the relationship
between actual turnover and required turnover for amounts up to and including 100% of required
turnover and 6% of front monies or a percentage thereof based on the relationship between actual and
required turnovers for amounts in excess of 100% of required turnover.


TURNOVER REQUIREMENTS

FRONT MONEY                      TURNS                   REQUIRED TURNOVER

20000                            18                              360000
30000                            16                              480000
40000                            15                              600000
50000                            14                              700000
60000                            14                              840000
70000                            13                              910000
80000                            13                              1040000
90000                            13                              1170000
100000                           12                              1200000
200000                           12                              2400000


COMMISSION CALCULATION EXAMPLE

When the full number of turns, relating to front money is met, the 9% commission is paid. If less than
the full amount is reached the commission is reduced accordingly.

Example:        Front monies $50,000

         Turnover reached               =                $550,000
         Required turnover              =                $700,000
         Turnover percentage            =                550000/700000 x 100
                                        =                78.57%
         Full commission at 9%          =                $ 4,500
         Commission payable             =                78.57% x $4,500
         Commission                     =                $3,536
If the turnover exceeds that required then the following example shows the method for calculating
commission:

Example: Front monies $50,000

         Turnover reached               =               $950,000
         Required turnover              =               $700,000
         Turnover percentage            =               950000/700000 x 10
                                        =               135.71%
         Full commission at 9%          =               4,500
         Full commission at 6%          =               $3,000
         Commission payable             =               100% x $4,500 + 35.71% x $3,000
         Commission                     =               $5,571


TURNOVER REQUIREMENTS AND COMMISSION AMOUNTS

FRONT           TURNS            REQUIRED               9% COMM                  6% COMM
MONEY                            TURNOVER

20000           18               360000         1800                     1200
30000           16               480000         2700                     1800
40000           15               600000         3600                     2400
50000           14               700000         4500                     3000
60000           14               840000         5400                     3600
70000           13               910000         6300                     4200
80000           13               1040000        7200                     4800
90000           13               1170000        8100                     5400
100000          12               1200000        9000                     6000
200000          12               2400000        18000                    12000

To calculate the turnover requirements of a group, divide the total front monies by the number of rooms
booked for the group. Members in the group relate to rooms we are picking up, not individual
members, as rooms are the only external expense incurred by the Casino.

Example:        Front monies                    =               $800,000
                Rooms                           =               12
                Front money/rooms               =               800,000 / 12
                                                =               $66,666
                Turnover requirement            =               13
                Required turnover               =               13 x $800,000
                                                =               10,400,000

Turnover requirements are based, in this case on the individual bankroll of $66,666. As can be seen
from the table of turnover requirements this amount needs to be turned over 13 times for full
commission. Therefore for the operator to receive the full commission of 9% of the total front money
the group are required to turn over $10,4000,000. If this is the case, the commission payable would
equal $72,000.
CASINO REVENUE CALCULATION (CASH CHIP)

The following example of a Casino revenue calculation is taken from the internal junket procedure
manual, which has not been updated for some time so the example may no longer be valid. Validity of
the assumptions of the program was based upon will be examined later in the text in detail.

                 Front money                        =       $50,000
                 Turnover reached                   =       $700,000
                 House edge                         =       1.26% (Baccarat edge)
                 Theoretical win                    =       1.26% x $700,000
                                                    =       $8,820

                 Expenses

                 Gaming tax                         =       20% x $8,8820
                                                    =       $1,764
                 Operators commission               =       $4,500
                 Room                               =       $45
                 Food & Bev internal                =       $150
                 Wages                              =       $120 based on $8/hr for 15 hrs
                 Total expenses                     =       $6,579
                 Theoretical win                    =       $8,820
                 Expenses                           =       $6,579
                 Casino net                         =       $2,241

“This calculation is given as an example only of how the Casino is able to estimate the profitability of a
junket player. There may be added costs to this depending on the group‟s outside activities such as
tours and transfer costs which may also need to be included.”

RATING OF PLAYERS

If an operator wishes to rate all his/her players together, this can be done. This is beneficial to the
Casino especially if there are a number of junket groups in at one time, as it eases the requirements
placed on the raters and thus increases the accuracy of the recorded information. However, if the
operator does wish all members of the junket group to be rated individually or some to be rated
individually and the others to be rated as a group, this may also be carried out. Where there is the case,
the amount of front monies per individual must be determined.

RATING OF CASINO GAMES

The various games offered by the Casino are rated slightly differently according to the nature of the
game being played.

BACCARAT AND MINI BACCARAT

All bets placed on “Player, “Banker” or “Tie” are recorded by the rater excepting where a “Tie” occurs
in which case bets made on either “Player” or “Banker” are NOT recorded. This is due to the fact that
the program has been set up utilising relative probabilities for this game.

BLACKJACK

All original bets are recorded in this case, that is, bets made prior to the initial deal only or insurance
bets. Additional wagers to double or split are not recorded so as to offset the recording of bets made
where a standoff occurs.
AMERICAN ROULETTE

In the case of Roulette, all wagers are recorded by the rater. This is done by adding the amount of
losing bets made by the player to the amount of winning wagers on the table. Calculation of the amount
of losing wagers is done by chipping up the losing wagers from the salad.

NB In the case of rating junket action, this must be completed on a turnover tracking sheet by a staff
member designated to record junket play.


2.4.2            Profit Analysis (After Tax and Commission Only)
                 Utilising Baccarat Edge

BAC. EDGE               TAX              FULL
                                         COMMISSION

0.0126                  0.2              0.09


FRONT REQ              REQ         FULL         THEO      CASINO NET              COMM       NET
MONEY TRANS            T/OV        COMM         NET       NET    WIN              WIN        COMM %
                                                                 %                %

20000       18       360000          1800        4536       1829      40.32        39.68     101.60
30000       16       480000          2700        6048       2138      35.36        44.64      79.20
40000       15       600000          3600        7560       2448      32.38        47.62      68.00
50000       14       700000          4500        8820       2556      28.98        51.02      56.80
60000       14       840000          5400       10584       3067      28.98        51.02      56.80
70000       13       910000          6300       11466       2873      25.05        54.95      45.60
80000       13      1040000          7200       13104       3283      25.05        54.95      45.60
90000       13      1170000          8100       14742       3694      25.05        54.95      45.60
100000      12      1200000          9000       15120       3096      20.48        59.52      34.40
200000      12      2400000         18000       30240       6192      20.48        59.52      34.40


2.4.3            Profit Analysis (after tax and commission only)
                 Utilising Budgeted Edge (89/90)

BAC. EDGE               TAX              FULL
                                         COMMISSION

0.0135                  0.2              0.09
FRONT REQ              REQ        FULL         THEO        CASINO NET            COMM         NET
MONEY TRNS             T/OV       COMM         NET         NET    WIN            WIN          COMM
                                                                  %              %            %

 20000       18       360000        1800        4860       2088        42.96          37.04   116.00
 30000       16       480000        2700        6480       2484        38.33          41.67    92.00
 40000       15       600000        3600        8100       2880        35.56          44.44    80.00
 50000       14       700000        4500        9450       3060        32.38          47.62    68.00
 60000       14       840000        5400       11340       3672        32.38          47.62    68.00
 70000       13       910000        6300       12285       3528        28.72          51.28    56.00
 80000       13      1040000        7200       14040       4032        28.72          51.28    56.00
 90000       13      1170000        8100       15795       4536        28.72          51.28    56.00
100000       12      1200000        9000       16200       3960        24.44          55.56    44.00
200000       12      2400000       18000       32400       7920        24.44          55.56    44.00

2.4.4 Profit Analysis (after tax, commission and expenses)
      Utilising Budgeted Edge Based on Initial Program Assumptions

BUD.        TAX          FULL         ACCOMM STAY              WAGE/           PLAY/
EDGE        COMM                      DAY    DAYS              HOUR            DAY


0.0135         0.2         0.09          100           3           8             5


FRONT REQ              REQ        FULL         THEO        CASINO NET            COMM         NET
MONEY TRNS             T/OV       COMM         NET         NET    WIN            WIN          COMM
                                                                   %              %            %

 20000       18       360000        1800        4860       1668        34.32         37.04     92.67
 30000       16       480000        2700        6480       2064        31.85         41.67     76.44
 40000       15       600000        3600        8100       2460        30.37         44.44     68.33
 50000       14       700000        4500        9450       2640        27.94         47.62     58.67
 60000       14       840000        5400       11340       3252        28.68         47.62     60.22
 70000       13       910000        6300       12285       3108        25.30         51.28     49.33
 80000       13      1040000        7200       14040       3612        25.73         51.28     50.17
 90000       13      1170000        8100       15795       4116        26.06         51.28     50.81
100000       12      1200000        9000       16200       3540        21.85         55.56     39.33
200000       12      2400000       18000       32400       7500        23.15         55.56     41.67

From this information it can be seen that when the junket program was devised, certain basic
assumptions were made which provided the junket operator with between approximately forty and sixty
percent of the theoretical win in commission if the turnover requirements were met. This was I relative
proportion with the policies determined for the premium player market, where the maximum return to
players in complimentaries extended was equal to 50% of the net theoretical win. Net theoretical win
equalling theoretical win less tax and staff costs, in this case.
Maintaining these initial basic assumptions let us now consider the effect of the average turnover
experienced which is approximately twenty times front money, on the Casino revenue.

2.4.5 Profit Analysis (After Tax and Commission and Expenses)
      Utilising Budgeted Edge Based on Initial Program Assumptions &
      Average Turnover

BUD.       TAX        COMM        COMM       ACCOMM STAY/                   WAGE             PLAY/
EDGE                                                DAY(S)                                   DAY


0.0135        0.2         0.09      0.06        100            3               8               5


FRONT           REQ              REQ             FULL              FULL COMM
MONEY           TRNS             T/OV            COMM 9%           6%

 20000           18               360000           1800              1200
 30000           16               480000           2700              1800
 40000           15               600000           3600              2400
 50000           14               700000           4500              3000
 60000           14               840000           5400              3600
 70000           13               910000           6300              4200
 80000           13              1040000           7200              4800
 90000           13              1170000           8100              5400
100000           12              1200000           9000              6000
200000           12              2400000          18000             12000


FRONT ACT              ACT         FULL       THEO        CASINO NET/              COMM       NET
MONEY TRNS             T/OV        COMM       NET         NET    WIN               WIN        COMM
                                                                 %                 %          %

 20000         20      400000        1933       5400         2100     38.89          35.80     108.62
 30000         20      600000        3150       8100         3360     41.48          38.89     106.67
 40000         20      800000        4400      10800         4620     42.78          40.74     105.00
 50000         20     1000000        5786      13500         5880     43.56          42.86     101.63
 60000         20     1200000        6743      16200         7140     44.07          42.86     102.84
 70000         20     1400000        8562      18900         8400     44.44          45.30      98.11
 80000         20     1600000        9785      21600         9660     44.72          45.30      98.73
 90000         20     1800000       11008      24300        10920     44.94          45.30      99.20
100000         20     2000000       13000      27000        12180     45.11          48.15      93.69
200000         20     4000000       26000      54000        24780     45.89          48.15      95.31


This information shows that if the “average” turnover is achieved, the program assumptions provide
virtually equal profit margins for the Casino operator and the junket operator. Given the above
information, the effect of alterations to the basic assumptions should be analysed.
2.4.6      Casino Net Analysis (After Tax, Commission and Expenses)
           Utilising Budgeted Edge (90/91)
           Based on Varied Program Assumptions Given

“AVERAGE” EXPENSES

AVERAGE EXPENSES                          STAFF COSTS            1421
PER ROOM                                  OVERSEAS OFFICE        618
                                          ACCOMMODATION          552
                                          FOOD & BEVERAGE        336
                                          TRAVEL/AIRFARE         183
                                          TOTAL                  3110

BUD.       TAX             COMM                   COMM
EDGE

0.0133     0.2             0.09                   0.06

FRONT    REQ       REQ            FULL       THEO        CASINO    NET/ WIN %
MONEY    TRNS      T/OV           COMM       WIN         NET


 20000    18      360000           1800       4788        1080          22.55
 30000    16      480000           2700       6384         703          11.01
 40000    15      600000           3600       7980         326           4.09
 50000    14      700000           4500       9310         162           1.74
 60000    14      840000           5400      11172         427           3.83
 70000    13      910000           6300      12103         272           2.25
 80000    13     1040000           7200      13832         755           5.46
 90000    13     1170000           8100      15561         239           7.96
100000    12     1200000           9000      15960         658           4.12
200000    12     2400000          18000      31920        4426          13.87


COMM/WIN %       NET COMM %                NET/F.M.%

37.59            59.99                     5.40
42.49            26.04                     2.34
45.11            9.06                      0.82
48.34            3.61                      0.32
48.34            7.91                      0.71
52.05            4.32                      0.39
52.05            10.49                     0.94
52.05            15.29                     1.38
56.39            7.31                      0.66
56.39            24.59                     2.21
This information displays the adverse effect the changes to the basic assumptions have had. Rapidly
increasing costs have severely limited the on-going viability of the junket program at various levels of
front monies. From this, let us now look at the effect of the average number of turns on the profitability
of the program.


“ACTUAL” EXPENSES AND “AVERAGE” TURNOVER


FRONT        REQ          REQ           FULL        THEO         CASINO       NET
MONEY        TRNS         T/OV          COMM        WIN          NET          WIN %

 20000         20       400000           1933        5320         -788          -14.80
 30000         20       600000           3150        7980          124            1.55
 40000         20       800000           4400       10640         1002            9.41
 50000         20      1000000           5786       13300         1744           13.11
 60000         20      1200000           6943       15960         2715           17.01
 70000         20      1400000           8562       18620         3224           17.32
 80000         20      1600000           9785       21280         4129           19.40
 90000         20      1800000          11008       23940         5034           21.03
100000         20      2000000          13000       26600         5170           19.44
200000         20      4000000          26000       53200        13450           25.28


COMM/WIN%                NET/COMM%                NET/F.M.%

    36.34                      -40.74               -3.94
    39.47                        3.93                0.41
    41.35                       22.77                2.50
    43.50                       30.14                3.49
    43.50                       39.10                4.52
    45.98                       37.66                4.61
    45.98                       42.20                5.16
    45.98                       45.73                5.59
    48.87                       39.77                5.17
    48.87                       51.73                6.72


This data shows that even if the “individual” meets the “average” turnover amount for the “individual‟s”
front money the relationship between the Casino net and the operator‟s commission no longer resembles
that on which the program was based. The comparison of this data is displayed below.


2.4.7           Casino Net to Commission Percentage Comparisons (Initial
                Assumptions to “Actual”) For 20 Turns
FRONT           NET/COMM %               NET/COMM                 VARIANCE
MONEY           INITIAL                  % ACTUAL                 INITIAL-ACT

   20000              108.62                  60.37                 168.99
   30000              106.67                   8.63                 115.30
   40000              105.00                  13.41                  91.59
   50000              101.63                  22.75                  78.88
   60000              102.84                  32.71                  70.13
   70000               98.11                  32.29                  65.82
   80000               98.73                  37.34                  61.39
   90000               99.20                  41.27                  57.94
  100000               93.69                  35.86                  57.83
  200000               95.31                  49.16                  46.15

All this information is of course based on an equal distribution of peripheral costs such as the overseas
office costs, and an equal number of turns as an “average” etc. Variations on these assumptions will be
examined in detail at a later stage. However, equal distribution of costs does serve to highlight expected
program performance if all junkets were to fall into any one of the front money categories. Thus for
example, if all junkets were to fall into the $20,000 “individual” front money category, the junket
program would no longer be viable. This of course, is not the case, as the $20,000 “individual” front
money junket has become infrequent, due to the lack of incentive for operators to bring in groups of this
type, because of the low return. Thus the program is protected to some degree by the cost factors which
effect the junket operator (airfares and incidentals). Operators will however include a number of
smaller bankroll players in a group if the group also comprises of one or two larger players, this is more
a “safety in numbers” or “atmosphere stimulating” approach, rather than a true cost based decision. To
further analyse the effect of expenses on the junket program peripheral expenses fore the various front
monies shall be allocated on the basis of the actual frequency of junket groups at the various levels of
front monies.

2.4.8           Breakdown of Expenses for Various Front Monies Given Frequency
                of Front Monies

FRONT        FREQ %       AVG ROOMS            % TOTAL         STAY           EXTRA
MONEY                                                                         STAFF

20 – 50K         10                23              25.84%          6               25
50 – 100K        30                11              37.08%          6               20
100 – 150K       15                 8              13.48%          5               15
150 – 200K       15                 5               8.43%          4               14
200 – 250K       15                 5               8.43%          4               14
 250K+           15                 4               6.74%          3               14


AVERAGE EXPENSES                        STAFF COSTS                       1011
20 – 50K                                OVERSEAS OFFICE                    239
                                        ACCOMMODATION                      690
                                        FOOD & BEVERAGE                    420
                                        TRAVEL/AIRFARE                      71
                                        TOTAL                                              2431
AVERAGE EXPENSES            STAFF COSTS               1691
50 – 100K                   OVERSEAS OFFICE            500
                            ACCOMMODATION              690
                            FOOD & BEVERAGE            420
                            TRAVEL/AIRFARE             148
                            TOTAL                     3449

AVERAGE EXPENSES            STAFF COSTS               1453
100 – 150K                  OVERSEAS OFFICE            688
                            ACCOMMODATION              575
                            FOOD & BEVERAGE            350
                            TRAVEL/AIRFARE             204
                            TOTAL                     3269

AVERAGE EXPENSES            STAFF COSTS               1736
150 – 200K                  OVERSEAS OFFICE           1100
                            ACCOMMODATION              460
                            FOOD & BEVERAGE            280
                            TRAVEL/AIRFARE             326
                            TOTAL                     3902

AVERAGE EXPENSES            STAFF COSTS               1736
200 – 250K                  OVERSEAS OFFICE           1100
                            ACCOMMODATION              460
                            FOOD & BEVERAGE            280
                            TRAVEL/AIRFARE             326
                            TOTAL                     3902

AVERAGE EXPENSES            STAFF COSTS               1628
250K+                       OVERSEAS OFFICE           1375
                            ACCOMMODATION              345
                            FOOD & BEVERAGE            210
                            TRAVEL/AIRFARE             408
                            TOTAL                     3965

2.4.9      Casino Net Calculations (Revised Expenses)
           20 Turns (Edge 1.33%)

FRONT ACT T/OV FULL COMM THEO WIN CASINO NET            NET/F.M.%
MONEY

 20000    400000     1933        5320          -108          -0.54
 30000    600000     3150        7980           803           2.68
 40000    800000     4400       10640          1681           4.20
 50000   1000000     5786       13300          2423           4.85
 60000   1200000     6943       15960          2376           3.96
 70000   1400000     8562       18620          2885           4.12
 80000   1600000     9785       21280          3790           4.74
 90000   1800000    11008       23940          4695           5.22
100000   2000000    13000       26600          5011           5.01
200000   4000000    26000       53200         12658           6.33
This information shows the effect of the actual distribution of costs on the profitability of the program at
the current time. Monitoring of costs on the above basis will determine program profitability
remembering that the operator‟s costs will effect levels of front money that are brought into the Casino.
Break-even turnover to front money requirements are displayed below:

BREAK-EVEN TURNOVER REQUIREMENTS (REVISED EXPENSES)

FRONT           REQ TRNS            REQ T/OV      FULL             THEO             CASINO
MONEY                                             COMM             WIN              NET

 20000               20.75             415000         1983           5520               1
 30000               16.12             483000         2714           6432               1
 40000               13.10             524000         3144           6969               0
 50000               11.55             577500         3713           7681               1
 60000               13.65             819000         5265          10893               0
 70000               13.16             921200         6352          12252               1
 80000               11.60             928000         6425          12342               0
 90000               10.31             927900         6424          12341               0
100000               10.41            1041000         7808          13845              -1
200000                6.21            1242000         9315          16519              -2

Let us now compare the break-even levels for the cash chip system with the Casino net profitability if
the non negotiable commission structure is used (detailed analysis of the non negotiable system is
carried out in the non negotiable section).


2.4.10          Casino Net Comparisons (Cash Chip for Non Negotiable) at Cash
                Chip Breakeven Levels


FRONT        COMM CASH              CASINO NET         COMM              CASINO NET
MONEY          CHIP                    CASH            NON NEG            NON NEG

 20000        1983              1                         2675                  -690
 30000        2714              1                         3318                  -603
 40000        3144              0                         3820                  -676
 50000        3713              1                         4388                  -674
 60000        5265              0                         5895                  -630
 70000        6352              1                         6706                  -354
 80000        6425              0                         7040                  -615
 90000        6424              0                         7340                  -916
100000        7808             -1                         8205                  -398
200000        9315             -2                         9315                    -2

This data serves to highlight one of the advantages of the cash chip system. As the commission
structure is linked to the required turnover, and the required turnover amounts vary in proportion to the
front monies, this provides a greater incentive for the junket operator to only bring in players with larger
amounts of front money. Approximate information on current levels of expenses incurred by junket
operators is shown below:


2.4.11          Junket Operator’s Expenses Per Person


AIRFARES
LOCATION                ECONOMY                  BUSINESS                  FIRST CLASS

SINGAPORE                   870                        2600                         3240
TAIPEI                     1945                        3470                          N/A
KUALA LUMPUR                810                        1870                         2450
JAKARTA                    1270                        2540                         3310
BANGKOK                    1280                        2480                         3230
HONG KONG                  1530                        3220                         3950



INCIDENTALS APPROXIMATE
                                                          (20K– 50K)       (50K–100K) (100K+)


AIRPORT TRANSFERS (NOT ADELAIDE)                    100              100             100
HOTEL COSTS (OTHER THAN ROOM)                                 100            150            200
DEVELOPMENT COSTS (MIN)                                       500             750          1000


Junket operators do different deals with different players and these deals vary from operator to operator,
therefore it is difficult to provide an accurate assessment of the costs incurred by junket operators. For
larger players, the junket operator may also give that player a percentage of the operator‟s commission.
As an approximately guide, junket operators provide economy airfares for 20K to 50K players, business
class airfares for 50K to 100K players and first class airfares for 100K + players. Hotel costs and
development costs will also vary according to player‟s bankroll amounts. Approximate totals of
operator‟s costs are shown below.

2.4.12          Operator’s Costs (Approximate)

LOCATION                          COSTS                   COSTS                     COSTS
                                  (20-50K)                (50-100K)                 (100K+)

SINGAPORE                           1570                    3600                      4540
TAIPEI                              2645                    4470                       N/A
KUALA LUMPUR                        1510                    2870                      3750
JAKARTA                             1970                    3540                      4610
BANGKOK                             1980                    3480                      4530
HONG KONG                           2230                    4220                      5250
AVERAGE                             1984                    3697                      4536
2.4.13           Casino Net to Operator’s Net Comparison (Revised Expenses)
                 20 Turns, Edge 1.33


FRONT                OP NET               CASINO NET           OP-CAS
MONEY

 20000                   -51                    -108                 57
 30000                  1166                     803                363
 40000                  2416                    1681                735
 50000                  3802                    2423               1378
 60000                  3246                    2376                870
 70000                  4865                    2885               1980
 80000                  6088                    3790               2298
 90000                  7311                    4695               2616
100000                  8464                    5011               3453
200000                 21464                   12658               8806


This information, combined with the break-even levels may be useful if it is determined that the
required turnover levels need to be altered or the program modified in any way. It may be considered
pertinent, for example, to ensure that the break-even levels for the junket operator and the Casino are
relatively close so as to provide a greater incentive for the junket operator to bring in players of value
not only to him or herself but also to the Casino.


2.4.14           Possible Junket Program Modifications

FRONT             REQ TRNS            REQ T/OV            FULL COMM           FULL COMM
MONEY                                                         9%                  6%

 20000                  21              420000                   1800                1200
 30000                  19              570000                   2700                1800
 40000                  16              640000                   2600                2400
 50000                  15              750000                   4500                3000
 60000                  14              840000                   5400                3600
 70000                  14              980000                   6300                4200
 80000                  13             1040000                   7200                4800
 90000                  13             1170000                   8100                5400
100000                  12             1200000                   9000                6000
200000                  12             2400000                  18000               12000


FRONT                    TRANS            OP NET                    CASINO           OP-CAS
MONEY                                                               NET

20000                        19.13           -344                         0             -345
30000                        13.73           - 33                         1             - 34
40000                        12.12            743                         0              742
50000                        10.48           1160                         0             1159
 60000                     13.65            1568                        0               1568
 70000                     11.70            1568                        0               1568
 80000                     11.60            2728                        0               2728
 90000                     10.31            2727                        0               2727
100000                     10.41            3272                       -1               3272
200000                      6.21            4779                       -2               4781


2.4.15          Comparison of Required Turns (Existing to Modified)

FRONT                     REQ TURNS                REQ TURNS
MONEY                     EXISTING                 MODIFIED

20000                              18                      21
30000                              16                      19
40000                              15                      16
50000                              14                      15
60000                              14                      14
70000                              13                      14
80000                              13                      13
90000                              13                      13
10000                              12                      12
20000                              12                      12

If modification to the program was considered necessary then the above modifications could be utilised
to meet the specified criteria. However before altering any aspect of the junket program the total impact
on the program must be considered. When considering the operator‟s profit levels in the above
calculations, it must be remembered that the operator‟s costs shown are the very minimum costs that
he/she would incur in bringing players to Adelaide. The payback of commission to players will
severely limit operator‟s profits as will the extension of credit players, where this credit on occasion
goes unpaid. Bad debt is becoming one of the operator‟s biggest areas of expense. The operators have
had to extend credit in order to attract clients. This has further limited the viability to the operators of
bringing their clients to Adelaide. Therefore before placing any restrictions on operators or reducing in
any way their commission levels, it must be remembered that if bringing junkets to Adelaide does not
remain a viable prospect for the operators, they will take their custom elsewhere. This would obviously
not be the desired result from the Casinos point of view and hence even minor alterations to junket
program policy should be given careful consideration.


2.4.16          Conclusion

The cash chip system for calculating commission is an extremely versatile program which can easily be
modified to fulfil any criteria set. The system is functional at all levels of front monies and offers a
number of advantages over the non negotiable system especially at individual front money levels which
are less than $100,000.

The advantages of the system are:
1.      All games are available
2.      Games may be played in any location of the Casino
3.      Actual turnover is recorded
4.      Required turnover levels are related to front monies on an external cost allocation (per room
        basis)
5.      Profitability on levels of front money under $100,000 is maintained for lower levels of turnover
6.      Continuous changing of cash chips to cheque credits is not necessary
7.      Commission calculations are independent of win/loss
8.      Individual turnover may be recorded
9.      Commission calculations are up to date, and
10.     The program may be modified without altering the commission percentages.

Therefore it may be stated that the cash chip system should be given consideration when setting up any
junket program, especially if the 20K to 100K market is to be targeted.


2.5             Non Negotiable Chip System
2.5.1           Introduction

This system is offered to meet the market demands. Many junket operators and players who go to
Macau use this system and feel comfortable with it. In fact, operators have used this system for many
years. This is because the system offers a method for both the operator and the Casino to measure
turnover and thus calculate commission payable to the operator. It is therefore an independent method
and thus calculate commission payable to the operator. It is therefore an independent method of
commission calculation which both the operator and Casino may follow.

The system itself is one whereby the junket deposits an amount of money, known as “front monies” and
is issued with cheque credits to an amount equal to the front monies clearly marked with the words
NON NEGOTIABLE on the front thereof. These non negotiable cheque credits may then be
exchanged for non negotiable chips only at the gaming tables. The non negotiable cheque credits issued
are listed by the Casino operator on what may be referred to as a cage turnover schedule with returned
non negotiable chips and cheque credits being deducted from this schedule total at settlement. Any cash
chips which the operator returns to the cage may be converted to further non negotiable cheque credits if
required. Cash chips are issued to the junket players at the appropriate game odds when winning non
negotiable chip wagers are being paid. When the non negotiable chip wager loses, it is placed in the
gaming table float as per a normal wager. Therefore the system is basically a measure of player‟s losses
of non negotiable chips and/or cheque credits through the play of Casino games. The purpose of this is
to calculate a commission amount payable to the junket operator based on the level of play of the
players that he or she brings to gamble in the Casino. These are players with large amounts of money
from overseas who, without the junket operator, would not have come to the particular Casino.
Therefore the commission is an incentive for the operator to bring his or her associates to a particular
Casino.
This system is utilised by the Adelaide Casino in the following manner.


2.5.2           Games Available

Gaming is restricted to the International Room on this program and only Baccarat, mini Baccarat and
Blackjack can be played.


2.5.3           Deposits and Number of Players

The minimum deposit is $400,000. The minimum per person is $50,000. The minimum number of
players is four.


2.5.4           Commission Structure

Commission structure = 2%, 2%, 2%, 1% unlimited based on the number of turns through the cage.
The turns through the cage being the number of times the amount of the initial front monies is lost in
non negotiable chips. Therefore 1 turn through the case is the equivalent of the group either losing all
their front monies or converting the non negotiable chips and cheque credits to cash chips.

The minimum turnover requirements are 4 times (turns), if a group falls under this the commission is
reduced to 1.5%, 1.5% or 1.5% times the number of turns through the cage.

Therefore the commission percentage for the non negotiable system equals the number of turns through
the cage broken down into units multiplied by the commission percentage structure

For example:

5 turns through the cage = 1 turn + 1 turn + 1 turn + 1 turn + 1 turn.

The commission structure where the turns through the cage is greater than or equal to 4 is 2%, 2%, 2%,
1% unlimited (that is the 1% figure is used thereafter).

Therefore for 5 turns the commission percentage = 2% + 2% + 2% + 1% + 1% = 8% or to show this
more simply:

The commission percent is equal to the number of turns + 3 if the turns are greater than or equal to 4.

Therefore for 5 turns the commission percentage = (5 + 3)% which is 8%.

Where the turns through the case is less than 4 then the commission structure becomes 1.5%, 1.5%,
1.5%.
For example:

3    turns through the cage = 1 turn + 1 turn + 1 turn

Therefore the commission percentage equals 1.5% + 1.5% + 1.5% = 4.5% or to show this more simply:

The commission percent is equal to the number of turns multiplied by 1.5% if the turns are less than 4.

2.5.5           Operators’ Responsibilities

The operator is responsible for the changing of cash chips for hi/her players.

2.5.6           Commission Calculation Example

Commission is calculated on monies turned over through the cage. The groups are rated as one.

Calculation of commission:

Example: Front monies $1,500,000

Monies turned over and recorded by the cage $21,000,000

Operator has:            $600,000 non negotiable chips

                         $250,000 non negotiable cheque credits

                         $ 50,000 cash chips

The only concerns in the calculation of the commission are the non negotiable chips, cheque credits and
the cage turnover schedule. Cash chips are converted to cash and recorded separately.

All non negotiable chips and cheque credits are deducted from the turnover schedule. Commission is
based on the chips that have been lost.

CAGE TURNOVER SCHEDULE                   =        $21,000,000
LESS RETURNED NON NEGS                   =        $850,000 (chips and cheque credits)
HENCE CAGE TURNOVER                      =        $20,150,000
TURNS                                    =        CAGE TURNOVER/FRONT MONIES
TURNS                                    =        $20,150,000/$1,500,00
TURNS                                    =        13,4333
ADD 3 TO NUMBER OF TURNS                  =       COMMISSION PERCENTAGE (TURNS>=4)
COMMISSION PERCENTAGE                     =       16.4333%
COMMISSION PAYABLE                        =       commission percentage times front monies
COMMISSION PAYABLE                        =       16.4333% x $1,5000,000
COMMISSION PAYABLE                        =       $246,500

If the cage turnover is less than 4 times the front monies, the commission is calculated as follows.

Operator has non negotiable chips of $30,000

FRONT MONIES                              =       $1,500,000
CAGE TURNOVER SCHEDULE                    =       $5,580,000
LESS NON NEGS.                            =       $30,000
CAGE TURNOVER                             =       $5,550,000
TURNS                                     =       5,550,000/1,500,000
TURNS                                     =       3.7
COMMISSION PERCENTAGE                     =       turns x 1.5%
COMMISSION PERCENTAGE                     =       5.55%
COMMISSION PAYABLE                        =       5.55% x FRONT MONIES
COMMISSION PAYABLE                        =       $83,250


2.5.7           Revenue Calculations

The revenue calculations for this system require the conversion of the known cage turnover (cage
turnover) schedule amount, minus returned non negotiable chips and cheque credits) to a theoretical
turnover. The theoretical turnover being a calculation of the theoretical total amount wagered on the
game given the house edge and the odds payable. It is essential that this amount be correctly
approximated for commission payable structures to be calculated and the system to be profitable to the
Casino operator. At this point in time revenue calculations have been made on the basis that the amount
turned over through the cage needed to have been wagered twice on the tables which as is shown later,
is a reasonable approximation of the general theorem for calculating theoretical turnover from cage
turnover, given the restriction of the games available for play using the non negotiable system.

2.5.8           Other Information

It is noted in the internal junket procedures manual that this policy has the potential to be exploited by
the junket operators trying to bring in lower levels of front monies, as there are no turnover
requirements. It is also suggested in this manual that by monitoring play and players, one can keep the
situation well under that Casino‟s control.
2.5.9           Splinter Program

Also available to players who do not wish to be associated with a junket operator is a splinter program
which, on the non negotiable program, pays 1% of cage turnover to the player as commission. This
program also offers the player full charges for the duration of their stay to be met by the Casino.

2.5.9           Commission Calculations Analysis

It is extremely important to fully understand exactly how and why the non negotiable chip system
operates in regard to commission calculations.

Firstly it is important to recognise the fact that commissions calculated on this system are based on
chips that have been LOST not on the basis of the cash chips that are returned to the cage and redeemed
to further non negotiable cheque credits. This is because we deduct from the cage turnover schedule the
amounts of returned non negotiable chips and cheque credits prior to commission calculations. Due to
this fact, initial front monies are recorded on the cage turnover schedule as well as cash chips redeemed
for further non negotiable cheque credits.

Consider the following: a junket buys in for $1,000,000 and therefore receives this amount in non
negotiable cheque credits, should the group then decide not to play and return these cheque credits then
the returned cheque credits are deducted from the cage turnover schedule which would have been
credited with the initial front monies of $1,000,000. This of course provides a net cage turnover of zero
which in turn relates to a commission payable of zero. The non negotiable cheque credits may then be
redeemed for cash, cheque, etc. by the operator.

Therefore Point 1:

The non negotiable commission calculation is based on players’ losses only.

Secondly, it is important to understand the validity of the statement “Once through the cage, equals
twice over the tables.”

This statement is ROUGHLY accurate for the non negotiable chip system when considering EVEN
CHANCE PLAY ONLY. Consider firstly an unbiased game with an even chance of winning or losing.
In this game non negotiable chips are wagered and if the wager wins then these chips are paid in cash
chips, if the wager loses then the non negotiable chips are lost. As the number of wagers increases then
the percentage of wins and losses will tend toward an even split of 50/50, however even in this case it
should be noted that, whilst the percentages should tend toward 50% as the number of trials increases
the actual numerical variance may still increase. However, if a large number of trials are considered
then the expected result in a non biased even chance game would be to retain 50% of the non negotiable
chips wagered and to be paid 50% in cash chips giving a total win/loss tending towards 0%. Therefore,
of the total amount of non negotiable chips wagered, one half of these would be paid in cash chips and
one half lost.
Therefore Point 2:

“Once through the cage, equals twice over the table” is an approximately valid statement given a large
number of trials and an unbiased even chance game or a game where the percent return to the player in
non negotiables equals 50%.

Thirdly, compare the cash chip commission system to the non negotiable commission calculation using
the above formula that turnover equals cage turns multiplied by two.

COMMISSION COMPARISON – CASH TO NON NEGOTIBLE:

(TURNOVER = CAGE TURNOVER X 2)


CASH CHIP SYSTEM

FRONT       REQ           REQ.         FULL         FULL        ACT.             COMM
MONEY       TURNS         T/OVER       COMM         COMM        T.OVER           PAID.
                                         9%           6%

 20000        18           360000         1800         1200          360000        1800
 30000        16           480000         2700         1800          480000        2700
 40000        15           600000         3600         2400          600000        3600
 50000        14           700000         4500         3000          700000        4500
 60000        14           840000         5400         3600          840000        5400
 70000        13           910000         6300         4200          910000        6300
 80000        13          1040000         7200         4800         1040000        7200
 90000        13          1170000         8100         5400         1170000        8100
100000        12          1200000         9000         6000         1200000        9000



NON NEGOTIABLE SYSTEM

FRONT         REQ           REQ             CAGE           TURNS          COMM.       COMM.
MONEY         TURNS         T/OVER          T/OVER         NON            NON         CASH
              CASH          CASH            NON NEG        NEG            NEG         CHIP
              CHIP          CHIP

 20000          18          360000            180000          9.0         2400            1800
 30000          16          480000            240000          8.0         3300            2700
 40000          15          600000            300000          7.5         4200            3600
 50000          14          700000            350000          7.0         5000            4500
 60000          14          840000            420000          7.0         6000            5400
 70000          13          910000            455000          6.5         6650            6300
 80000          13         1040000            520000          6.5         7600            7200
 90000          13         1170000            585000          6.5         8550            8100
100000          12         1200000            600000          6.0         9000            9000
COMMISSION COMPARISON

FRONT     ACT          COMM.         TURNS         COMM.        VARIANCE
MONEY     T/OVER.      CASH CHIP     NON NEG       NON NEG

20000      360000      1800          9.00          2400         600
30000      480000      2700          8.00          3300         600
40000      600000      3600          7.50          4200         600
50000      700000      4500          7.00          5000         500
60000      840000      5400          7.00          6000         600
70000      910000      6300          6.50          6650         350
80000     1040000      7200          6.50          7600         400
90000     1170000      8100          6.50          8550         450
100000    1200000      9000          6.00          9000           0


COMMISSION COMPARISON WHERE CAGE TURNS EQUALS 3

FRONT     ACT          COMM.         TURNS         COMM.        VARIANCE
MONEY     T/OVER.      CASH CHIP     NON NEG       NON NEG

20000     120000 600          3.00           900          300
30000     1800001013          3.00          1350          338
40000     2400001440          3.00          1800          360
50000     3000001929          3.00          2250          321
60000     3600002314          3.00          2700          386
70000     4200002908          3.00          3150          242
80000     4800003323          3.00          3600          277
90000     5400003738          3.00          4050          312
100000    6000004500          3.00          4500            0


COMMISSION COMPARISON WHERE CAGE TURNS EQUAL 4

FRONT     ACT          COMM.         TURNS         COMM.        VARIANCE
MONEY     T/OVER.      CASH CHIP     NON NEG       NON NEG

20000      160000       800          4.00          1400          600
30000      240000      1350          4.00          2100          750
40000      320000      1920          4.00          2800          880
50000      400000      2571          4.00          3500          929
60000      480000      3086          4.00          4200         1114
70000      560000      3877          4.00          4900         1023
80000      640000      4431          4.00          5600         1169
90000      720000      4985          4.00          6300         1315
100000    800000       6000          4.00          7000         1000
COMMISSION COMPARISON WHERE CAGE TURNS EQUALS 5

FRONT           ACT              COMM.            TURNS           COMM.            VARIANCE
MONEY           T/OVER.          CASH CHIP        NON NEG         NON NEG

 20000          200000               1000                5.00         1600               600
 30000          300000               1688                5.00         2400               713
 40000          400000               2400                5.00         3200               800
 50000          500000               3214                5.00         4000               786
 60000          600000               3857                5.00         4800               943
 70000          700000               4846                5.00         5600               754
 80000          800000               5538                5.00         6400               862
 90000          900000               6231                5.00         7200               969
100000         1000000               7500                5.00         8000               500


COMMISSION COMPARISON WHERE CAGE TURNS EQUALS 6

FRONT           ACT              COMM.            TURNS           COMM.            VARIANCE
MONEY           T/OVER.          CASH CHIP        NON NEG         NON NEG

20000             240000          1200            6.00            1800             600
30000             360000          2025            6.00            2700             675
40000             480000          2880            6.00            3600             720
50000             600000         3857             6.00            4500             643
60000             720000         4629             6.00            5400             771
70000             840000         5815             6.00            6300             485
80000             960000         6646             6.00            7200             554
90000            1080000         7477             6.00            8100             623
100000           1200000         9000             6.00            9000               0

From this information it can be seen that the two systems become comparatively equal on a commission
basis when the front money is greater than or equal to $100,000 and the turns through the cage is greater
than or equal to 6. When these criteria are met the commission structure is such that the commission
payable from either system is virtually the same. When these criteria are not met the non negotiable
commission exceeds that of the cash chip system.

Therefore Point 3 is:

The commission structure of the non negotiable system is such that profitability is reduced when junkets
play non negotiables if their front monies is less than $100,000 per person and the turns through the
cage are less than 6.

Fourthly, given that Casino games are not unbiased what effect does this have on commission payments
and profitability. Given that the non negotiable system is a loss based system, consider the effect of the
house edge on the relationship between the cage turnover and the actual turnover. To perform these
calculations it is necessary to utilise the theoretical house edge for the various games and consider
situations where the initial front monies is non negotiables are reduced to zero, given even chance play.
THEORETICAL TURNOVER TO CAGE TURNOVER COMPARISONS:
(FRONT MONIES REDUCED TO ZERO)



GAME     HOUSE      % RETURN % RETURN      % RETURN   %LOSS NON
         EDGE       PLAYER   CASH          NON NEG.   NEG

AR        2.7        97.3       48.65      48.65      51.35
BJ        1.3        98.7       49.35      49.35      50.65



GAME      FRONT      WAGER      CASH       NON NEG.
          MONEY

AR        20000      20000.00    9730.00   9730.00
                      9730.00    4733.65   4733.65
                      4733.65    2302.92   2302.92
                      2302.92    1120.37   1120.37
                      1120.37     545.06    545.06
                       545.06     265.17    265.17
                       265.17     129.01    129.01
                       129.01      62.76     62.76
                        62.76      30.53     30.53
                        30.53      14.85     14.85
                        14.85       7.23      7.23
                         7.23       3.52      3.52
                         3.52       1.71      1.71
                         1.71       0.83      0.83
                         0.83       0.40      0.40
                         0.40       0.20      0.20
                         0.20       0.10      0.10

          TOTALS     38948.21   18948.30      0.10



THEORETICAL T/OVER TO CAGE T/OVER COMPARISONS:
(FRONT MONIES REDUCED TO ZERO)


GAME      FRONT      WAGER      CASH       NON NEG.
          MONEY

BJ        20000      20000.00    9870.00   9870.00
                      9870.00    4870.85   4870.85
                      4870.85    2403.76   2403.76
                      2403.76    1186.26   1186.26
                      1186.26     585.42    585.42
                       585.42     288.90    288.90
                       288.90     142.57    142.57
                       142.57      70.36     70.36
                        70.36      34.72     34.72
                        34.72      17.14     17.14
                                     17.14             8.46            8.46
                                      8.46             4.17            4.17
                                      4.17             2.06            2.06
                                      2.06             1.02            1.02
                                      1.02             0.50            0.50
                                      0.50             0.25            0.25
                                      0.25             0.12            0.12

                TOTALS           39486.43         19486.55             0.12

Front monies is non negotiable chips being reduced to zero will equate with the cage turnover equalling
the front monies ie 1 turn. The total of non negotiable wagers to achieve this is shown in the first totals
column, this would be the theoretical turnover amount.

From this data it can be seen that the relationship between actual turnover and losses of non negotiable
chips, that is cage turnover, varies according to the percentage return to the player for the particular
game. With the actual turnover being theoretically less than double the initial amount of front monies.

For Roulette this relationship can be expressed as:

Theoretical turnover = {front monies + (18/19 x front monies )} 18/19 being an accurate representation
of the return to player in non negotiable/loss of non negotiables.

Where front monies = Cage turnover in this case.

For Blackjack the relationship can be expressed as:

Theoretical turnover = {front monies + 49.35/50.65 x front monies)}

Where front monies = Cage turnover in this case.

This is applicable if, and only if, EVEN CHANCE play is being considered.

The game of Baccarat will be examined later as this game needs to be considered in detail as it is the
preferred game of the junket players.

Therefore Point 4 is:

The theoretical turnover is slightly less than twice the amount of front monies when considering even
chance play on Roulette and Blackjack.

The effect on probability of this fact can be displayed as below.
COMMISSION COMPARISON ROULETTE

FRONT           ACT.          COMM        CAGE           TURNS         COMM            VARIANCE
MONEY           T/OVER        CASH        T/OVER         NON NEG       NON NEG.
                              CHIP.

 20000          360000          1800      184865          9.24            2449               649
 30000          480000          2700      246486          8.22            3365               665
 40000          600000          3600      308108          7.70            4281               681
 50000          700000          4500      359459          7.19            5095               595
 60000          840000          5400      431351          7.19            6114               714
 70000          910000          6300      467297          6.68            6773               473
 80000         1040000          7200      534054          6.68            7741               541
 90000         1170000          8100      600811          6.68            8708               608
100000         1200000          9000      616216          6.16            9162               162


COMMISSION COMPARISON BLACKJACK

FRONT           ACT.   COMM               CAGE TURNS     COMM VARIANCE
MONEY           T/OVER CASH              T/OVER NON NEG NON NEG.
                        CHIP.

 20000          360000        1800        182340         9.12        2423              623
 30000          480000        2700        243120         8.10        3331              631
 40000          600000        3600        303900         7.60        4239              639
 50000          700000        4500        354550         7.09        6055              655
 70000          910000        6300        460915         6.58        6709              409
 80000         1040000        7200        526760         6.58        7668              468
 90000         1170000        8100        592605         6.58        8626              526
100000         1200000        9000        607800         6.08        9078               78

From this data it can be seen that the theoretical commission payable for non negotiable junkets will
exceed that of cash chip junkets when considering even chance play on Blackjack and Roulette.

The comparisons for Baccarat are more complicated due to the percentage return to the player being
variable dependant on levels of play on the various wager areas and the 5% commission payable on
winning bank bets.


COMMISSION COMPARISON BACCARAT

WAGER           HOUSE % RETURN % RETURN % RETURN % LOSS
                EDGE   PLAYER     CASH    NON NEG. NON NEG

PLAYER          1.36            98.64            49.32           49.32            50.68
WAGER    FRONT      BET        CASH        NON NEG.
         MONEY

PLAYER   20000     20000.00      9864.00   9864.00
                    9864.00      4864.92   4864.92
                    4864.92      2399.38   2399.38
                    2399.38      1183.37   1183.37
                    1183.37       583.64    583.64
                     583.64       287.85    287.85
                     287.85       141.97    141.97
                     141.97        70.02     70.02
                      70.02        34.53     34.53
                      34.53        17.03     17.03
                      17.03         8.40      8.40
                       8.40         4.14      4.14
                       4.14         2.04      2.04
                       2.04         1.01      1.01
                       1.00         0.50      0.50
                       0.50         0.25      0.25
                       0.25         0.12      0.12

         TOTALS    39463.06    19463.18       0.12


COMMISSION COMPARISON BACCARAT


WAGER    HOUSE % RETURN % RETURN % RETURN             % LOSS NON
         EDGE    PLAYER     CASH   NON NEG                NEG

PLAYER   1.17      98.83       48.15       50.68          49.32



WAGER    FRONT      BET        CASH        NON NEG.
         MONEY

BANKER   20000     20000.00      9630.00   10136.00
                    10136.00     4880.48    5136.92
                     5136.92     2473.43    2603.39
                     2603.39     1253.53    1319.40
                     1319.40      635.29     668.67
                      668.67      321.97     338.88
                      338.88      163.17     171.75
                      171.75       82.70      87.04
                       87.04       41.91      44.11
                       44.11       21.24      22.36
                       22.36       10.76      11.33
                       11.33        5.46       5.74
                        5.74        2.76       2.91
                        2.91        1.40       1.47
                        1.47        0.71       0.75
                        0.75        0.36       0.38
                        0.38        0.18       0.19
                                      0.19            0.09             0.10

                 TOTALS          40551.11         19525.36             0.10

Therefore from this information it can be seen that for the game of Baccarat if the player were to wager
an even amount on “Player” band “Banker” then the relationship between the cage turnover figure and
the theoretical turnover IS in fact 1 to 2. Hence the statement “Once through the case, equal twice over
the tablets” is correct for the game of Baccarat if, and only if, an equal amount of play on “Player” and
“Banker” occurs.

The relationship between front monies and actual turnover can be expressed as:

         theoretical turnover = {front monies + (49.32/50.68 x front monies)} for player.

         where front monies equals Cage turnover in this case and;

         theoretical turnover = {front monies + 50.68/49.32 x front monies)} for banker.

         Where front monies equals cage turnover in this case.

Front monies equals cage turnover in both cases due to the fact that in the examples shown, the initial
front monies were reduced to zero. This equates to losing all the non negotiable chips and cheque
credits initially issued and therefore equals 1 turn.

Variations in the levels of play on the various wager areas will effect the amount of commission payable
when compared to the cash chip system. Commission comparisons are shown below given 100% play
on either “Player” or “Banker”.


COMMISSION COMPARISON BACCARAT (100% PLAY ON “PLAYER”)


FRONT            ACT.   COMM              CAGE TURNS     COMM                     VARIANCE
MONEY            T/OVER CASH             T/OVER NON NEG NON NEG
                         CHIP.

20000             360000         1800        182448       9.12            2424              624
30000             480000         2700        243264       8.11            3333              633
40000             600000         3600        304080       7.60            4241              641
50000             700000         4500        354760       7.10            5048              548
60000             840000         5400        425712       7.10            6057              657
70000             910000         6300        461188       6.59            6712              412
80000            1040000         7200        527072       6.59            7671              471
90000            1170000         8100        592956       6.59            8630              530
100000           1200000         9000        608160       6.08            9082               82
COMMISSION COMPARISON BACCARAT (100% PLAY ON “BANKER”)


FRONT           ACT.   COMM              CAGE TURNS     COMM VARIANCE
MONEY           T/OVER CASH             T/OVER NON NEG NON NEG.
                        CHIP.             NEG

20000            360000         1800     177552         8.88             2376             576
30000            480000         2700     236736         7.89             3267             567
40000            600000         3600     295920         7.40             4159             559
50000            700000         4500     345240         6.90             4952             452
60000            840000         5400     414288         6.90             5943             543
70000            910000         6300     448812         6.41             6588             288
80000           1040000         7200     512928         6.41             7529             329
90000           1170000         8100     577044         6.41             8470             370
100000          1200000         9000     591840         5.92             8918             -82

The commission saving in comparison 2, for the $100,000 example, is offset by the theoretical win
being reduced because of the lesser house edge on “Banker” bets as compared to “Player” bets.
However, if the commission payments only, are compared, then it can be seen that there is a
commission saving when 100% of wagers are placed on “bank”. Hence it may be stated that for the
game of Baccarat the non negotiable chip system commission structure is EQUAL to that of the cash
chip commission calculation when the front monies exceed $100,000 and the turns through the cage is
greater than or equal to 6 if there is an equal distribution of wagers on “player” and “bank”.

Yet another important comparison can be carried out giving consideration to play on Roulette on bets
other than even chance bets. This entails more rapid conversion of non negotiable chips to cash chips
than occurs due to even chance play.


ROULETTE (ACCELERATED CONVERSION OF NON NEG. TO CASH CHIPS)

WAGER                   FRONT                   BET             CASH             NON NEG
                        MONEY

STRAIGHT                20000                   20000.00        18918.91         540.54
UPS                                               540.54          511.32          14.61
                                                   14.61            3.82           0.39
                                                    0.39            0.37           0.01
                                                    0.01            0.01           0.00

TOTALS                                          20555.56        19444.44           0.00
WAGER                    FRONT                    BET              CASH            NON NEG
                         MONEY

DOZEN                    20000                    20000.00         12972.97        6486.49
COLUMNS                                            6486.49          4207.45        2103.73
                                                   2103.73          1364.58         682.29
                                                    682.29           442.57         221.28
                                                    221.28           143.53          71.77
                                                     71.77            46.55          23.28
                                                     23.28            15.10           7.55
                                                      7.55             4.90           2.45
                                                      2.45             1.59           0.79
                                                      0.79             0.52           0.26
                                                      0.26             0.17           0.08
                                                      0.08             0.05           0.03
                                                      0.03             0.02           0.01
                                                      0.01             0.01           0.00

TOTALS                                            29600.00         19200.00            0.00


From this it can be stated that the relationship between cage turnover and actual turnover varies in direct
proportion to the odds payable and the expected return to the player in non negotiable chips.

Previously it was noted that the relationship for Roulette on even chance play only was:

        theoretical turnover =   {front monies + (18/19 x front monies)}

        where front monies equal cage turnover in this case.

The relationship for dozen and column play on Roulette could be shown as:

        theoretical turnover = {front monies + (12/25 x front monies)}

        where front monies equal cage turnover in this case.

The relationship for straight up play on Roulette could be shown as:

        theoretical turnover = {front monies + 1/36 x front monies)}

        where front monies equals cage turnover in this case.

From this information it is possible to carry out commission comparisons for Roulette for the various
wager types.
COMMISSION COMPARISON ROULETTE (100% PLAY ON STRAIGHT UPS)

FRONT           ACT.   COMM                CAGE TURNS     COMM VARIANCE
MONEY           T/OVER CASH               T/OVER NON NEG NON NEG.
                        CHIP.               NEG

20000            360000          1800       350270         17.51              4103          2303
30000            480000          2700       467027         15.57              5570          2870
40000            600000          3600       583784         14.59              7038          3438
50000            700000          4500       681081         13.62              8311          3811
60000            840000          5400       817297         13.62              9973          4573
70000            910000          6300       885405         12.65             10954          4654
80000           1040000          7200      1011892         12.65             12519          5319
90000           1170000          8100      1138378         12.65             14084          5984
100000          1200000          9000      1167568         11.68             14676          5676


COMMISSION COMPARISON ROULETTE (100% PLAY ON DOZENS AND COLUMNS)

FRONT           ACT.   COMM                CAGE TURNS                  COMM          VARIANCE
MONEY           T/OVER CASH               T/OVER NON NEG               NON
                        CHIP.                                           NEG.

20000            360000          1800       243243         12.16            3032            1232
30000            480000          2700       324324         10.81            4143            1443
40000            600000          3600       405405         10.14            5254            1654
50000            700000          4500       472973          9.46            6230            1730
60000            840000          5400       567568          9.46            7476            2076
70000            910000          6300       614865          8.78            8249            1949
80000           1040000          7200       702703          8.78            9427            2227
90000           1170000          8100       790541          8.78           10605            2505
100000          1200000          9000       810811          8.11           11108            2108

From this it can be seen that, on the commission basis as it stands presently, it is more cost effective to
rate play on a cash chip basis for Roulette rather than use the non negotiable chip system. This is not to
say that the commission structure is not profitable on Roulette, as the greater house edge on Roulette as
compared to Baccarat compensates for the extra commission payments. The comparison of the
theoretical win after commission for Baccarat and Roulette where the Roulette play is straight ups only
and the Baccarat play is an equal proportion of “Player” and “Banker” bets is shown below:

THEORETICAL WIN COMPARISON AFTER COMMISSION FOR BACCARAT AND
ROULETTE, NON NEGOTIABLE SYSTEM

FRONT           ACT              CAGE T/OVER                  CAGE T/OVER
MONEY           T/OVER               BA                         AR

20000            360000                   180000            350270
30000            480000                   240000            467027
40000            600000                   300000            583784
50000            700000                   350000            681081
60000            840000                   420000            817297
70000            910000                   450000            885405
80000           1040000                   520000           1011892
90000           1170000                   585000           1138378
10000           1200000                   600000           1167568
THEORETICAL WIN COMPARISON AFTER COMMISSION FOR BACCARAT AND
ROULETTE, NON NEGOTIABLE SYSTEM CONT.

THEO WIN LESS                 THEO WIN LESS                          VARIANCE
 COMM AR                    COMM BA

         5617                            2136                               3481
         7390                            2748                               4642
         9162                            3360                               5802
        10589                            3820                               6769
        12707                            4584                               8123
        13616                            4816                               8800
        15561                            5504                              10057
        17506                            6192                              11314
        17724                            6120                              11604

THEORETICAL WIN COMPARISONS AFTER COMMISSION FOR ROULETTE, STRAIGHT
UP PLAY ONLY (NON NEG AND CASH CHIP SYSTEM)

FRONT            ACT             CAGE THEO WIN                 THEO WIN            VARIANCE
MONEY           T/OVER           T/OVER LESS COMM              LESS COMM
                                           NN                     CC

20000            360000           350270           5617            7920            2303
30000            480000           467027           7390           10260            2870
40000            600000           583784           9162           12600            3438
50000            700000           681081          10589           14400            3811
60000            840000           817297          12707           17280            4573
70000            910000           885405          13616           18270            4654
80000           1040000          1011892          15561           20880            5319
90000           1170000          1138378          17506           23490            5984
10000           1200000          1167568          17724           23400            5676

Therefore the non negotiable chip system is best suited to even chance play, however it is still functional
on games such as Roulette due to the high house edge.

Point 5:

Rating cash play on games where payout odds exceed even money is more cost effective than using the
non negotiable system to calculate commission.
Point 6:

The non negotiable commission calculation can be valid for all Casino games, but is most effective
when considering the game of Baccarat when front monies is greater than $100,000, the turns thought
the cage is greater than 6, and there is equal play on “player” and “bank” or a greater percentage of
play on “bank”.

Point 7:

Rating non negotiable play using raters whilst calculating the commission using the non negotiable
commission system is a pointless exercise unless that information is used for other important statistical
analysis.

Point 8:

The general theorem for calculating theoretical turnover given only cage turnover is: theoretical
turnover equals the cage turnover plus the theoretical return to the player in non negotiable chips
divided by the theoretical loss of non negotiable chips multiplied by the cage turnover.

Or

theoretical turnover = {Cage turnover x (theoretical return to player in non negotiables/theoretical loss
to the player of non negotiables x cage turnover)}

Where the theoretical percentage loss to the player of non negotiables = 100 – the theoretical percentage
return to the player in non negotiables.

The theoretical turnover will equal the cage turnover when the return to the player in non negotiables
equals zero. Thus if a player were to wager an amount of non negotiables on one hand and this wager
were to lose then that amount would be recorded as turnover on the cage turnover schedule. Conversely
if the wager were to win then the cage turnover would equal zero as no loss of non negotiables has
occurred. From this it can be seen that where a junket group loses a greater percentage of wagers than
the expected or theoretical percentage, then the commission payable will also exceed the expected.
Also the reverse is true where a junket group‟s win exceeds the expected then the commission will be
less than expected. Where the expected commission in both cases is based on actual turnover and not
cage turnover.

If winning non negotiable chip wagers were converted to cash chips when paying a winning non
negotiable wager, then this would provide an exact measure of turnover. This is cage turnover would
equal actual turnover as the return to the player in non negotiables would equal zero in all cases. This is
considered impractical in Casino operations due to game protection as well as the speed of the games
being reduced.

Point 9:

Cage turnover will equal theoretical turnover when the return to the player in non negotiables equals
zero.
2.5.10          Revenue Calculations

When setting up a non negotiable program and commission structure it is imperative to calculate the
relationship between theoretical turnover and cage turnover and to perform revenue calculations from
this data.

Example:

BACCARAT: (EQUAL PLAY ON “PLAYER” AND “BANK”)

EDGE                                    = 1.26%

THEORETICAL TURNOVER = 2 X CAGE TURNOVER

CASINO TAX                      = 20% WIN

THEORETICAL WIN                 = EDGE X TURNOVER

THEORETICAL WIN                 = 1.26% X (2 X CAGE TURNOVER)

THEORETICAL WIN                 = 2.52% X CAGE TURNOVER

THEORETICAL WIN (after tax)             = 2.52% X CAGE TURNOVER – 20% (WIN)

WIN AFTER TAX                           = 2.016% X CAGE TURNOVER

WIN AFTER TAX                           = 2.016% PER TURN


REVENUE CALCULATION COMPARISONS ( 1 – 10 TURNS) FOR VARIOUS GAMES
AFTER TAX AND COMMISSION

GAME            WAGER           EDGE      THEO TURN             EDGE PER        EDGE TAX
                                 %        CAGE TURN             TURN            PER TURN

BACCARAT        PLAYER          1.36            1.9732          2.6836          2.1468
                  BANKER        1.17            2.0276          2.3723          1.8978
                 50/50 PB       1.26            2.0000          2.5200          2.0160
BLACKJACK                       1.30            1.9743          2.5666          2.0533
ROULETTE         EVEN           2.70            1.9470          5.2569          4.2055
                 CHANCE
                 SRT UPS   2.70                 1.0280          2.7756          2.2205
                 DOZ & COL 2.70                 1.4800          3.9960          3.1968


CASINO NET % OF FRONT MONEY AFTER TAX AND COMMISSION BUT PRE
EXPENSES FOR VARIOUS CAGE TURNS
TURNS BACC     BACC                 BACC        AR       AR EVEN        AR    DOZ & COL
      “PLAYER” “BANK”               BJ50/50              CHANCE         STRA-
                                      PB                                IGHT


1        0.6468         0.3978      0.5160      0.5533      2.7055      0.7205     1.6968
2        1.2937         0.7957      1.0320      1.1065      5.4110      1.4410      3.3936
3        1.9405         1.1935      1.5480      1.6598      8.1166      2.1614      5.0904
4        1.5874         0.5913     1.0640       1.2131      9.8221      1.8819      5.7872
5        2.7324         1.4892      2.0800      2.2664    13.0276       3.1024      7.9840
6        3.8810         2.3870      3.0960      3.3196     16.2331      4.3229    10.1808
7        5.0279         3.2848      4.1120      4.3729    19.4386       5.5434    12.3776
8        6.1747         4.1827      5.1280      5.4262    22.6442       6.7638    14.5744
9        7.3216         5.0805      6.1440      6.4794    25.8497       7.9843    16.7712
10       8.4684         5.9783      7.1600      7.5327    29.0552       9.2048    18.9680

Given this information, which is independent of front monies, it is necessary to calculate average
individual expenses as a percentage of front monies. This will then provide information as to what
levels of cage turns and front monies are required to ensure the profitability of the program. The
“average” expenses are based on actual figures over the period 12 month period for the total junket
program, and includes equal allocation of expenses for the Singapore office attributable to junkets.
Average expenses have been considered the same in all cases for this analysis so as to assess program
viability if groups were to solely bring in these levels of front monies. Also this is possibly a more
appropriate method for analysing the non negotiable chip system as turnover requirements are not based
on individual front money amounts.

AVERAGE EXPENSES                 STAFF COSTS                    =       1421
                                 OVERSEAS OFFICE                =       618
                                 ACCOMMODATION                  =       552
                                 FOOD & BEVERAGE                =       336
                                 TRAVEL/AIRFARE                 =       183

                                 TOTAL                          =       3110


FRONT                   AVERAGE                 PERCENT
MONEY                   EXPENSES

20000                   3110                    15.55
30000                   3110                    10.37
40000                   3110                    7.78
50000                   3110                    6.22
60000                   3110                    5.18
70000                   3110                    4.44
80000                   3110                    3.89
90000                   3110                    3.46
100000                  3110                    3.11
200000                  3110                    1.56

NET CASINO PERCENTAGES FOR THE NON NEGOTIABLE JUNKET PROGRAMME FOR
VARIOUS LEVELS OF FRONT MONIES ON A PER ROOM BASIS

FRONT       TURNS NET CAS % NET CAS  NET CAS       NET CAS
MONEY              50/50 PB      %       %       %
                              “PLAYER” “BANKER” BLACKJACK
20000      1    -15.04       -14.90      -15.15    -15.00
           2    -14.25       -14.26      -14.76    -14.44
           3    -14.00       -13.61      -14.36    -13.89
           4    -14.49       -13.96      -14.96    -14.34
           5    -13.47       -12.82      -14.06    -13.28
           6    -12.46       -11.67      -13.16    -12.23
           7    -11.44       -10.52      -12.27    -11.18
           8    -10.42        - 9.38     -11.37    -10.13
           9    - 9.41        - 8.23     -10.47    - 9.07
           10   - 8.39        - 7.08     - 9.57    - 8.02


FRONT    TURNS NET CAS %   NET CAS NET CAS   NET CAS
MONEY           50/50 PB       %       %        %
                           “PLAYER” “BANKER” BLACKJACK

50000      1    -5.70        -5.57       -5.82     -5.67
           2    -5.19        -4.93       -5.42     -5.11
           3    -4.67        -4.28       -5.03     -4.59
           4    -5.16        -4.63       -5.63     -5.01
           5    -4.14        -3.49       -4.73     -3.95
           6    -3.12        -2.34       -3.83     -2.90
           7    -2.11        -1.19       -2.94     -1.85
           8    -1.09        -0.05       -2.04     -0.79
           9    -0.08         1.10       -1.14      0.26
           10    0.94         2.25       -0.24      1.31


FRONT    TURNS NET CAS % NET CAS NET CAS     NET CAS
MONEY           50/50 PB    %        %          %
                         “PLAYER” “BANKER”   BLACKJACK

100000     1    -2.59        -2.46       -2.71     -2.56
           2    -2.08        -1.82       -2.31     -2.00
           3    -1.56        -1.17       -1.92     -1.45
           4    -2.05        -1.52       -2.52     -1.90
           5    -1.03        -0.38       -1.62     -0.84
           6    -0.01         0.77       -0.72       0.21
           7     1.00         1.92        0.17       1.26
           8     2.02          3.06       1.17      2.32
           9     3.03          4.21       1.97       3.37
           10    4.05          5.36       2.87       4.42
FRONT       TURNS NET CAS % NET CAS NET CAS                           NET CAS
MONEY              50/50 PB    %        %                                 %
                            “PLAYER” “BANKER”                         BLACKJACK

100000          1       -1.04               -0.91                -1.16            -1.00
                2       -0.52               -0.26                -0.76            -0.45
                3       -0.01                0.39                -0.36             0.10
                4       -0.49                0.03                -0.96            -0.34
                5        0.52                1.18                -0.07             0.71
                6        1.54                2.33                 0.83             1.76
                7        2.56                3.47                 1.73             2.82
                8        3.57                4.62                 2.63             3.87
                9        4.59                5.77                 3.53             4.92
                10       5.60                6.91                 4.42             5.98

The breakdown of the percentage of the total market of junket players with various levels of front
monies is as follows:

25K – 50K = 20%                                  50K – 75K = 40%
75K – 100K = 30%                                 100K+ = 10%

From this data it can be seen that with the current levels of tax, commission and expenses on the non
negotiable program, the profitability of the program is reduced where front monies are less than
$100,000 and the turns through the cage are less than 6.

This also shows that to maintain the profitability of the program, the level of non fixed expenses must
be continually monitored and reviews. This is to say that house edge, Government tax and the operators
commission percentages are fixed and that expenses vary according to inflation etc. Hence periodic
review of expenses will provide an indication as to whether the entry level requirements of the program
need to be adjusted or the program altered in such a way as to limit or reduce Casino expenses. When
increasing entry level requirements for the total program, consideration must be given to the actual
percentage of players who fall into the various categories and whether by increasing the required level
of front monies these players would be lost.

Point 10:

Expenses as a percentage of front monies on a per person/room basis need to be continually reviewed to
maintain program profitability.

Point 11:

Entry level requirements to the program require adjustment on the basis of Casino net profitability.
Such requirements should not deter the total market, but should target the desired market. Alternative
should then be provided for the market segment which no longer meets the previous requirements, for
example the cash chip system should then be promoted in this case as commission payments are based
on front monies.
Point 12:

Non essential expenses to the program should be limited and maximum efficiency promoted as long as
this does not decrease the level of service provided.

Point 13:

Staff costs severely limit the profitability of the junket program especially at the lower levels of front
monies.


2.5.11           Conclusion

The non negotiable program is one which is best suited to high levels of front monies and Casino games
where the percentage return to the player in non negotiables equals 50% or greater, that game being of
course Baccarat. For Casino games where this is not true, or the front monies per person do not exceed
$100,000, then the cash chip system is a much more viable concern.

When setting up a non negotiable program it is essential that the revenue calculations for the system are
computed correctly and that the Casino net percentages are fully understood. The relationship between
cage turnover and theoretical turnover for the program requires understanding for the various Casino
games offered on the program.

The percentage of expenses to front monies is an essential tool in monitoring the entry requirements to
the program, minimum front monies and turn requirements.

Expenses must be kept under control on any junket program but especially the non negotiable program
if entry levels are not set correctly.

There is obviously a case for using only the non negotiable system, this being when the junket group
wishes to play only Baccarat and their front monies is greater than or equal to $100,000 per person and
the Casino operating procedures do not require their play of non negotiable chips to be rated by an
additional staff member.

Therefore the non negotiable chip system is an interesting system which is generally misunderstood by
Casino operators and thus applied incorrectly. It is a system which MAY have a place in a junket
program if, and only if, the correct criteria are set or the junket operator and player will only accept this
system and not the cash chip program which is generally more functional at all levels of front monies
and on all Casino games.

2.6              Premium Player 0.5% (Splinter Policy)
The following is an extract from the Adelaide Casino Internal Junket Manual:

This program is offered to players with bankrolls of $100,000 or higher who wish to come in by
themselves or no longer wish to be associated with a junket operator.

The program can be used with cash chips or non negotiable chips. The cash chip system offers 0.5%
commission on turnover, the non negotiable offer 1%.

The non negotiable was introduced as the Casino felt there was a need for this in the market. The
majority of players who come in on this program seem to find the cash chip system the easiest to deal
with, as the system basically works on 6%. A player with a bankroll of $100,000 needs to turn this over
12 times, $1,200,000.
For example, $1,200,000 x 0.5% = $6,000 or 6% of $100,000 or 0.5% x 12 x $100,000 = (0.5% x
12) x $100,000.

With non negotiable chips the money will represent $600,000 through the cage. This figure can appear
misleading to an operator as it would indicate less money needs to be turned over, as has been explained
in the “Non negotiable chips” section. This is, in fact, not the case.

For this type of play the Casino will pick up all room, food and beverage costs. All other expenses such
as travel expenses will be met by the player.

As with the other chip system, where the player can play will depend on what program the player
chooses.

Under certain circumstances, the Casino may accept a player with a bankroll of less than $100,000,
however, this would only occur with players who have proven to us their play warrants such
considerations. It would not happen with a player visiting the Casino for the first time whose level of
play is unknown”.

2.6.1           Commission Agents Program

It is with pleasure that we forward to you documentation outlining the various incentive programs
currently available at the Adelaide Casino.

Ms. Loh Pek Lim, Adelaide Casino Marketing Coordinator – Asia, is available at our office to answer
any enquiries and assist with Visa applications.

In order to ensure that we retain our fine reputation, we also have V.I.P. Hosts in Adelaide whose sole
duties are to service the needs of our V.I.P. clients.

Adelaide

        Mr. Andrew MacDonald
        Senior Executive Casino Operations
        Tel: 61-8-218-41781, Fax: 61-8-212-4047

        Ms. Christine Giam
        VIP Services Secretary
        Tel: 61-8-218-4254

Singapore

        Ms. Loh Pek Lim
        Marketing Coordinator
        Tel: 65-838-5310, Fax: 65-737-9084

For further enquiries please do not hesitate to contact the numbers listed.

1.      Prior to any person becoming a Commission Agent of the Adelaide Casino, approval and
        licensing by the Liquor Licensing Commissioner of South Australia must be obtained by the
        applicant.

2.      The player to the introduced to the Adelaide Casino will have to be an „unknown‟ and never
        visited the Casino before.

3.      However, if a player is introduced to the Casino by a Commission Agent, this player can make
        further visits to the Casino and the Commission Agent can continue to earn a commission on
      subsequent visits within a period of 1 year of the first visit when these visits are organised
      by the Commission Agent.

4.    Prior to any visit under this scheme taking place the VIP Services Department (which includes
      the Singapore office) must have the list of players submitted for screening and approval.

5.    Each player must have a minimum deposit of $5,000. This will be deposited with the Casino
      Cage at the commencement of each visit. If a player wishes to add to his front money during
      his visit this will be allowed.

6.    Cash and bank drafts are acceptable, however, if a draft is to be used, a copy must be forwarded
      by facsimile 48 hours before arrival, to enable our Finance Department to approve clearance.

7.    We also have bank accounts in Hong Kong, Singapore and Adelaide which can be used for
      deposits. If overseas deposits are made the bank will issue a receipt which should be faxed 48
      hours before arrival to our Finance Department.

8.    All players‟ names are to be faxed 48 hours before arrival to the Operations Executive Player
      Development and VIP Services.

9.    Commission may be withheld if bank drafts and bank deposits have not been cleared through
      our bank account.

10.   The following bankrolls and levels of play are required to receive the listed complimentaries
      and rebates.

      Front Money      Complimentaries
                       (example for 20 turns)

      $5,000           2 nights Accommodation Deluxe Room, Hyatt Regency Adelaide
                       In house food and beverage
                       Airport transfers

      $10,000          2 nights Accommodation Deluxe Room, Hyatt Regency Adelaide
                       Food & Beverage (to the value $250)
                       Airport transfers
                       Airfare Reimbursement (to the value $200)

      $20,000          2 nights Accommodation Deluxe Room, Hyatt Regency Adelaide
                       Food & Beverage (to the value $250)
                       Airport transfers
                       Airfare Reimbursement (to the value $1000)

      $30,000          2 nights Accommodation Deluxe Room, Hyatt Regency Adelaide
                       Food & Beverage (to the value $250)
                       Airport transfers
                       Airfare Reimbursement (to the value $1800)

      $40,000          2 nights Accommodation Deluxe Room, Hyatt Regency Adelaide
                       Food & Beverage (to the value $250)
                       Airport transfers
                       Airfare Reimbursement (to the value $2600)

      $50,000          2 nights Accommodation Deluxe Room, Hyatt Regency Adelaide
                       Food & Beverage (to the value $250)
                       Airport transfers
                       Airfare Reimbursement (to the value $3400)
      Should a player not reach the required turnover level then all complimentaries and
      rebates will be reduced proportionately. Complimentaries accrue at a rate of 0.4%
      of turnover.

11.   Commission is payable to the agents on turnover at a rate of 0.2%.

12.   Example of agents commissions are:-


      FRONT             TURNS                  TURNS NON             AGENT
      MONEY           CHIP (TABLE)            NEGOTIABLE CHIP          COMMISSION
                                              (through the Cashiers Cage)

       5,000                  20                       10                       $200
      10,000                  20                       10                       $400
      20,000                  20                       10                       $800
      30,000                  20                       10                      $1200
      40,000                  20                       10                      $1600
      50,000                  20                       10                      $2000


      Non-negotiable chips can only be played on the games of Baccarat, Mini-Baccarat and
      Blackjack in the International Room and other such areas as designated.

      The games of Craps and poker will not attract turnover ratings. All play will be tracked and
      monitored to give the Casino the required information on qualification. Each player will be
      provided with a rating card which must be shown at the start of play on every new table to
      ensure that the player is credit with the correct levels of turnover.
13.     Commission will be payable to the Commission Agent by cash disbursement if the Agent is
        present or by cheque or telegraphic transfer to the Agent. This will be carried out at the end of
        each visit and is conditionally subject to clearance of any bank drafts/deposits.

14.     If the Commission Agent is not present at settlement, commission will be calculated on the
        figures of turnover as recorded by the Adelaide Casino. Such calculations will be considered
        correct and final.

2.6.2           Banking Details

Accounts are provided at the following locations for your convenience.

SINGAPORE               Aitco Pty. Ltd.
                        (Trading as Adelaide Casino)

                        Singapore Dollar Account Number: 141-278036-001

                        Malaysian Ringgit Account Number: 260-350079-186

                        Hong Kong & Shanghai Banking Corp.
                        01-01 Ocean Building
                        10 Collyer Quay
                        Singapore 0104

HONG KONG Aitco Pty. Ltd.
                  (Trading as Adelaide Casino)

                        Hong Kong Dollar Account Number: 567-343827-001

                        Hong Kong & Shanghai Banking Corp.

                        1 Queens Road
                        Central
                        Hong Kong

ADELAIDE                Aitco Pty. Ltd.
                        (Trading as Adelaide Casino)

                        Australian Dollar Account Number: 931-556-640

                        State Bank of South Australia
                        97 King William Street
                        ADELAIDE 5000

2.7             Player Loss
                (How to Deal with Actual Loss in the Casino Industry)

By Andrew MacDonald, Senior Executive Casino Operations

Paper prepared for the Ninth International Conference on Gambling and Risk Taking
Submitted to Jennifer Crawford, Assistant Conference Coordinator, Institute for the Study of
Gambling and Commercial Gaming, University of Nevada, Reno, NV 89557-0016.

Most complimentary and junket programs utilise either theoretical win or turnover upon which to
calculate player complimentaries or rebates. In some cases, particularly in the United States, junket
programs rebate a percentage of loss to the junket organiser or player.

Dealing with actual loss, however, is a difficult and often misunderstood issue. A common premise is
that “so and so is a born loser” or “the money‟s in the bank” or “they do it in Vegas (or at
Caesars/Hilton etc)” and therefore giving a percentage of loss back to the player is all right.

The problem is that the percentage rebated is often plucked from the air and has no mathematical basis.
This then leads to the fact that often no one knows what the theoretical or long term cost of such a
policy is to the Casino company.

In most business organisations understanding cost implications are a central premise to operating
effectively. Casino Operations should be no different particularly in an area where the rebate is a totally
hard cost.

Therefore, what is the cost of rebating a percentage of loss to a player or junket organiser?

Firstly, it is important to recognise that the theoretical loss by a player is a combination of all winning
and losing events experienced by a player in a game for a given number of results. Because most
Casino games are fundamentally biased against the player, that result is a negative from the player‟s
perspective. Simply, that result may be calculated by multiplying the house advantage by the number of
decisions and the average bet. Rebating a percentage of theoretical loss takes into account therefore
both winning and losing situations and provides a long term validity to the policy of rebating a
percentage of theoretical loss.

Thus, when theoretical loss is dealt with factors such as average bet, time played, decisions per hour and
house advantage are incorporated. However, when actual loss is being dealt with most policies only
deal with the amount of the loss. It is critical that other factors such as the number of decisions are
incorporated, as criteria are essential to ensure that the policy is valid. This is because it is erroneous to
believe that the percentage of actual loss rebated provides the same percentage of theoretical loss. In
fact, if a policy rebates a fixed percentage of loss which is something greater than the house advantage,
then the theoretical cost to the company will range from approximately the rebate percentage divided by
twice the house advantage and would minimise at the rebate percentage. If the rebate on loss percentage
were 10% and the house advantage 1.25%, then the theoretical cost of the rebate will range from
roughly 400% of theoretical win at maximum, in an even chance game, and minimise at 10%.

The maximum cost would be realised if only one hand were played and then the player settled and were
paid the rebate, with the minimum theoretical cost occurring if the player didn‟t settle until they had
played a very large number of hands. Many would argue that no one would play only one hand and
then settle or that of course no rebate would be paid
under such a scenario. The real problem is that without play criteria it is the customer who may be
in control of the net outcome. Much like the transition from paying complimentaries as a percentage of
drop or credit line to basing these on calculations of theoretical casino win, so to must rebate on loss
policies change to mathematically sound business decisions.

When rebating on loss, what must be calculated is the conditional mean of all situations where the
player loses. In all cases because we are dealing with biased games that value will exceed or equal the
mean of all possible events, both winning and losing, which we refer to as the player‟s theoretical loss.

If a rebate on loss policy is to be sound, it is a percentage of the latter which should be utilised to
calculate an equivalent rebate on loss percentage for a given number of decisions. That can be
accomplished by determining the percentage of theoretical loss relative to the conditional mean of only
player losses.

In a simple one hand example on an even money game, if normally the Casino were prepared to pay
back 50% of theoretical loss then for each $1 wagered the player would receive 50% of the house
advantage multiplied by the number of decisions. If the edge were 1.2% then 0.6% of $1 would be paid
back to the player regardless of whether they won or lost. If it were only the player who lost to be
rewarded then that player could be provided nearly twice as much, as the net position would be
compensated by the winning player receiving nothing. Why slightly less than double? Because the
player would lose 50.6% of the time and thus paying 1.186% of actual loss if settlement occurred after a
single hand would be the equivalent of paying 50% of theoretical loss for the example cited.

As the number of hands increases so to does the percentage of actual loss which may be rebated until
such time as the number of hands played is so large that in virtually every instance the player loses and
thus the rebate percentage on actual loss may equal the percentage of theoretical loss. This is due to the
fact that in such a case the theoretical loss (mean) and the conditional mean are one and the same. If
50% of theoretical loss were the general policy to be returned, then the maximum rebate on actual loss
would also be 50%.

How large a value for the number of hands would this take?

In an even chance game with a 1.2% house advantage the following could be calculated.

One standard deviation = square root (N)

Where N is the number of hands

99.7% of all results fall within three standard deviations of the mean.

Therefore, 99.85% of all results would fall to the right of minus three standard deviations.
If we were to solve for when 0 were –3 standard deviations from the mean we find

3  (N) = mean

mean = N x edge

3  (N) = 1.2% N

  3            N
---  =       --------
1.2%            (N)

Therefore N = (3/1.2%)²

N = 62,500

Thus, if a player were to play approximately 62,500 hands and then settle it would be appropriate to pay
50% of whatever that player‟s actual loss were at the time.

We now know that for one hand it is appropriate to rebate 1.186% of actual player loss, whereas at
62,500 hands, 50% of actual loss may be repaid with both scenarios maintaining a 50% equivalency
relative to theoretical loss in an even money game.

To determine points in between these extremes of number of hands, it is necessary to determine the
conditional mean for each number of hands. To crudely demonstrate the process of integration the
following is provided:-

Number of hands N = 100

Edge = 1.2%

Even money game

The mean                  = 1.2% x 100
                          = 1.2

1 standard deviation      = square root (N)
                          = square root (100)
                          = 10

From basic statistics we know that 34.13% of results occur between the mean and one standard
deviation.

13.64% of results occur between one and two standard deviations and

2.23% of results are greater than two standard deviations

From this we may roughly calculate the conditional mean for all player losses.

To do this we take the probability range and multiply this by the mid point result.
34.13% x {(1.2 + (1.2 + 10))/2}

13.64% x {((1.2 + 10) + (1.2 + (2 x 10)))/2}

2.23% x {((1.2 + (2 x 10)) + (1.2 + (3 x 10)))/2}

and sum these which provides the conditional mean greater than the mean and then add the probability
of results between 0 and the mean multiplied by that midpoint.

Without referring to normal distribution tables this may be approximated by taking the mean divided by
the standard deviation and multiplying this by 34.13%, then multiplying that result by the midpoint of
zero and the mean.

= 1.2 / 10 x 34.13% x 1.2/2

Thus the conditional mean         = 2.116
                                         + 2.210
                                         + 0.584
                                         + 0.025
                                         = 4.935
This compares to the standard mean (theoretical loss) of 1.2 and thus if a 50% rebate on theoretical loss
were desired the rebate on actual loss based upon the above would be:

Rebate on actual loss % = 50% x 1.2 / 4.935
                        = 12.16%

As stated this is a very crude example provided for demonstration purposes only.

To more accurately calculate the percentage to be rebated, it is merely necessary to utilise smaller
sections when integrating and refer to normal distribution tables for the probabilities, or to utilise a
lesser known statistical function referred to as the “UNLLI” or Unit Normal Linear Loss Integral. This
is basically analogous to the sum of all possible values of a standard normal variables positive distances
above the number “a”, multiplied by their corresponding probabilities of occurrence.

To put this into practice the following steps may be followed:

1.      Find expected loss for the player.
2.      Find standard deviation of player result.
3.      Calculate z = expected loss/standard deviation.
4.      Look up UNLLI table corresponding to z (see table below).
5.      Multiply UNLLI value by standard deviation.
6.      Add number calculated from point 5 to number calculated from point 1.
7.      Take whatever percentage of point 1 is to be returned and divide by the result of point 6.
Example:-
Hands = 750, Edge = 1.25%

Payouts = even money

Theoretical loss equivalency = 50%

1.     750 x 1.25% = 9.375
2.     square root (N) 750 = 27.386
3.     9.375 /27.386 = 0.342
4.     UNLLI = 0.2508
5.     27.386 x 0.2508 = 6.868
6.     9.375 + 6.868 = 16.243
7.     9.375 x 50% / 16.243 = 28.859%

UNIT NORMAL LINEAR LOSS INTEGRAL

Z              .00              .02     .04     .06     .08

0.00           .3989            .3890   .3793   .3697   .3602
0.10           .3509            .3418   .3329   .3240   .3154
0.20           .3069            .2986   .2904   .2824   .2745
0.30           .2668            .2592   .2518   .2445   .2374
0.40           .2304            .2236   .2170   .2104   .2040
0.50           .1978            .1917   .1857   .1799   .1742
0.60           .1687            .1633   .1580   .1528   .1478
0.70           .1429            .1381   .1335   .1289   .1245
0.80           .1202            .1160   .1120   .1080   .1042
0.90           .1004            .0968   .0933   .0899   .0866
1.00           .0833            .0802   .0772   .0742   .0714
1.10           .0686            .0660   .0634   .0609   .0585
1.20           .0561            .0539   .0517   .0496   .0475
1.30           .0456            .0437   .0418   .0401   .0383
1.40           .0367            .0351   .0336   .0321   .0307
1.50           .0293            .0280   .0268   .0256   .0244
1.60           .0233            .0222   .0212   .0202   .0192
1.70           .0183            .0174   .0166   .0158   .0150
1.80           .0143            .0136   .0129   .0122   .0116
1.90           .0110            .0104   .0099   .0094   .0089
2.00           .0084            .0080   .0075   .0071   .0067
2.10           .0063            .0060   .0056   .0053   .0050
2.20           .0047            .0044   .0042   .0039   .0037
2.30           .0036            .0034   .0032   .0030   .0028
2.40           .0027            .0026   .0024   .0023   .0022
2.50           .0021            .0018   .0017   .0016   .0016
For the game of Baccarat it is then possible to calculate the following table:-

BACCARAT (PLAYER/BANK 50% EQUIVALENT)

HANDS        % REBATE ON                          HANDS            % REBATE ON
             ACTUAL LOSS                                           ACTUAL LOSS
____________________________             _______________________________

10               4.78%                    1300                     34.06%
50               9.96%                    1400                     34.79%
100             13.52%                    1500                     35.48%
200             17.96%                    1600                     35.96%
300             21.01%                    1700                     36.58%
400             23.47%                    1800                     37.01%
500             25.39%                    1900                     37.57%
600             27.06%                    2000                     37.95%
700             28.37%                    2500                     39.89%
800             29.54%                    3000                     41.34%
900             30.78%                    3500                     42.44%
1000            31.75%                    4000                     43.48%
1100            32.63%                    4500                     44.18%
1200            33.29%                    5000                     44.88%

The above table is interesting in that it depicts the percentages of loss which can be paid for various
numbers of hands to maintain a 50% rebate on theoretical loss equivalence. From this it can be seen
that quite attractive rebates may be paid. A central question which arises, however, is what is the best or
simplest manner by which to calculate the number of hands. While a simple method may be to take
time played and employ standard decision rates, that is inappropriate due to potentially widely divergent
bet levels.

This is important because when dealing with actual loss some bets may be statistically insignificant. To
demonstrate using extremes, if we had 1000 hands with bets of $1000 and one hand with a bet of
$1,000,000 clearly the player‟s final result will be primarily determined by whether they win or lose the
$1,000,000 hand. It can be said therefore that the 1000 hands are insignificant. Thus a reasonable
method of calculating the number of hands played for the purposes of determining a rebate on loss is to
divide the total turnover by the player‟s maximum bet. This criteria may be particularly useful when the
Casino permits a table differential to be employed which potentially allows an unlimited maximum bet
to be placed.

Determining the maximum bet placed is generally a simple proposition if dealing with an individual
player. In a junket group situation where members of the same group may for example bet against each
other on Baccarat, the bet could be considered to be the difference between the opposing bets, even
though the turnover is the sum of the opposing bets.

For other non-even pay off games such as Roulette, the mathematics remains similar, however, because
the player wins more when they do win but this occurs less often, the percentage of actual loss which
may be rebated is relatively less.
To incorporate this factor into the previously shown formula requires the calculation of the variance for
a specific game for one result. In an even money game such as Baccarat (when playing Bank or Player)
the variance may be approximated as one and therefore the previously shown formula was valid.

In any game the calculation of variance is accomplished by summing the square of the player wins
multiplied by the probability of the returns. The standard deviation then becomes the square root of the
number of hands multiplied by the average squared result.

In a game with multiple betting options at the same game with varying payoffs but the same house
advantage (eg Roulette) the variance figure utilised when calculating a rebate on loss would necessarily
be the maximum figure.

The appropriate numbers for various games are:-

Baccarat                 =       1 (exact figures 1.00 player, 0.95 bank)

Blackjack                =       1.26

Roulette                 =       34.1 (single number bets on single zero Roulette)

In games with multiple betting options at varying payoffs and house edges it would be appropriate to
fully calculate the rebate payable on every option and utilise the variance from the result which returns
the least to the player as otherwise any requirements on data collection by staff may be prohibitive.

When performing this calculation the following formula may be used:-

1.      Calculate the variance for one play.
2.      Find expected loss for the player.
3.      Find standard deviation of player result = √ (hands multiplied by variance (refer point 1))
4.      Calculate z = expected loss / standard deviation.
5.      Look up UNLLI table corresponding to z.
6.      Multiply UNLLI value by standard deviation.
7.      Add number calculated from point 5 to number calculated from point 2.
8.      Take whatever percentage of point 2 is to be returned and divide by the result of point 7.

This then produces the following example of a table of rebate percentages applicable to be paid for the
game of Roulette (when playing single numbers on a single zero game) and which maintains a 50%
equivalence on theoretical loss.
ROULETTE (SINGLE NUMBER PLAY ON SINGLE ZERO ROULETTE)

HANDS        % REBATE ON                          HANDS              % REBATE ON
             ACTUAL LOSS                                             ACTUAL LOSS
____________________________                      _____________________________

10               1.79%                            1300                     17.00%
50               3.93%                            1400                     17.57%
100              5.44%                            1500                     17.97%
200              7.52%                            1600                     18.50%
300              9.10%                            1700                     19.01%
400             10.33%                            1800                     19.35%
500             11.39%                            1900                     19.83%
600             12.33%                            2000                     20.14%
700             13.19%                            2500                     22.00%
800             13.98%                            3000                     23.48%
900             14.58%                            3500                     24.79%
1000            15.27%                            4000                     25.98%
1100            15.93%                            4500                     27.07%
1200            16.55%                            5000                     27.91%

What use is all this information?

Many would argue that this is all too complicated to be of practical application in the Casino industry.

Firstly, it provides a mechanism by which any existing rebate on loss policy can be analysed to assess
the long term or theoretical cost to the business.

Secondly, in the high level junket segment it provides a means by which variable percentage rebates on
loss can be structured which can be both attractive and may be combined with rebates on turnover or the
provision of other complimentaries. Being criteria based any policies so developed would possess a
long term validity.

Thirdly, it provides a challenge to incorporate a rebate on loss element into the standard calculation of
premium player complimentaries. One of the basic limitations of a theoretical loss based
complimentary system is that while fine in theory the players often complain that no consideration is
given should they incur a substantial loss. To any player, funds are a limiting factor which if depleted
will limit the turnover they can provide which may also mean that what would normally be comped, to
add insult to injury they may have to pay for. Some complimentary policies address this in a superficial
way but again these are not criteria based.

To say that incorporating the above formula into a player rating system would not be practical because it
could not be calculated or would not be understood by the player, is incorrect. Most player rating
systems in large Casinos are computerised which would certainly enable any calculation to be
undertaken.

Secondly, players already take most things on trust in terms of what complimentaries are provided. For
example, the decision rates per hour, house edges, average bet levels and
percentage of theoretical loss returned are generally unknowns from the player‟s perspective.
Therefore if the objective is to find the most equitable system upon which to base complimentaries,
some aspect of player loss should be incorporated, and from a business perspective that should equate to
a standard theoretical cost.

Structuring a program of this nature could be achieved by adding a rebate on theoretical loss to a
percentage rebate on actual loss, providing either, depending upon which is the greater of the two, or
relying solely on one or the other. Of course as in any player rating system success relies heavily on
capturing good data initially. To do this it is imperative that the gaming staff performing this function
realise its importance.

Finally if referring to UNLLI tables etc. is still considered too complex then the following
approximation of a rebate on loss percent calculation may be of use:-

b = a.                  Y √ (V.N) x 100
                         ---------------------
                 0.5Y √ (V.N) + 0.17 Y² + 0.4 V.N

where a =        the percentage of theoretical loss equivalent
         b =     the percentage of actual loss
         Y =     theoretical loss to the player
         N =     the number of hands played (turnover/maximum bet)
         V =     the average squared result for one game


Acknowledgements:-
-        Bill Eadington, Judy Cornelius and the staff at U.N.R.
-        Peter Griffin: Professor of Mathematics C.S.U.
-        Jim Kilby: Professor of Gaming U.N.L.V.
[This page is intentionally left blank]
Chapter 3                Card Counting




“Card counting systems are simple,
efficient and effective
It is possible for the player utilising a card
counting system to achieve a net
positive expectation in the game of
Blackjack as it is played in the Adelaide
Casino”
Chapter 3    Card Counting

3.1.    Brief Overview ……………………………………………………………                      95

3.2.      Legalities (Precedents) ……………………………………………………
          96
       3.2.1      Nevada …………………………………………………………………….                96
       3.2.2      New Jersey ………………………………………………………………..
       97
       3.2.3      Australia …………………………………………………………………..
       97

3.3 Counter Measures …………………………………………………………                         97
    3.3.1    Comment ………………………………………………………………….
    98

3.4 Profit Analysis …………………………………………………………….                        99
    3.4.1      Blackjack Formula …………………………………………………………             99
    3.4.2      Sensitivity Analysis (% Profit) …………………………………………….   100
    3.4.3      Comment …………………………………………………………………..                  102
    3.4.4      Conclusion …………………………………………………………………                 102
    3.4.5      Bibliography ……………………………………………………………….               103

3.5 Blackjack Simulation Experiment December 1990 ………………………..
    104
    3.5.1     Aim ………………………………………………………………………..                     104
    3.5.2     Method …………………………………………………………………….                    104
    3.5.3     Simulation ………………………………………………………………….                 105
    3.5.4     Results ……………………………………………………………………..                  105
    3.5.5     Conclusion …………………………………………………………………                  106
3.1.            Brief Overview
Blackjack, unlike most other Casino games, is a game which involves varying degrees of skill
depending upon an individual player‟s competence. This is due in a large part to the fact that the
probabilities associated with the game vary whenever a card is removed from the shoe, and that players
may vary their play accordingly.

This really is a direct contrast to other Casino games which have a constant in-built house percentage.
For example, on Roulette where each spin is an independent event, it is of no concern to the player that,
for example, 15 blacks have been spun consecutively, the odds of black being spun again are still 18-19,
ie, fractionally less than even money. Therefore, there is no such thing as a good or bad Roulette player,
only lucky or unlucky players in the short term. In the long-term, if measured over a considerable
period of time, the player should lose 2.70% of his turnover on Roulette. The house percentage on most
Casino games is between 1 and 28%, with table games (excepting Blackjack) averaging around 4% and
Keno being around 26% on average.

With the use of good basic strategy at Blackjack, however, the house percentage fluctuates, rarely to a
large extent, between approximately +3 and –3 percent.

This, of course, means that if a player could determine when the house percentage was negative and
only place bets under those circumstances or greater sized bets, then over a long period of time that
player would win. The amount won would be determined by the extent of the player‟s advantage
related to the amount of turnover from that player.

This system of play has been developed and is called “card counting”. The development of card
counting was pioneered in America, utilising computers and software development for the simulation
and analysis of Blackjack play.

This determined that the house percentage was directly related to the relationship of high cards
(10,J,Q,K,A) to low cards (2,3,4,5,6) and that when this relationship showed an increase in the number
of high cards in the remaining decks then the house percentage decreased. Such a deck is said to be 10
rich and in favour of the player.

To determine whether a deck is ten rich or not various systems have been developed with varying
degrees of complexity and efficiency. A simple yet effective method is the Braun Plus Minus Count. In
this count system the cards 10, J, Q, K and Ace are assigned a value of –1 with the cards of low value
(2,3,4,5, and 6) being assigned a value of +1. The cards 7,8 and 9 are prescribed no value.

Now to put the system to use, as each card is withdrawn from the shoe a running count is maintained by
the player of the high cards to low cards. For example, 10, K, 5, J, 3 is a running count of –1.
Obviously this must be related to the number of cards remaining in the shoe, as, if there are a large
number of cards remaining this dissipates the effect or advantage to the player. Hence, the calculation
of a “true count” is required. This is done by dividing the running count by twice the number of decks
remaining in the shoe (depending on the system used). This true count provides the player the
advantage of knowing approximately the house percentage or his or her own advantage at any stage.

Knowing merely when to bet is not sufficient however, as this must be related to both a betting strategy
and a playing strategy.
Betting strategies are generally related to the true count with a base unit being played on a positive
count. This of course varies dependent on the player, with some card counters merely waiting for a high
positive true count and then placing as many wagers as they can at the table maximum. This method of
play brings attention to the player and many authorities on card counting prefer more subtle betting
strategies where the counter would never wager more than 3 times the base unit, or strategies which
enable a card counter to play and win without being detected by Casino management. Betting strategies
are important and some “counters” work in teams of two or more. One player keeps a true count on the
deck whilst another player is concerned with the betting and playing strategies.

The playing strategies, or basic strategy as it is known, is determined by analysing the results of
computer simulated Blackjack play over a large number of hands determining what actions provide the
player with the best results. The Blackjack program must simulate play as it would occur in the Casino,
operating within the confines of the game rules. Therefore, basic strategy within Australia varies from
State to State as the rules also vary from State to State. However, generally the tables shown in the
Appendix provide an outline of good basic play. This is, of course, by no means foolproof but again
relies on percentage plays. This basic strategy may also be varied in relation to the true count with some
plays being more advantageous when the true count is at a specific level.

For example, although insurance is generally regarded as a bad bet, having a high house percentage, if
the true count is excessively positive, insurance may be a good bet for the player.

Similarly other situations vary in accordance with the count. When to hit, stay, double down or split are
all important, and of course make the game more interesting to the player.

Therefore it can be seen that good Blackjack play is a combination of knowing when to bet, how much
to bet and the correct method or strategies of play.

To offset the advantages that a good card counter maintains over the house, Casino operators and
regulators have included counter measures into the Rules of the Game. The argument behind this policy
being that if card counters remain unfettered then the operator would lose money and subsequently
Blackjack, as a Casino game, would cease to exist. These counter measures include exclusion of card
counters from the Casino, shuffles being initiated by Casino supervisors when a known card counter
substantially increased a wager, cutting the deck up to two thirds of the way in from the back of the
pack and preclusion or restriction to minimum wagers if the player misses the first or any subsequent
round of play prior to the reshuffle of cards. Therefore, even though card counting can be by no means
described as cheating, it definitely poses problems to both the operator and regulator from a technical
aspect.

Another argument is that there are so few technically proficient card counters that they pose no threat to
the game, and that these few provide good publicity for the game.

This argument tends to suggest an aura of complexity on the subject which is not substantiated by the
simplicity of the systems themselves.
Most card counting systems are simple, efficient and effective being able to be mastered by anyone with
time and patience, and this is the real problem with card counting.

3.2.              Legalities (Precedents)
3.2.1             Nevada

“N.R.S. 465.15 “Cheat” means to alter the selection of criteria which determine:

a.      The result of a game or,
b.      The amount or frequency of payment in a game”

“N.R.S. 465.083 Cheating Prohibited. It is unlawful for any person, whether he is an owner or
employee of or a player in an establishment, to cheat at any gaming game”.

The Nevada Supreme Court held in 1983 in the case of Sheriff vs Martin declared that counting cards
was not cheating in violation of N.R.S. 015.

The court held:

“The attributes of the game – its established physical characteristics and basic rules – determine the
probability of the games various possible outcomes. Changing those attributes to affect those
probabilities is a criminal act. By way of contrast a card counter – one who uses a point system to keep
track of the cards that have been played – does not alter any of the basic characteristics of the game.
He merely uses his mental skills to take advantage of the same information that is available to all
players”.

3.2.2             New Jersey:

1.      “On May 11, 1981, the Appellate Division of the New Jersey State Supreme Court ruled that
        card counters may not be barred by the Casinos. This was the result of a suit brought by
        Kenneth Uston. Immediately after this ruling, however, the Casinos obtained a stay pending
        appeal to the State Supreme court. Thus far no final ruling has been made on this matter….”

        (Playing Blackjack in Atlantic City by C. R. Chambliss and TC Roginski C1981.)

2.      “Lawsuits

        My lawsuit against Resorts International went all the way to the New Jersey Supreme Court
        who decided in my favour …….”

        (The Gambling Times Guide to Blackjack – Chapter Eleven by Ken Uston c1983)

3.2.3             Australia:

No legal undertakings in this regard have been tested to date. However, each State Government
regulatory body has an individual broad policy on card counting and allowable counter measures which
are written into the rules of the game.
3.3             Counter Measures

To combat the effectiveness of card counting systems, Casino operators in this country and around the
world have implemented various counter measures. A brief outline of some of these is listed below:-

(NB the current counter measures employed by the Adelaide Casino are marked with an asterisk)

The listing of some of the other counter measures is not intended to imply support for their use.

*a.     Use of more than one deck. Multi deck games increase the starting advantage of the Casino,
        as well as substantially decreasing the fluctuations in percentage advantage experienced
        throughout the shoe. The Adelaide Casino utilises eight decks in the play of all Blackjack
        games.

*b.     Lesser deck penetration prior to reshuffling. As card counting systems rely on information
        relating to changing deck composition, lesser deck penetration reduces the degree of certainty in
        the short term. Conversion of a running count to a true count by the card counter is done by
        dividing the running count by twice the number of decks remaining (dependent on the system
        used). Therefore, the true count is inversely proportional to twice the number of decks
        remaining in this case. The true count is utilised by the card counter to make betting and
        playing decisions. As the divisor is increased (decks remaining) the result will obviously
        decrease. Also fluctuations in advantage are substantially flattened as deck penetration is
        reduced, as is the percentage advantage experienced reduced. The Adelaide Casino standard
        policy is that normally the cut card (shuffle marker) is placed one deck in from the end of the
        stack. If, however, a card counter is playing the cut card is placed up to four decks in from the
        end of the stack.

*c.     Restriction on bet size to the table minimum if a player enters a Blackjack game after the
        initial round or first two rounds of play have been dealt, or if a subsequent round of play is
        missed prior to reshuffling. This requirement obliges the card counter to play all hands of a
        shoe and not just wait till he/she has a positive expectation. This substantially decreases the
        counters percentage advantage as they then must play minimum bets for most of the shoe at
        negative expectation (see (d) for Adelaide Casino usage).

*d.     Restriction on the number of boxes playable by one player. This requirement reduces the
        betting potential of the card counter in positive situations to either one or two boxes at the table
        maximum.

        The Adelaide Casino provisions relating to (c) and (d) are:-

        1. A player who has not made a wager on either of the first two rounds of play in any shoe
           may enter the game on a subsequent round of play, but may be restricted by the Casino
           operator to wagering on a maximum of two boxes, to the minimum limit posted at the table
           on each box, until the cards are re-shuffled and a new shoe is commenced.
        2. A player who after placing a wager on either of the first two rounds of play, declines
           to place a wager on the third or any subsequent round of play may be restricted by the
           Casino operator to wagering on a maximum of two boxes, to the minimum limit posted at
           the table on each box, until the cards are reshuffled and a new shoe is commenced.

e.      Exclusion of the player from the premises. Barring techniques vary widely. In Atlantic City
        at one time the following statement was read to suspected card counters:-

        “You are considered to be a professional card counter. You are not allowed to gamble at a
        Blackjack table in this Casino. If you attempt to do so, you will be considered a disorderly
        person and be evicted from this Casino. If you subsequently return to the Casino, you will be
        subject to arrest for trespassing. You may participate in games other than Blackjack offered by
        the Casino.”

        This practice has been discontinued in Atlantic City after Mr. K. Uston‟s litigation. Nevadan
        Casinos have also excluded card counters from the premises as have most European Casinos at
        one stage or another. Australian Casino operators generally do not exclude card counters from
        the premises due to State Government regulation.

*f.     Restriction on the unit increase allowable by players at a Blackjack table. This stops the card
        counters from increasing his/her bet from the table minimum to the table maximum in one step.
        Some Casino operators prohibit a unit increase of more than three times the previous bet. This
        practice reduces the card counters potential advantage by decreasing the allowable amount to
        bet in situations where the player has a positive expectation. In Adelaide a recognised player
        may be restricted to a maximum bet of ten times the table minimum (per box).

g.      Reshuffling of the deck when a card counter substantially increases his/her bet. This obviously
        returns the deck to the Casino‟s starting advantage.

h.      Continuous automatic shuffling machines within the dealing shoe. These machines return the
        deck to standard after each round of play. However, they are bulky and the technology does not
        appear to have been developed sufficiently at this stage.

i.      Rule changes which make the game as a whole less attractive. This practice has the effect of
        increasing the Casino house percentage and thus changes the probability of situations with
        negative expectations.

j.      Preclusion from play at the game of Blackjack. This policy is structured on the basis that a
        betting transaction at a game is in essence a contract with there being no obligation on either
        party in entering into such a contract. That is just because the operator offers the game of
        Blackjack does not mean that the operator must accept bets from any player. Whilst this is true
        in contract law other questions are raised such as anti discrimination laws, civil liberties and the
        practice of free trade. The Jupiters Casino in Queensland currently follows this practice.

*k.     Second cutting card. This is employed to negate the productivity decrease which occurs if all
        Blackjack games operate with only one cutting card and substantially reduced deck penetration
        when card counters are present in the Casino.

3.3.1           Comment

Both positive and negative aspects apply to the counter measures listed and these will be addressed later
in the text. As can be seen Casinos view the potential threat of persons utilising card counting systems
very seriously. The erosion of bottom line profitability by these players can be substantial which then
places the viability of operating Blackjack games at risk.

The development of a universally acceptable counter measure is thus of paramount importance.
3.4               Profit Analysis

The profit potential of any Blackjack game may be determined by a simple formula, which may be
referred to as the “Blackjack Formula”.

The formula is:

        % profit = BA + PA + RA + SA

        BA = Betting Advantage

        PA = Playing Advantage

        RA = Rule Advantage

        SA = Starting Advantage


The starting advantage is the advantage off the top of the deck. This is also what the long run
expectation would be playing basic strategy, employing no count for either betting or playing purposes.
There are two factors to take into consideration in determining the starting advantage, the number of
decks in play, and the rule variations of the game.

The playing advantage is the percentage of profit which may be realised by altering play from basic
strategy. The variables taken into account in computing the playing advantage are, the number of decks
in play, the percentage of the cards being dealt out, and the playing efficiency of the system being used.

The betting advantage is dependent on the following four variables:-

1.      The number of decks in play

2.      The percentage being dealt out

3.      The betting spread used and

4.      The betting correlation of the system being used.
The betting spread is the ratio of the lowest bet to the highest bet. The betting correlation of a
system is the efficiency of that system in determining advantage for betting purposes.

Rule advantage considers the effect of different rule variations. Variables considered are, percent
dealt, number of units of high bet, number of decks and sum of effects of rule variations.

The % profit is therefore dependant on a large number of variables. Shown below is a calculation of the
% profit for one counting system given set circumstances:-

3.4.1            Blackjack formula

TOTAL NUMBER OF DECKS 8                                    DECK ADV                  -0.54

DECKS DEALT OUT                   4                        RULE ADV                  -0.064

COUNT SYSTEM USED                           WONG HALVES             PLAY EFF                  0.57

MAX UNIT IN SPREAD                          10                      BET CORR                  0.99

STARTING ADVANTAGE                          -0.6040

PLAYING ADVANTAGE                           0.0566

BETTING ADVANTAGE                           1.0821

RULE ADVANTAGE                    -0.0113

% PROFIT                                    0.5233

A sensitivity analysis of the same system showing % profit with various deck penetration levels and
maximum units is as follows:-

3.4.2            Sensitivity Analysis (% Profit)

WONG HALVES
MAX UNITS                                   DECKS DEALT OUT
                         3                  4              5                6                 7

2                        0.45               -0.37          -0.28            -0.17             0.03
3                        0.33               -0.24          -0.11             0.04             0.22
4                        0.22               -0.11           0.03             0.20             0.40
6                        0.02                0.11           0.27             0.47             0.70
8                        0.18                0.32           0.49             0.70             0.95
10                       0.38                0.52           0.70             0.92             1.18
12                       0.58                0.73           0.91             1.13             1.39
14                       0.78                0.93           1.11             1.34             1.60
16                       0.98                1.13           1.31             1.54             1.81
18                       1.18                1.32           1.51             1.74             2.01
20                       1.38                1.52           1.71             1.94             2.21
When reviewing this table it is advisable to be conservative in approximating the value of the maximum
unit, this is particularly true in multi-deck games. Due to the diminishing frequency with which
progressively higher “true” counts occur, player advantage will be more accurately approximated by
valuing the maximu8m unit as the most frequent high unit in relation to the average unit.

The table shown is particularly interesting from the point of view of the effect of deck penetration.
Where less decks are dealt out a card counter must increase his/her unit spread to achieve the same
percentage profit. In doing so the counter is at greater risk of succumbing to the effects of statistical
variance and thus may incur severe losses. If the player does not have enough funds available to sustain
such losses then obviously that player no longer poses a threat to the Casino. To be unable to withstand
a negative fluctuation of three standard deviations would be neither investing or speculating, but
gambling. Standard deviation must always be calculated according to the specific circumstances of
average betting unit and number of hands. Displayed below is a calculation of percent gain per hand for
an eight deck Blackjack game with Adelaide Casino Rules and a 50% penetration level. Also shown is
the expected win and standard deviation given the level of betting shown.


EDGE      HANDS         BET/ TOTAL            TOTAL       HANDS          BETS            BETS
           /100         HAND BET               GAIN       PLAYED         SQRD           SQRD x
                                                                                         NO OF
                                                                                         BETS

 -4.65%      0.0         0         0           0.00           0
 -4.15%      0.0         0         0           0.00           0
 -3.65%      0.0         0         0           0.00           0               0              0
 -3.15%      0.0         0         0           0.0            0               0              0
 -2.65%      0.5        25        12.5        -0.33           0.5            62            312.5
 -2.15%      1.5        25        37.          0.81           1.5           625            937.5
 -1.65%      6.0        25       150          -2.48           6             625           3750
 -1.15%     13.0        25       325          -3.74          13             625           8125
 -0.65%     55.5        25      1387.5        -9.02          55.5           625          34687.5
 -0.15%     13.0        25       325          -0.49       13625            8125
  0.35%      6.0       500      3000          10.50           6          250000       1500000
  0.85%      3.0      1000      3000          25.50           1         2250000       2250000
  1.35%      1.0      1500      1500          20.25           1         2250000       2250000
  1.85%      0.5      2000      1000          18.50           0.5       4000000       2000000
  2.35%      0.0         0         0           0.00           0               0             0
  2.85%      0.0         0         0           0.00           0               0             0
  3.35%      0.0         0         0           0.00           0               0             0
  3.85%      0.0         0         0           0.000          0               0
  4.35%      0.0         0         0           0.00           0               0             0
  4.85%      0.0         0         0           0.00           0               0             0
  5.35%      0.0         0         0           0.00           0               0             0
                             TOTALS        10737.5           57.894         100.C     8805937.50
HANDS PLAYED                                        100
AVERAGE BET/HAND                                    $107.38
UNIT BET EQUALS                                     $1
GAIN/HAND                                           $ 0.5789
% GAIN PER HAND                                     0.539%
STD DEV/HAND                                        326.423
STD DEV/960 HANDS                                   1 =       $10,114
                                                    2 =       $20,228
                                                    3 =       $30,342
                                                    4 =       $40,455
EXPECTED WIN 960 HANDS                              $556
WIN PER HOUR                                        $69.47
HANDS NOT PLAYED                                    0
TOTAL HANDS                                         960
BASED UPON 120 hands dealt/hour (2 boxes/player)
TOTAL PLAYING TIME 8 hours



STAND DEV          % OCCUR          RANGE           RANGE
                                    FROM            TO

        1              68.00%        ($9,558)       $10,670
        2              95.00%       ($19,672)       $20,783
        3              99.70%       ($29,786)       $30,897
        4              99.999%      ($39,900)       $41,011

Whilst the win per hour and percent gain per hand appear favourable, the potential losses that may be
incurred short term are severe. Any card counter playing under these conditions and using this betting
pattern must be able to sustain a $30,000 loss in one session otherwise they are in fact gambling. Most
genuine authorities on card counting do not recommend playing in any eight deck game let alone one
which is cut to the 50% level. However, if this is the only game available and the player has a large
bankroll then it is still possible for the player in the long term to achieve a reasonable profit. Also, if the
card counter can play in a reasonable percentage of games with greater levels of penetration, then a
much greater potential gain is achievable (refer sensitivity analysis).

3.4.3            Comment

It is possible for a player utilising a card counting system to achieve a net positive expectation in the
game of Blackjack as it is played in the Adelaide Casino. To quantify the potential gain it is necessary
to establish the values of specific variables. The most important of which are deck penetration, unit
spread and standard deviation. Games with high levels of deck penetration offer the card counter the
greatest potential gain and at the same time reduce the bankroll requirement for these players.

3.4.4            Conclusions

Card counting systems are simple, efficient and effective. They may be mastered by anyone with time
and patience and provide the competent user with substantial profits under the right conditions.
This trend is substantiated throughout the world in Casinos where card counters may play unfettered. In
Tasmania for example the, Wrest Point Casino has had a growing problem with these players since
approximately 1980. In that time the number of known or recognised card counters has increased to
some 30 players whose winnings total not in the thousands or even hundreds of thousands but in the
millions of dollars.

The counter measures available to any Casino are controlled to varying degrees by the Government
regulatory body which controls that Casino. Even though these players are obviously also effecting
Government revenue by reducing gross revenues, in some jurisdictions this factor is outweighed by the
objective of the regulatory body in remaining an arbitrary, unbiased statutory entity. Where this is the
case card counters may still play in the Casino but certain restrictions may be placed upon them.

Whilst these counter measures reduce the card counters potential profit they by no means negate the
advantage, also the counter measures that must then be used can themselves reduce profitability. For
example, when deck penetration is reduced the dealer must then shuffle more often, thus reducing the
turnover achieved by other players. This can have a substantial effect if all tables in a Casino or even in
a pit are cut to the 50% level if card counters are playing in the Casino. In an eight deck game this
increases shuffling time by approximately six minutes per table per operational hour. The magnitude of
this increase in non productive time is enormous when viewed in the context of the total number of
tables and the operational hours in a week or a year.

Obviously the ultimate countermeasure for the Casino operator is indeed the “ultimate” strategy or
system which is available to any potential player in a Casino of a negative expectation game, namely not
to play it. Whilst there is no obligation on any person to play any game in a Casino (which are all
negative expectation games for the unskilled player) why then must an obligation be placed upon the
Casino operator to accept all bets from all players? Whilst some authorities claim that this concept
infringes upon civil liberties, anti discrimination laws and the right of free trade the Queensland Casino
Control Division has a refreshing point of view on the subject. This control body maintains the
following philosophy:

The Government approved Casino legislation on the basis that Casinos would generate millions of
dollars in revenue both directly and indirectly. The games of chance which were approved for play
were approved on the assumption that they were positive expectation games from the Casino view point
and that the individual house percentages were authorised by the Control Division. Therefore, where a
player or players may jeopardise the revenue generated by “changing” the expectation of a game the
Casino operator need not be obliged to accept wagers at the game from these particular players. In fact
the Casinos themselves are not defined as public places and special right of entry by the Police had to be
written into the Casino Control Act.
Thus the Queensland Casinos after identifying card counters follow the policy of allowing them to play
any other game but Blackjack. At this stage no person who has been restricted in this manner has taken
legal action. Crown law advice has suggested that any legal undertakings would be unsuccessful on the
basis of contract law.

In Tasmania where the Gaming Commission considers itself to be more objective, the Casinos have
gone through what may be described as a war with the card counters. Restrictive measures have come
and gone with varying degrees of success. The Gaming Commission has authorised various rule
changes and procedures which may be applied to counters. The problem is recognised by the
commission in that without the counter measures the Casino operator may not be able to continue to
offer the game of Blackjack to the general public.

Perhaps another solution will eventually be the development of a continuous random shuffling device.

Until such time as this occurs the search for an equitable solution which satisfies Casino operators,
regulatory bodies and the law will continue.

3.4.5             Bibliography

The Blackjack Formula                                     Arnold Snyder
Beat The 8 Deck Game                                      Arnold Snyder
Million Dollar Blackjack                                  Ken Uston
Playing Blackjack in Atlantic City                        Chambliss and Roginski
Beat the Dealer                                           E.O. Thorp
The Theory of Blackjack                                   P Griffin
Blackbelt in Blackjack                                    A Snyder
How to Play Winning Blackjack                             J Braun
Professional Blackjack:                                   S Wong
Playing Blackjack as a Business                           L Revere
A Book on Casino Blackjack                                C Ionescu Tulcea
Blackjack                                                 Stanley Roberts
The Casino Gamblers Guide                                 Alan N Wilson
Break the Dealer                                          Patterson and Olsen
Turning the Tables on Las Vegas                           I Anderson
Blackjack: Is there any more to be said?                  E O Tuck
Siromath report:
The Development and Analysis of Winning
Strategies for the Casino game of Blackjack               J Braun
3.5            Blackjack Simulation Experiment
               December 1990
3.5.1          Aim

To quantify by computer simulation the house edge at the game of Blackjack played under Adelaide
Casino rules, where all players utilise basic strategy. To compare this result with a house edge
calculated using Arnold Snyder‟s “Blackjack Formula”.

3.5.2          Method

John H. Imming‟s Blackjack software, “Universal Blackjack Engine Version 4.0” (U.B.E.) was
configured to the following settings:-

A.      RULES

        1.     Cards dealt face down                  (Y/N)           set to N
        2.     Dealer shows burn card                 (Y/N)           set to N
        3.     Real World pick up                     (Y/N)           set to Y
        4.     Pickup type 2                          (Y/N)           set to Y
        5.     Dealer hits on soft 17                 (Y/N)           set to N
        6.     Surrender allowed                      (Y/N)           set to N
        7.     Early surrender                        (Y/N)           set to N
        8.     Macao surrender                        (Y/N)           set to N
        9.     Insurance allowed                      (Y/N)           set to Y
        10.    Dealer blackjack takes all             (Y/N)           set to Y
        11.    No hole card game                      (Y/N)           set to Y
        12.    Dealer peek on aces only               (Y/N)           set to N
        13.    No dealer peek                         (Y/N)           set to Y
        14.    Split any 2 tens                       (Y/N)           set to Y
        15.    D.D.N. on any number of cards          (Y/N)           set to N
        16.    Over/under                             (Y/N)           set to N
        17.    Double exposure                        (Y/N)           set to N
        18.    Double down after split                (Y/N)           set to Y
        19.    Only 1 split allowed                   (Y/N)           set to N
        20.    Cards for split as played              (Y/N)           set to Y
        21.    Aces split exactly as others           (Y/N)           set to N
        22.    One card for split aces                (Y/N)           set to N
        23.      Re-split for Aces                          (Y/N)               set to N
        24.      Blackjack pays 1 1/2 times                 (Y/N)               set to Y
        25.      Blackjack pays 60% bonus                   (Y/N)               set to N
        26.      Blackjack pays double                      (Y/N)               set to N
        27.      Dealer takes all ties                      (Y/N)               set to N
        28.      Dealer takes tie 17                        (Y/N)               set to N
        29.      Player wins on 5 cards                     (Y/N)               set to N
        30.      Player wins on 6 cards                     (Y/N)               set to N
        31.      Player wins on 7 cards                     (Y/N)               set to N
        32.      D.D.N. on hard 10 + 11 only                (Y/N)               set to N
        33.      D.D.N. on hard 9, 10, 11 only              (Y/N)               set toY
        34.      Insure blackjacks only                     (Y/N)               set to N
        35.      Abort all special cases                    (Y/N)               set to Y
        36.      Abort streak betting                       (Y/N)               set to Y
        37.      Penetration by round                       (Y/N)               set to N
        38.      Number of players                                              set to 7
        39.      Number of decks                                                set to 8
        40.      Penetration to ? cards (re-deal)                               set to 52
        41.      Penetration to ? rounds
        42.      Delay time (100th sec)                                         set to 1
        43.      Table limit max.                                               set to 2000
        44.      Table limit min.                                               set to 2


B.      Betting Strategy
Betting strategy was defined as flat betting for all players at a fixed unit.

C.      Playing Strategy

The basic strategy as shows in the appendix was entered.

This strategy was confirmed by three difference sources for these rules:

1.      E.O. Tuck – “Blackjack – is there anything more to be said?”

2.      C. Ionescu Tulcea – “A Book on Casino Blackjack”.

3.      Jady Davis – “Blackjack for profit”.

3.5.3            Simulation

The simulation was then allowed to run from approximately 17.30 hours on Friday, December 7th, to
09.30 hours Monday December 10th. In that time 71,543,288 rounds of Blackjack were played.
3.5.4           Results

RESULTS OF BLACKJACK SIMULATION CONDUCTED FROM 7.12.90 – 10.12.90

UTILISING R.W.C.U.B.E. v 4.0

The following results were obtained from a computer simulation of the game of Blackjack:-

NB       It had been noted prior to the experiment that player 1 was malfunctioning by negative betting
at high negative indices. All other player results may be considered valid.

                ROUNDS                    BET            WIN/LOSS                 WIN/LOSS%

Player 1   71 543 288              150 514 484            -962 174                -0.64%
Player 2   71 543 288              157 170 128            -966 129                -0.61%
Player 3   71 543 288              157 169 434            -964 045                -0.61%
Player 4   71 543 288              157 170 430            -936 456                -0.60%
Player 5   71 543 288              157 178 882            -924 008                -0.59%
Player 6   71 543 288              157 177 314            -964 353                -0.61%
Player 7   71 543 288              157 179 974            -945 521                -0.60%
HOUSE      71 543 288            1,093,560,646           6,662,686                 0.61%
LESS PLAYER 1                      943,046,162           5,700,512                 0.6045%

“Blackjack Formula” calculation:-

        Starting advantage = DA + V

        DA = Deck Advantage

        v = sum of the effect of the rule variations

        Deck advantage for an 8 deck game = -0.54%

        v = 0.064%

therefore starting advantage              = -0.54% + -0.064
                                          = -0.604%

Calculation of v:-

v = sum of – no soft double               = -0.091

                no hold card              = -0.113

                double after split        = +0.14

                                          = -0.064
In relation to Vegas Strip rules where, dealer stands on soft 17
double down on any two cards
no double after split
split any pair
re split any pair except aces
split aces receive only 1 card each
no surrender
dealer receives hole card

Deck advantage taken from Arnold Snyder‟s book “The Blackjack Formula” cross checked with Peter
Griffen‟s – “The Theory of Blackjack”.

Chambliss and Roginski‟s – “Playing Blackjack in Atlantic City”

Values used are for a 6 deck game rather than an 8 deck game, however, these should closely
approximate the correct values to within 0.05%. Thus, the house edge for the game of Blackjack using
Adelaide Casino rules, playing basic strategy was calculated empirically to be 0.604% +/- 0.05%.


3.5.5           Conclusion
Two entirely separate methods of calculation have provided a very similar result for the value of the
house edge at the game of Blackjack where all players use basic strategy.

The simulation method (Monte Carlo method), whilst laborious and subject to statistical variance, was
conducted for such a large number of trials as to negate this factor. In all nearly half a billion hands
were played providing a value for the house edge of 0.604%. This is the long term expectation at the
game of Blackjack given Adelaide Casino rules should all players play perfect basic strategy as per the
strategy table shown in the appendix. It would be anticipated however, that less than 10% of all players
at the Adelaide Casino would play perfect basic strategy. Studies conducted by Mr. Brian Feetham,
former Systems Analyst, concluded that the house edge for the average C.G.A. (common gaming area)
player was close to 2.0% due to the various misplays made by Blackjack players. The basic strategy
edge is therefore important only from the perspective of a minimum return given a no memory strategy.

For completeness let us also compare the value derived by computer simulation with professor E.O.
Tuck‟s value for a basic strategy house edge. Professor Tuck of the Adelaide University Applied
Mathematics Department in his 1986 NAG‟s paper, “Blackjack – is there anything more to be said?”,
calculates an edge of 0.785% for Adelaide Casino rules. Whilst this figure may at first appear to differ
substantially from the value derived by the experiment detailed, it is in fact very similar when Professor
Tuck‟s assumptions are examined. Firstly, Tuck‟s figure is the win/loss in relation to the amount
originally bet, not the total amount bet. This factor increases the edge calculation for the simulation
from 0.604% to 0.664%. Secondly, Professor Tuck utilised an infinite deck assumption as being
appropriate for an 8 deck game. This is arguably correct, however, according to Griffin in his book
“The Theory of Blackjack”, the deck advantage for an infinite deck is 0.65% as opposed to the 0.54%
deck advantage for a 6 or 8 deck game.


Taking this into account would reduce Tuck‟s edge calculation to approximately 0.675%. As can be
seen when compared on an equivalent basis Tuck‟s 0.675% edge and the simulated edge of 0.664% are
indeed very close showing a variance of only 0.011%.
[This page is intentionally left blank]
Chapter 4             Key Concepts




“…. including …..
the Extremely Silly Subject of Money
Management”
Chapter 4 Key Concepts

4.1    Sub Optimisation ………………………………………………………..                           111

4.2    Hold Percentage ………………………………………………………….                                   111

4.3    Law Of Averages ………………………………………………………….                            112
       4.3.1 The Law of Large Numbers ………………………………………                     113

4.4    Money Management ………………………………………………………                             114

4.5    Psychology of Gamblers ………………………………………………….                               115

4.6    Mathematical Expectation ………………………………………………..                             115

4.7    Standard Deviation (Repeated Trials) …………………………………….               117

4.8    Optimal Betting (Money Management In a Positive Expectation Game) … 117

4.9    House Advantage …………………………………………………………..                           118

4.10   Throwing out Ties (Absolute Versus Relative Probability) ……………….   119

4.11   Blackjack Win Percentage …………………………………………………                       120

4.12   Blackjack Formula …………………………………………………………                           121

4.13   Various Numbers of Decks (Blackjack) …………………………………..               123

4.14   Baiting the Hook …………………………………………………………..                          123

4.15   Baccarat and Chemin De Fer ………………………………………………                      124

4.16 Why People Gamble ……………………………………………………….                             125
    4.16.1 Gamblers Profile …………………………………………………                                  125
    4.16.2 Why ………………………………………………………………                                   125
    4.16.3 Other …………………………………………………………….                                 126

4.17   Customers Expectations Of Staff …………………………………………..                 126
4.1              Sub Optimisation
One of the serious organisational problems that has developed in the Casino business in the last few
years has been a growing sub optimisation of the overall hotel Casino performance. There have been
many reasons advanced for this situation. One of the most significant is that the importance of overall
profit performance has become a widely recognised ideal within various training programs as well as
traditional educational institutions over the past five to ten years. The result of this “profit focus” is that
new managers, usually trained in traditional areas of hotel management such as food and beverage
operations, tend to focus on the profitability of their individual departments and fail to recognise the
complex interplay between the service or support functions of the hotel and the primary revenue
generating function of the Casino.

The use of complex departmental profit and loss statements may have accelerated this process by
improperly focusing the attention on the bottom line of the departmental unit rather than the overall
hotel Casino operation. Thus the unfortunate situation arises where decisions are made to maximise the
departmental profit – or perhaps contribution – while the overall quality of Casino customers is slipping,
Casino revenues are decreasing or costs are being increased in the Casino area.

The problem of sub optimisation cannot be avoided simply by the use of one form of financial statement
or another, but the use of some types of financial statements that create the illusion of “bottom line
responsibility” may have contributed to some undesirable trends in hotel Casino management”

“Casino Accounting and Financial Management”

4.2              Hold Percentage
Mathematicians frequently confuse, and are confused by, Casino personnel in discussions of win rate
(or %) for a game like Roulette. The mathematician describes the house advantage as 5.26% for a
colour bet in Roulette because for every 38 units wagered the house expected to win a net of 20-18 = 2
units since there are 20 ways for it to win and only 18 ways for the player 2/38 = .0526 = 5.26% is then
the expected gain per bet made and is the “mathematical percentage”.

Casino bosses have, however, evolved a different method of describing the performance of, for instance,
a Roulette table. They might say that “The PC in Roulette is 20%” or “The Roulette table holds 20%”.
This figure is an empirical one necessitated by the type of book-keeping Casinos use to monitor
performance and appears greatly at variance with the mathematicians‟ 5%. Who‟s correct?

Well, a better question is “How is the 20% hold figure in Roulette arrived at?”. To illustrate the Casino
point of view we‟ll start with the simplest possible example: one Roulette table and only one gambler.
Suppose the player buys in for $100 worth of chips and plays for exactly one hour. He may
occasionally be ahead or possibly be wiped out within that hour, but lets imagine he terminates his play
(either of his own desire or because the Casino closes the table) with $80 worth of chips which he takes
to the cashier to be redeemed in money. The pit boss analyses the tables performance by comparing the
$100 drop in the cash box with the 80 missing chips in the money tray. The difference,
100-80 = 20, is the amount that this table “held” and the quotient of „hold” divided by “drop” or
20/100 = 20%, is the Casino‟s hold percentage.

It‟s important to realise that hold percentage is an empirical, even to some extent sociological, figure. It
varies from day to day, year to year, and especially it varies with the characteristics of the players. The
problem is greatly complicated when there are different ways to play a game such as Craps which have
difference mathematical percentages and when players, as they frequently do, carry chips from table to
table or game to game.

A couple of oversimplified examples may help to illustrate this dependence. First, suppose our
previously described solitary gambler has enormous endurance and is determined to play forever or until
he loses his entire $100 buy in. Since Roulette is an unfavourable game this latter eventuality is the
assured result. However long it takes, when our indefatigable gambler has finally lost all his money and
the Casino closes the tables it will be discovered that all of the chips are still there and so too is the
hundred dollar bill in the drop box. Hence the Casino won 100% of the drop. A mathematician keeping
score would count the, perhaps, 1900 dollars bets the gambler made and report the Casino win rate as
100/1900 = 5.26%.

Now lets introduce another table and another gambler. Mr A buys in for $100 at a table #1, plays for a
while, and then walks away a net loser of $20. Mr B buys in at table #2 for just one dollar, wins a
dollar, a walks to the cashier a net winner. Now Mr A walks over to table #2 with the 80 chips He
bought at table #1. He plays for an hour and only loses two chips at table #2. How will the Casino hold
performance look for the two tables? As in the very first example, table #1 will show a 20/100 = 20%
win rate. But what about table #2? Mr B took away two chips, the one he bought and the one he won.
Mr A left two chips, the ones he lost. Hence the table has as many chips as it started with and concludes
it “held” all of the drop (Mr B‟s drop incidentally, and he was a winner), or 100%.

As insusceptible as win/drop is to precise mathematical prediction it does nevertheless remain a useful
method of description for Casinos. The empirical percentages derive a long term validity because of the
large flow of action. Perhaps one exception to this is the game of blackjack where education of the
players has probably reduced the Casino hold percentage over the years, although not the profits which
continue to grow because of increased volume.

“Gambling Ramblings: Extra Stuff” P Griffin

4.3              Law Of Averages
A general idea that many people hold goes something like this:

The longer a series of chance events goes on, the more likely it is that things will “even up”. For
example, the longer you drive a car, the more likely you are to have your share of flat tires. The more
children you have, the more likely you will have an equal division of boys and girls (assuming an even
number of children). The longer you flip a coin, the more likely the number of heads and tails will
equalise.

Actually, the latter two examples are identical, if certain simple assumptions are made. In the case of
the coin, we shall suppose that the coin is “fair‟, so that on any one flip, head and tail are equally likely.
In the case of the children, we shall rule out twins or other multiple births, and shall assume that the
parents do not have any tendency to produce
children of one sex as preferred to the other. Of course there is the practical consideration that one
can flip a coin a lot more times than a woman can bear a child. So, it is more natural to use the coin for
purposes of illustrating large samples. But for small samples, there is something unique about each
child, which makes the family a marvellous illustration for stressing certain points.

4.3.1            The Law of Large Numbers

I have never actually seen a statement of a law of averages as such in any book on probability or
statistics. However, I have seen references to a law of large numbers, which in rather loose language
could be expressed this way: the greater the number of trials, the smaller will be percentage fluctuations
away from the expected (or average) number of successes, but the larger will be the absolute
fluctuations. Note carefully that this deals with fluctuations about the expected number of successes,
and not with the expected number itself.

Let‟s see how this applies to our example of children in the family (or to the flipping of a coin). We
shall consider the various boy-girl combinations that can occur in successively larger families, starting
with two children, and ranging on up through 4, 6, 8, 10, 100, 10,000 and 1,000,000. In the last three
cases, we shall, of course, switch over mentally from children to coins. We shall find these examples
very instructive.

At each birth, there are two possibilities for the sex of the child, B (boy) or G (girl). In a two child
family, therefore, there are 2x2 = 4 possible orders in which the two children are born. There are
indicated in the following Table.

DISTRIBUTION OF BOY-GIRL BIRTHS IN TWO-CHILD FAMILY

                 BOTH BOYS                 EQUAL DIVISION                    BOTH GIRLS

                 B-B                       B-G/G-B                           G-G
Chance           1/4                       2/4                               1/4

As A % 25%                        50%                                25%

Now we move on to the four child family. There are 2x2x2x2 = 16 possible orders. (A more compact
way to represent this is 2-4 which means 2 to the power 4, or the produce of four 2s.) These 16
possibilities tabulate as in the following Table.

DISTRIBUTION OF B-G IN FOUR CHILD FAMILY

 4B                 3B and 1G           2B and 2G            1B and 3G           4G

B-B-B-B             B-B-B-G             B-B-G-G              B-G-G-G             G-G-G-G
                    B-B-G-B             B-G-B-G              G-B-G-G
                    B-G-B-G             B-G-G-B              G-G-B-G
                    G-B-B-B             G-B-B-G              G-G-G-B
                                        G-B-G-B
                                        G-G-B-B
1/16                4/16                6/16                 4/16                1/16
6 %              25%                 37               25%                 6 
Notice that in the four child family, there is less chance of an exactly equal boy-girl split than in the
two-child family. It is 37  percent versus 50 percent.

The next case is that of the six child family. There are 26 = 64 combinations. These are simple enough
to write down, but they are too numerous to spend the space on here. However, we can at least make a
tabulation of the relative numbers involved

THE SIX CHILD FAMILY

6B 0G         5B1G           4B2G          3B3G           2B4G          1B5G           0B6G

          6/64           15/64         20/64          15/64         6/64           1/64


We see that the chance of an exactly equal boy-girl split is again less than in the previous case. Hence
we have 20/64 or about 31 percent.

As we move on to larger families, the numbers tend to pyramid. The information for all cases up
through ten children is now summarised compactly in the following Table.


DISTRIBUTION IN TEN-CHILD FAMILY

 CHILDREN            DISTRIBUTION OF COMBINATIONS                              TOTAL
                                                                               COMBINATIONS

 2                   1-2-1                                                     4
 4                   1-4-6-4-1                                                 16
 6                   1-6-15-20-15-6-1                                          64
 8                   1-8-28-56-70-56-28-8-1                                    256
 10                  1-10-45-120-210-252-210-120-45-10-1                       1024


In each case, the center entry in the pyramid, divided by the corresponding number of total
combinations indicated in the right hand column, gives the chance of an exactly equal boy-girl split. In
the ten child family, this chance is 252/1024, or about 25 percent. As our sample gets bigger, it is quite
clear that the probability of an exactly even split gets progressively smaller.

Now lets get back to the law of averages, this notion that the more trials we have, the more likely it is
that things will “even up”. We have just convinced ourselves that the larger the sample, the less likely
is an exactly even split.

“The Casino Gamblers Guide” Allan N Wilson

4.4              Money Management
“The Extremely Silly Subject of Money Management”
I see it in print all the time. “What‟s that?” you ask. Its those silly words “money management”. I‟m
sure you have read it too. If you don‟t have good money management then you can‟t win and should
expect to go broke. Also, money management will allow you to beat all sorts of games like Roulette,
Craps, slot machines, and many pseudo authorities will tell you that this is the most important aspect of
gambling. The reader shall see that I don‟t exactly agree with this. In fact, nothing could be further
from the truth. Now I‟m not the first to say this, but, “I hate money management”. I hate it because it is
a bunch of junk.

The theme of money management seems to be constantly on the mind of the losers. Now here is an
absolute truth. If you are a loser, and you keep gambling, you will lose it all no matter how you handle
your money. Anyone who tells you otherwise is just plain wrong. If this was not absolutely correct,
there would not be so many large Casinos in Nevada, New Jersey, and throughout the world.

One well known gambling book, that I read, recommends in its large money management section to
only play those games where the house has no more than a small advantage. This author “smartly” rules
out games like Roulette and keno. But if you only play games like Craps and baccarat, and play them
long enough, you are assured of losing. So why play them at all?

One possible reason to play the low house percentage game is that these bets really don‟t cost very
much and you can maximise your time at the “very exciting gaming tables”. Is this really true? Well
suppose you compare baccarat to keno, where do you lose your money faster. At baccarat, the house
has an edge of just over 1 percent, while at keno it is approximately 30 percent. The problem is that you
can get more bets down at the baccarat table, in a specified period of time, than you can sitting in a keno
lounge. It seems to me that you might actually be better of playing keno, even though the house edge in
this game is “astronomical”.

“Gambling Theory and Other Topics” M Malmuth

“Throughout this whole chapter we have continually rephrased, reiterated, and re-emphasised a salient
point: When the odds are against you in each single play in a game, there is no system whatsoever by
which this game can consistently be beaten”

“The Casino Gamblers Guide” Allan N Wilson

4.5             Psychology of Gamblers
1.      Negative Recency – This refers to the belief people have that because an event has not happened
        for a while then it is more likely to happen now…..what people feel creates psychological
        pressure in them and people who may not have bet…..will do so.

2.      Utility – This means the attraction of winning a lot for a little…This attraction may incline you
        to put money into these forms of gambling rather than those that would have a better chance of
        return, albeit a smaller one, in other forms of betting.
3.      Skill – One of the marketing “skills” in promoting gambling games is to make the game
        seem more skilful than it actually is. Strickland in 1966 found that people bet less in a dice
        throwing and gambling situation if they had already thrown the dice, but, of course, did not
        know the result. They would bet more if they could bet before throwing the dice…..

        This “myth of skill” is tremendously important. …the average punter believes they are more
        skilful than they really are, and this can influence them to bet more than is wise. If your ego
        really gets caught up, it can be difficult to stop betting….

4.      Subjective and Objective Probability - ..As far back as 1948 Preston and Baretta noted that
        longer priced choices in a gambling situation were selected more often than they should be, with
        shorter priced choices being selected less often. A number of studies (Synder, Griffith) at the
        racetrack confirm this. In other words we assess the chances of a 10/1 chance as being better
        than they actually are. That 10/1 shot should really be 15/1 or 20/1. Conversely the 6/4 chance
        is psychologically disliked because of the short price, but it really should be 5/4 or shorter.

5.      Superstition - …many otherwise logical people can become quite influenced by their
        superstitions, and they can even cloud their judgement making them bet more than logic
        suggests is wise. And occasionally such bets come off – meaning the superstitions are
        REINFORCED and likely to remain with a vengeance.

6.      Risky Shift and Cautious Shift – Some studies have shown that when groups get together and
        make a choice in a gambling situation that the group is more cautious than the individual in their
        choice, and other studies have shown the groups to be less cautious. It seems likely that the size
        of the bet is the factor – when the group is betting much more than the individual members
        themselves would, they will be more cautious.

“The Guide to Good Gambling” Clive Allcock and Mark Dickerson

4.11            Blackjack Win Percentage
Let‟s suggest, that in our attempt to determine some H/A value for twenty one, we start with the
understanding that one hand will be dealt from a freshly shuffled deck (single) and that the player will
use the exact same strategy that the house uses. In this case, the player will “mimic” the house, hitting
all 16‟s and standing on all 17‟s, unable to split or double down.

What if the Player “mimics” the dealer?

* The Dealer will bust 28% of the time.

Mathematically, it can be determined that the dealer will bust out approximately 28% of the time. Of
course, if the player “mimics” the dealer he will also bust out 28% of the time. But the most important
fact regarding why the game of twenty-one wins for the house is:-

* The player will bust before the dealer 28% of 28% or about 8% of the time.
This is the reason why the Casino has an edge over the player because if the players busts out first, the
dealer‟s hand does not have any effect on the final outcome. Does this mean that the house has an 8%
H/A over the “mimic” player? We have to add one more ingredient:-

* The player gets a bonus for blackjacks

The blackjack bonus, which occurs approximately once every 21 hands, pays three units for ever two
units wagered, altering the H/A by about 2.5%. This lead us to our final result of 5.5%.

* A “mimic” player‟s house advantage is 5.5%.

But how many of you have seen someone who actually mimics the dealer? Not very many. So, this
leaves room for speculation that a “truer” house advantage in twenty one could be more or less than our
calculations.

The next question we must ask is, “can a player improve the “mimic” strategy and lessen the house
advantage?” Let‟s examine four different changes the player can make and note the gains made over
the “mimic” player.

What effect will the player have by changing his strategy?

Proper standing with a stiff vs stiff                              3.2% gain

(playing holding a total of 12-16 vs the upcard of 2-6)

Double Down properly                                               1.6% gain
Hitting soft hands properly                                        .3% gain
Splitting Proper combinations                                      .4% gain
                                                                   5.5% gain overall


By using a proper or BASIC STRATEGY, the player can gain 5.5% over the “mimic” strategy and
actually reduce the houses advantage to nothing. How can this be? These calculations indicate that the
correct house advantage in twenty-one is zero. If this is true, how have the Casinos been making money
on twenty-one all this time? First, not many players know the correct strategies for playing twenty-one.
Below is a list of approximate house advantages for the different styles of players:-

Blackjack players parameters – The worst and the best

Worst                     15% H/A
Mimic                     5.5% H/A
Average                   1.4% H/A
Basic strategy            Even (0% H/A)
The “worst” player is arrived at by Peter Griffin in his book, The Theory of Blackjack. Griffin states
that the “worlds worst player …” by violating a list of rules including always insuring, standing on all
stiffs against the dealer showing a high card, hitting on all stiffs against the dealer showing a small card,
never doubling down, splitting incorrectly and failing to hit any soft hand,” … seems unlikely that any
but the deliberately destructive could give the house more than a 15% edge”.

The “average” player has been determined by Griffin in his presentation at the 7th Gambling Conference
held in Reno, Nevada, August 1987. His paper, Mathematical Expectation for the Public‟s Play in
Casino Blackjack concluded that the average player‟s H/A is 1.41%.

“Card Counting For The Casino Executive” – Bill Zender

Griffin actually concluded the average players disadvantage as being 1.41% greater than the basic
strategy edge.

4.12             Blackjack Formula
BA + PA + RA + SA = % PROFIT

BA =    Betting Advantage
PA =    Playing Advantage
RA =    Rule Advantage
SA =    Starting Advantage

SA = DA + v

h = number of units of high bet
n = number of decks
c = percent dealt out
x = number of extra players
BC = betting correlation
PE = playing efficiency
v = sum of effects of rule variations
DA = deck advantage

STARTING ADVANTAGE BY NUMBER OF DECKS
DECKS                    DECK
                         ADVANTAGE


1                        +.02
2                        - .31
3                        - .43
4                        - .48
5                        - .52
6                        - .54
8                        - .58


EFFECT OF RULE VARIATIONS BY # OF DECKS


                                                           DECKS
VARIATION                                          1       2    3            4       5        6
(1) NO DBL ON 11                         -.820    -.775    -.760    -.753    -.748    -.745
(2) NO DBL ON 10                         -.510    -.480    -.470    -.465    -.462    -.460
(3) NO DBL ON 9                          -.130    -.103    -.094    -.090    -.087    -.085
(4) NO DBL 8,7,6                           .000     .000     .000     .000     .000     .000
(5) NO SOFT DBL                          -.130    -.107    -.099    -.095    -.092    -.091
(6) HITS SOFT 17                         -.190    -.205    -.210    -.213    -.214    -.215
(7) NO RESPLITTING NON – ACES            -.014    -.027    -.031    -.033    -.034    -.035
(8) NO SPLITTING ACES                    -.160    -.170    -.173    -.175    -.176    -.174
(9) NO SPLITTING NON – ACES              -.210    -.230    -.237    -.240    -.242    -.243
(10) NO HOLE CARD                        -.100    -.108    -.110    -.111    -.112    -.113
(11) DBL AFTER SPLITS                    +.140    +.140    +.140    +.140    +.140    +.140
(12) DBL ANY # CARDS                     +.240    +.232    +.230    +.229    +.228    +.227
(13) DBL ON 11 AFTER SPLIT               +.070    +.070    +.070    +.070    +.070    +.070
(14) DBL ON 14 AFTER SPLIT               +.050    +.050    +.050    +.050    +.050    +.050
(15) RE-SPLIT ACES                       +.030    +.055    +.063    +.067    +.070    +.072
(16) DRAW TO SPLIT ACES                  +.140    +.140    +.140    +.140    +.140    +.140
(17) SURRENDER                           +.024    +.054    +.065    +.070    +.073    +.075
(18) SURRENDER (HITS SOFT 17)            +.030    +.065    +.077    +.082    +.086    +.088
(19) EARLY SURENDR                       +.630    +.630    +.630    +.630    +.630    +.630
(20) EARLY SURENDR (HITS SOFT 17)        +.730    +.730    +.730    +.730    +.730    +.730
(21) 2 TO 1 BJ PAYOFF                    +2.320   +2.285   +2.273   +2.267   +2.264   +2.262



SYSTEM COMPARISONS

SYSTEM                  2      3    4    5        6        7        8        9    X      A

Wong‟s halves           +1.5   +1   +1   +1.5     +1       +1.5      0       -1.5 -1    -1
Revere Point Count      +1     +2   +2   +2       +2       +1        0         0  -2    -2
Dubner/Hi – Lo          +1     +1   +1   +1       +1        0        0         0  -1    -1
Ian Anderson            +1     +1   +1   +2       +1       +1        0        -1  -1    -2
Revere Advanced (‟73)   +2     +2   +3   +4       +2       +1        0        -2  -3     0
Uston Point Count       +1     +2   +2   +3       +2       +2       +1        -1  -3     0
Hi-Opt II               +1     +1   +2   +2       +1       +1        0         0  -2     0
Revere Advanced +/-     +1     +1   +1   +1       +1        0        0        -1  -1     0
Einstein/ Hi-Opt 1       0     +1   +1   +1       +1        0        0         0  -1     0
Canfield Expert          0     +1   +1   +1       +1       +1        0        -1  -1     0
Gordon                  +1     +1   +1   +1        0        0        0         0  -1     0
Ten Count               +1     +1   +1   +1       +1       +1       +1       +1 -2.5    +1



“The Blackjack Formula” Arnold Snyder
4.13            Various Numbers of Decks (Blackjack)
Of vastly greater importance than uncommon bonus hands are the effects which arise from using
various numbers of decks. As we have already stated, a single-deck game is significantly more
advantageous to the player than is a multiple-deck game which uses the same rules. But why is this so?
There are several reasons. Let us compare a single-deck game with the eight deck shoe game which
now prevails in Atlantic City. In a single deck game the likelihood of a player being dealt a blackjack
1/20.72. In an eight deck game it is 1/21.07. What is greatly increased in the latter case, however, is the
probability that both the dealer and the player will have blackjack in the same round. In the single deck
game this is 1/27.22, but in the eight deck game this is increased to 1/21.71. If you have blackjack and
the dealer doesn‟t, you are paid off at 1.5 times your original wager. But if the dealer also has
blackjack, it is a stand off and you win no money. Since blackjack pushes are 20% more likely in the
eight deck case than with single decks, it is clear that your earning potential will be reduced when
multiple decks are used.

Another significant adverse factor in a multiple deck game is the fact that the player‟s expectations for
most doubling situations are significantly reduced from what they are in the single deck case. A good
hand suitable for doubling such as 10 or 11 usually consists of two relatively low and undesirable cards.
Their removal from the deck increases the likelihood of getting a good hit. Consider the case of
doubling on 11 in a situation in which the dealer‟s up card is other than ten or ace. In the single deck
case the probability of reaching 21 is 16/49 or 0.3265. In the eight deck case this is reduced to 128/413
or 0.3099. Thus a player in the latter game is 5% less likely to reach 21 by doubling on 11 than he is if
he is playing a single deck game.

“Fundaments of Blackjack” Chambliss and Roginski.

4.14            Baiting the Hook
Casinos use a variety of ingenious techniques to encourage people to gamble longer, more frequently,
and for higher stakes. You will never see a clock on the wall in any gambling Casino. Management
doesn‟t want you leaving the table to run off to some
appointment, or worrying that you have squandered too much of the day gambling, or feeling that you
should pack it in because its getting near bedtime. Coupled with the lack of windows in the Casinos, the
absence of clocks helps create an unreal, timeless atmosphere removed from everyday reality, one in
which it is only too easy to follow the path of least resistance and keep gambling until your money runs
out. This atmosphere is strengthened by the ever present cocktail waitresses serving free drinks.
Alcohol has never been noted for promoting a responsible attitude toward either time or money.

It has been said that the most brilliant invention in the history of Casino gambling is the use of chips
instead of money for betting. When betting those clay and plastic chips it is easy to forget they
represent real money. If betting currency, it is likely that a player would consider more carefully before
risking a weeks wages on one roll of the dice. The use of chips is one more element contributing to the
unreal feeling that so much of the Las Vegas experience has – the atmosphere that prompts one to act
without weighing the real life consequences.
Chips are also used to encourage players to up their bets. When a player is winning substantially, the
dealer will start paying him off in higher denomination chips. For example, if a player bets two five
dollar chips on a blackjack hand and gets a natural, the dealer may collect the bet and give him a twenty
five dollar chip in return. This practice is known as coloring up. The dealer follows this practice
partially to keep his stock of chips from getting too depleted in any one denomination. However, the
procedure serves a more subtle purpose. Before long, the winning player who had been betting five
dollar chips may find that all his money has been converted to twenty five dollar chips. As we have
seen, it is generally a good strategy to increase ones bets when winning. However, make sure you are
doing it because you want to and not because you have been subtly pressured into it by the house.
Remember, you can always ask the dealer to change your chips back to a lower denomination.

No detail is too small for the Casinos to consider in their endless quest to win your money. Even the
placement of slot machines is carefully thought out. There are always rows of slots within easy reach of
the long lines that form as people wait to enter the showroom. If the waiting gets boring, the machines
are there to provide a little diversion. Similarly, in many Casino coffee shops, if one wants to go to the
rest room, he must leave the restaurant and wander through a long maze of slot machines to get there. If
the last time you were having a snack in a Casino coffee shop, your girlfriend excuses herself to go to
the ladies room and took forty five minutes to get back, now you know why.

Of the many strategies both blatant and subtle that Casinos use to encourage you to gamble, none is
more complex than the granting of complimentary items to players. To get your business, a Casino may
be willing to give you not only free drinks, but free food, free lodging, free transportation, free shows,
free gifts, and even free money in the sense that Casino credit to players is interest free.

“Darwin Ortiz on Casino Gambling”

4.15            Baccarat and Chemin De Fer
The rules may look involved, but they stem from simple considerations. It is reasonable
for the player to want to draw if he has a greater chance of raising his total than of lowering it. Consider
an initial total of 7, for example. Two draw cards will improve this hand (ace and 2) four cards will
leave it unchanged (10,J,Q,K) and seven cards will make it worse (3 through 9). Clearly, the player
should stand on 7. A similar argument applies to 6, where the odds of improvements/no
change/deprovement are in the radio 3:4:6.

For a total of 5, these odds would appear to be 4:4:5, suggesting that the player stand. However, gross
odds no longer serve to tell the story. It must now be borne in mind that the banker definitely does not
have a two card total of 8 or 9 (for, if he had, he would already have turned those hands over), and this
fact exerts a strong compensation. So, in baccarat, the player is required to draw to 5. In Chemin de
Fer, this draw is optional and leads to various interesting strategies. When the players hand is worth 4
or less, in either game, he is more likely to do better, and therefore draws in all these cases.
To sum up, the player stands on 6 or 7, and draws on 5 or less. Now, if the banker were to follow the
identical rules, the game would be “symmetrical” and neither side would have an advantage. To
provide an edge for the banker, certain alterations are made so that the bankers choice depends on the
players draw card. As we have seen, the mere fact that the player has drawn gives a clue to the players
original two card total, and hence an indication of his final total. Accordingly, it is easy to work out, for
any given case, whether it is to the bankers advantage to draw or to stand.

Take for example the case where the bankers two card total is 3, and the player has drawn an 8. With a
low total like 3, it might seem reasonable to expect the banker to draw. But it turns out that the banker
is better off if he stands. If he draws, he has a 6.3 percent advantage, but if he stands, he has a 6.7
percent edge. Supporting calculations are shown in Table 13-2. The crux of the explanation lies in the
fact that, in just standing pat on his 3, the banker will beat the player more often than not. The bankers
hand requires improvement only when the players total is 8 or 9, but the banker must then draw 5 or 6 to
accomplish any good. Since the chance of so doing is relatively slight, the possible gain is overcome by
the chance of the banker getting a worse hand than he had to begin with, and thereby losing to a player
total that he would otherwise have beaten.

On the other hand, where the banker‟s total is 3, and the player has drawn anything but 8, the banker is
better off if he draws. In all such cases he has a greater advantage, or at least a lesser disadvantage
(money wise, this amounts to the same thing).


Rules for Baccarat

PLAYER

Value Held                                Action
1-2-3-4-5-10                              Draws a card
6-7                                       Stands
8-9                                       Turns cards over

BANKER

Value Held               Draws when giving                          Does not draw when giving
3                        1-2-3-4-5-6-7-9-10                         *8
4                        2-3-4-5-6-7                                *1-8-9-10
5                        4-5-6-7                                    *1-2-3-8-9-10
6                        *6-7                                        1-2-3-4-5-8-9-10
7                        Stands
8-9                      Turns cards over
10-1-2                   Draws a card

Picture cards and 10s count zero

Note: * = show departures from the “symmetrical” game.
In baccarat, the play in all situations is clearly spelled out by the rules. There are no options for either
player or banker. In Chemin de Fer, however, certain options exist. These relatively minor variations
constitute the only difference in the playing of the hands in the two games. The options will be
mentioned later.

“The Casino Gamblers Guide”                Allan N Wilson


4.16               Why People Gamble
4.16.1           Gamblers Profile

1. High energy
2. Susceptible to boredom
3. Superstitious
4. Fatalist
5. Impulsive
6. Egotist – group centred
7. Pleasure seekers (novelty, adventure)


4.16.2           Why
1. Ego, power, illusion of control
2. Grandiose risk taking
3. Escapism – relief from mundane, humdrum of daily life
4. Challenge – winning, action
5. Adrenaline high
6. Risky
7. “Fun”
8. Personal recognition and reward
9. Something to look forward to. Special event
10. Winning


4.16.3           Other
1. Gambling as a factor from early childhood
2. Social contact (informal)
3. Positive reinforcement by remembrance of winnings and exaggerations thereof
4. Energy
5. Adult play with consequences
6. Benefits are often a complex set of intangibles
7. Return to childhood or high levels of energy


4.17            Customers Expectations Of Staff
1. To be greeted
2. Acknowledgement via eye contact
3. Friendly attitude, cheerful, polite, respectful
4. Skilled professional approach to tasks
5. Impartiality in disputes
6. Empathy
7. Acknowledgement of patrons by incoming/outgoing staff
8. Sound knowledge of what the Casino can offer
9. Prompt service
10. Consistency
11. Patient, approachable staff who will answer politely customers questions
12. Recognition for repeat visitors
Chapter 5      Inspector’s Duties




  “For every complaint received, the
  average company in fact has 26
  patrons with problems”

  “Perfection is not attainable. But if
   we chase perfection, we can catch
   excellence.”
Chapter 5    Inspector’s Duties

5.1     Inspector Job Specification ………………………………………………..           129
5.1.1   Inspector in The Work Environment ……………………………………….         129
5.1.2   Game Supervision …………………………………………………………                    129
5.1.3   Personnel …………………………………………………………………..                      130
5.1.4   Patrons ……………………………………………………………………..                       130
5.1.5   Inter Department Co-operation …………………………………………….           131
5.1.6   Documentation ……………………………………………………………..                    131
5.1.7   Reminders ………………………………………………………………….                       131

5.2     Inspectors Manual ………………………………………………………….                  131
5.2.1   General ……………………………………………………………………..                       131
5.2.2   Points Of Game Protection …………………………………………………              132
5.2.3   Complaints …………………………………………………………………                       134

5.3     Blackjack Game Protection ………………………………………………..             136
5.3.1   General …………………………………………………………………….                        136
5.3.2   Common Errors in Blackjack ……………………………………………...            137

5.4     Roulette Game Protection …………………………………………………               137
5.4.1   General …………………………………………………………………….                        138
5.4.2   Specific Cheat Moves ……………………………………………………..                140

5.5     Building Extraordinary Casino Patron Service ……………………………   141
5.5.1   The Competitive Edge …………………………………………………….                 141
5.5.2   Startling Statistics ………………………………………………………….               141
5.5.3   Player Contact ……………………………………………………………..                   142
5.5.4   Building Rapport …………………………………………………………..                  144
5.5.5   Six Rules for Saying “Thank You” ………………………………………..         145
5.5.6   The Patron’s Top Ten ……………………………………………………..                146
5.5.7   Casino Patrons …………………………………………………………….                    146

5.6     Casino Supervision – A Basic Guide ……………………………………..        147

5.7     I am Your Guest …………………………………………………………..                   148

5.8     Extract from the Pit Boss Training Manual ……………………………….    148
5.1             Inspector Job Specification
An Inspector‟s position is one of responsibility.

A position that encompasses game security, public and employee relations, supervision of dealers,
accurate reporting of financial aspects (game and player info).

As an Inspector you will have to use your past experience as a dealer to assist in the making of decisions
and judgement calls that ensure the smooth operation of the game.

You are required to pass on all relevant information to your Pit Boss or Acting Pit Boss and to make
sure it is accurate and concise, as that same information may be used to make on the spot decisions or
relayed to upper management levels.

Professionalism, accuracy and decisiveness are the requirements to ensure the Adelaide Casino‟s
integrity.

5.1.1           Inspector in the Work Environment

1.      Check equipment to be sure it is ours and report any need of repair/replacement.

2.      Make yourself aware of limits on assigned tables, when starting shift or returning from breaks.

3.      Communicate needs to Pit Boss/Acting Pit Boss.

        a.      Fills and credits – required/arriving
        b.      Evaluate the play and if required, request higher denominations.
        c.      On change of shifts make sure floats are adequately filled but do not wait till you are
                about to finish, as this is the busiest time for cage and security as well as pit.
        d.      Do not order fills unless necessary.

4.      In any emergency situation inform Pit Boss or Acting Pit Boss.

5.      Always know the status of the table

        a.      Fills, credits.
        b.      Win/loss (table and player).
        c.      Be aware of the drop.
        d.      Any large changes in win/loss or drop, inform Pit Boss or Acting Pit Boss immediately.

6.      The Pit Boss or Acting Pit Boss must be notified immediately of any irregularities.

5.1.2           Game Supervision

As an Inspector your responsibilities and duties are varied and you must have a professional approach to
ensure each game runs smoothly.

1.      Communicate with Pit Boss or Acting Pit Boss.
2.      Knowledge of and protection against possible cheat situations is essential.

        a.      Instruct dealers in procedures and follow up with positive reinforcement.
        b.      Be aware of suspicious activity.
        c.      Avoid distraction (conversation to a minimum).
        d.      Do not leave games unprotected, if assistance is needed call Acting Pit Boss or Pit Boss
                immediately.
        e.      Be alert.
        f.      Do not stay at one table longer than necessary.
        g.      Find best observation position.
        h.      Focus attention where most needed without jeopardising other games.
        i.      You must not leave your assigned work area. Relay any message to Acting Pit Boss or
                Pit Boss.

3.      Make sure all relevant information is passed on to swing Inspector before leaving on your
        break.

4.      Markers:- Pit Boss must be informed of colour on Roulette marked up to a higher denomination.

5.1.3           Personnel

An Inspector needs a good rapport with the dealers, work on a first name basis and introduce yourself to
the ones you don‟t know.

1.      You need to be able to:-

        a.      Motivate – praise, reprimand, instil ambition.
        b.      Teach – aspects of job, the “why” of instructions (lessons), speed and accuracy.
        c.      Set examples – patron and personnel relations.
        d.      Inform – instruct, with explanation, changes in policies and procedures.
        e.      Listen – to what people have to say. Be approachable, be understanding.

2.      You are required to be accountable for your own work as well as evaluating others. It is
        important to reward good work (Thank You‟s, Recommendations) and encourage both the top
        and bottom performers. Always be prepared to help and develop those who need it.

3.      All the above can help create a comfortable working environment which in turn will lead to a
        better quality of work by us all.

5.1.4           Patrons

They are our main asset, so we must provide them with good, efficient, friendly service.

1.      Patron requests:-

        a.      Drinks – served to tables?
        b.      Information – we must be aware not only of the Casino operation but also of the facility
                and all it offers.
        c.       Comps. – Accuracy is very important. Relay information to the Pit Boss or Acting Pit
                 Boss with recommendation.

2.      Patron complaints:-

        a.       Gather the facts.
        b.       Diplomacy.
        c.       Make decisions consistent with policies and procedures and within bounds of authority.
        d.       Once you make a decision act on it.
        e.       Know the limits of your authority and when to ask for assistance.
        f.       Control emotion.
        g.       Relay facts to superiors.

3.      Creating repeat and new business:-

        a.       Greet and acknowledge.
        b.       Introduce yourself and the Pit Boss/Acting Pit Boss.
        c.       Gather information ie names, new patron or not.
        d.       Monitor and rate their play – accuracy is paramount.
        e.       Friendliness.
        f.       Observe their patterns of play.
        g.       Offer assistance but not advice.


5.1.5            Inter Department Co-operation

Co-operation is essential with all departments as they are as much involved in service to the patrons as
are we.

1.      Don‟t give orders, ask for cooperation.
2.      Know the people who may have access to gaming tables (waitress, bar usefuls etc).

5.1.6            Documentation

In this area accuracy is essential, if there is anything you are unsure of, ask for verification. Legibility is
also very important.

5.1.7            Reminders

1.      Communication: - To Pit Boss/Acting Pit Boss

        a.       Large buy-in or wagers.
        b.       Personnel problems or commendation.
        c.       Suggested limit increases/decreases.
        d.       Any large win/loss
        e.       Any large change in win/loss.

2.      Patron service – essential.

3.      To dealers be open and approachable.

4.      Know limits of authority.

5.      Responsibility for games and personnel assigned to you.
6.   Conduct yourself in a manner consistent with policies.

7.   Be professional in appearance and attitude to both staff and patrons.
5.2 Inspectors Manual
5.2.1           General

In the Casino industry Inspectors and Dealers have a very important role to play in the promotion of the
Casino in which they work. Attitudes as presented to the general public are extremely relevant to the
creation of harmony and satisfaction which will benefit the Casino by increasing the numbers of
satisfied patrons.

Professional appearance promotes professional behaviour. Clothes certainly don‟t make the man or
woman, but visual impressions are very important in presenting a professional image of your capability.

An Inspector must remain emotionally stable at all times, they must never lose their temper, they must
remain calm and composed whether a table is losing or winning, and they must appear to be confident.

Tact and diplomacy must be exercised at all times even in the face of offensive or abusive behaviour.
Inspectors must impress upon their dealers that a Casino‟s reputation depends largely upon the attitudes
of its dealing staff.

The prime concern of an Inspector is the smooth running of the game. To achieve this, their relationship
with the dealers must be amicable, and they should try to instil in their dealers a sense of professional
pride. Bored dealers make boring games which make for bored players.

A Casino Inspector should be aware that whenever people and money come together, the temptation to
steal becomes overwhelming for many. All sorts of clever and sophisticated schemes have been devised
to defraud Casinos. One of the main functions of an Inspector is to look for cheats and detect them
before they do too much damage.

Remember, a Casino derives its profits from only a very small win percentage, but on a great volume.
When a thief steals money through some kind of ploy, then the volume has to be even greater to make
up for the loss. Many Casinos throughout the world have gone “bust” because management was not
aware of the many thefts occurring.

Each Casino sets up elaborate surveillance and security systems. In spite of these, Casinos still get
ripped off daily. Cheating schemes vary from the very simple to the ingenious.

The protection of any game against cheating by the players depends on the vigilance of this personnel
running that game. The following suggestions will increase your knowledge in this important area:-

There are three main elements in game protection; the following of set procedures on the game; basic
knowledge of cheat moves that the Dealer/Inspector can guard against; and knowledge of the more
sophisticated moves that the Inspector and Pit Bosses can be aware of.
The purpose of procedural rules is to protect the Casino‟s edge from those who would cheat or
otherwise steal from the game. At the same time, Casino personnel should be flexible enough to allow
for honest mistakes due to the lack of game knowledge.

A profitable Casino seeks always to maintain an atmosphere in which the honest players know that the
games are being run fairly.


5.2.2           Points of Game Protection


The alert, informed Inspector should:-

   know and memorise the bankrolls at all times. Have a good knowledge of where the money has
    gone and game shortage.
   determine, by observations, the betting and winning system of all players.
   continuously observe games.
   pay close and particular attention to players and dealers on each game.


Dealer behaviour – all games

   Watch for any departure from regular dealing procedure.
   Beware of nervous dealers on a small game.
   Watch for eye movements or smiles between dealer or player.
   Is the dealer watching your eyes, is he nervous of your presence, if so why?


Strategy – all games

   Continually scan the layouts.
   Listen. While watching one table listen to transactions on other tables.
   Be constantly alert. Develop roving eyes.
   Keep moving at all times. When it is necessary to pass information on, do not look at the person
    you‟re talking to, keep watching the games.
   Watch the players playing styles. You can resolve most disputes if you are aware of your patrons‟
    betting patterns.
   Be aware of all patrons at your table and know what denomination chips they are playing.
   Keep note of how much a large stake player is in for.
   Be aware of each dealer‟s composure when confronted with an argumentative or belligerent patron.
   Make sure that dealers understand the correct pacing of a game, that it must satisfy the players and
    the house.
   Try to instil in the dealers a sense of professional pride.
   Always know and use the dealer‟s name. Also, get to know the other employees in the pit.
   If any part of a dispute involves a dealer‟s mistake, the player has the benefit of the doubt, within
    the rules and regulations. If in doubt, call your Pit Boss.
   Develop an awareness for agitated or nervous people – potential cheats often broadcast their guilt.
   Avoid the appearance of being tied up on a game. If you are involved in resolving a dispute on one
    table, do not turn your back on the other tables. Stand at an angle slightly facing the other tables.
    The tables you are not watching are the insecure ones and are potentially dangerous.
   Do not allow a disturbance at one end of the table to consume your attention. The other end may, in
    fact, be the location of the real trouble.
   Never let a player become aware that he is being watched. If he is not a thief, he will be offended
    and get annoyed. If he is a thief, he will merely leave your tables.
   Watch for spilled drinks. They can mark cards, contaminate chips, ruin a layout and close a game.
   Be aware of the appearance of a high roller on one of your games. Is a fill necessary to
    accommodate his action?
   Notify the Pit Boss of an excess of chips as soon as they become a hindrance.
   Ensure that all fills and credits are checked thoroughly before being signed for.
   Ensure that all signatures, dates and amounts are correct on all accounting slips.
   Keep a notebook handy to jot down the names of your best patrons.
   Always have pen and paper handy.
   When your relief comes in, give them the run down of play, eg good players and their style of play,
    trouble makers, etc.
   Memorise the tables banks – are there any 5‟s, 25‟s, 100‟s, unaccounted for, particularly on an
    empty game.
   Practice tact and diplomacy at all times.
   An Inspector must never lose his or her temper.
   Never discuss a player within his hearing range or point at a player.
   Dead games require as much security as live games.
   Beware of two friends playing together.
   Watch for eye movements or smiles between player and dealer.
   Be careful of players who can shuffle chips.
   Watch for players sitting next to big players.
   Watch the player‟s eyes. Is the player watching you? If so, why?
   Is the player putting chips in his pocket?
   Watch players with high denomination chips who are only playing small amounts.
   Be suspicious of overly friendly players.

5.2.3           Complaints

Prevention

Remember that most disputes can be prevented by your own efficiency in monitoring the game. If you
have noticed a mistake made by the dealer, intervene and correct the error immediately, especially a
short payment. Prompt and efficient action taken by the Inspector instils confidence and respect from
the player. If they are aware that you are thoroughly on top of your job, they are far more likely to abide
by your decision should a dispute be settled against their favour.
Remember that players are far more involved in the actual game than you are, and if one mistake goes
unnoticed by the Inspector, your position in maintaining security and authority over the game is
weakened considerably. Those players prone to occasional cheating are far more likely to become
aggressive if they have noticed that you have been unobservant.

You are there to protect the clientele as well as the house. You should seek to gain respect and promote
goodwill towards your players.

Handling

    Hear the complaint from the patron.
    Hear the dealers version.
    Decide whether the complaint can be handled without further disruption to the game.
    While keeping the communication between yourself and the patron on a calm level, allow the patron
     to fully vent his feelings. Be sympathetic, try to find feelings with which you can identify and tell
     him that you understand. Hurt feelings breed aggression and merely extend the dispute.
    While the patron is talking, assess the situation. Is he a regular patron? How much money has he
     dropped? How much does he still have? How many chips does he have in front of him? Has he
     lost a great deal? Lost all his chips? Is the player genuinely angry? Does the player believe he is
     right? Is he sure? Is there any hesitation? Is his anger spontaneous? Has he caused trouble before?
     What sort of character is he? Generally, a persons personality will reveal itself in conversation,
     listen politely.

Decide on what course of action to take. If it is within your power and you are confident that you know
how to remedy the situation act affirmatively. If you are uncertain, refer the matter directly to your
supervisor. Do not delay or protract the situation longer than is necessary.

Bear in mind that a complaint should be considered an opportunity to promote goodwill towards your
clientele. It is the time to be most gracious, polite and understanding. Don‟t be defensive, this breeds,
an overbearing attitude which will alienate and further aggravate a patron. You don‟t have to win every
beef, think about the long term results.

Explain to the dealer when the patron was paid. Do this when the dealer goes on a break. Never discuss
a player or situation on the game in front of players.

Points to note

1.       Recognise at all times and under all circumstances that you are dealing with people and not
         machines – people with (real or imagined) emotions, purposes, prejudices, sympathies, feelings
         and ideals both on and off the job.

            Communicate the message that you respect your people.
            Always greet your Casino associates with a smile. Use “please” and “thank you”
             generously.
            Never underestimate the value of sincere courtesy on the job to both those above and below
             you.
2.    Recognise that there are two sides to every situation and that you do not know the whole story
      until you have heard both sides. In every situation keep your mind open until all the facts are
      out.

3.    Recognise the importance of proper time and place for dealing with people. Pick the most
      favourable time and the most favourable place for giving employees good news or bad news, for
      giving them criticism or a pat on the back, for granting a request or denying one.

4.    Do not unnecessarily contribute to employee dissatisfaction when it is caused by your own
      carelessness, sharp tongue, bad temper, poor planning or lack of fairness.

5.    Remember that when you are on the job, you live in a glass house. People see more than you
      realise, and measure you more by your actions than by your words. Set an example – a very
      good one.

6.    Be genuinely interested in your staff‟s welfare.

7.    Smile …… it can be your best ally.

8.    A person‟s name is the most important word to him or her. Learn to remember names.

9.    Be willing to accept responsibility for your own mistakes. People like a person who is big
      enough to admit when he is wrong and if they cannot like him, they at least respect him.

         Show that you trust the people who work for you. Employees are less inclined to hide their
          own errors if they know the boss is not perfect.
         Be personal. Showing your employee that you can be human in many personal situations
          indicates that you can be trusted.

10.   Recognise that credibility is a major key to your influence on staff. Establishing the kind of
      credibility that wins the trust of others is based on honesty.

         Managers who are always “selling” people, even to the point of shading the truth, diminish
          the credibility.
         Do you level with them as often as possible.
         Are you alert to their problems?
         Do you stick up for them when necessary?
         Do you advance their causes?
         Do you avoid recriminations?

11.   Know the true executive qualities that build and maintain employee respect.

         CONFIDENCE. People have to believe that you can do your job. They have to be
          confident that you know what is going on.
           TRUST. Employees have to know that you will not exploit them or take advantage of their
            subordinate position. Manipulation is a way in which trust is often violated.
           FAIRNESS. Employees want to have their achievements recognised and rewarded. They
            want to feel confident that you will treat them fairly.

Conclusion:

Even “tough” bosses can come across as supportive if your answers to the preceding questions are
mainly “yes”.

5.3             Blackjack Game Protection
5.3.1           General

           Verify change for mistakes or counterfeit money.
           Be especially aware of the original bet when players are splitting, doubling, insuring.
           A blackjack payout is always a mistake-prone bet.
           Any unusual or heavy play must be brought to the attention of the Pit Boss.
           Do not allow the players to touch the cards.
           Check the discard holder. Make sure that nothing is obscuring it from your view. Do not
            allow patrons to play with anything next to the discard holder.
           The cards in the shoe and the cards in the discard rack must equal the total.
           Be aware of your table banks at all times. Be aware of its needs and deficiencies, the type
            of patron who is playing, how he plays, will the table bank be adequate, pass all patron and
            bankroll information onto the incoming Inspector?
           The best way to distract a card counter is to talk to him, draw him into a conversation. How
            does he react? Does he look startled, as though you‟ve broken his concentration?
           Do not allow waitresses to serve during a hand – this blocks your vision and disrupts the
            game.
           Ensure that all cards are dealt correctly and kept in the proper order on the pick up.
           Ensure that all dealers announce all necessary transactions.
           Ensure that dealers follow correct procedure at all times.
           Keep a continuous eye on the shoe.
           Be aware of habitual late bettors.
           The game is vulnerable during the shuffle, so do not take the shuffle lightly. Watch cards
            closely during the entire procedure. This is also a good time to see how the game stands.
            Know how to compare your opener, fill and credits against drop. Is the game winning or
            losing?
           Watch the positions of the player‟s hands – there should be a gap between their hands and
            the box.
           Does a player habitually touch the cards when he is splitting even when told not to?
           Watch a player whose eyes follow every card.
           Watch for anyone varying their bets considerably.
           Watch for fast hand movements when a bet is being doubled, insured or split. Watch the
            original stake.
           Watch for anyone or anything obscuring the discard holder.
           Watch for players watching you.
           Watch the tray, is it neat or are the chips often left in a “dirty stack”?

Be looking for something at all times. Look inside and outside the pit. Avoid developing any obvious
habits in working the pits. Cheats look for patterns of behaviour that are predictable.

(a)     Never turn your back on a game. Know your equipment.

(b)     Continually check dealers for procedure adherence.

(c)     Watch the floats.

(d)     Be alert to any quick motion or unusual moves. People are creatures of habit.

(e)     Make sure players signify a card, ie the dealer is not playing the hand.

(f)     Watch how the player draws against a dealers card.

(g)     Be very cautious when players or dealers send you on errands.

Do not think of inexperience as a handicap. In some cases it is best not to know – you are completely
unbiased and stand a good chance of catching a cheat even though you do not know the moves.

5.3.2           Common Errors in Blackjack

           Picking up cards before paying.
           Failure to cut the deck after shuffle.
           Looking around the Casino while the game is in progress.
           Giving double card before additional money was put in box.
           Allowing patrons to cap chips on double.
           Not calling stand-offs.
           Puts change in box.
           Turning away from the game with cards in play.
           Not calling the Inspector when a situation arises.
           Allowing a player to hold currency in his hand until change was given.
           Dealing to an empty box.
           Burning cards without Inspector‟s consent.
           Paying off backwards one hand against another when a player plays two hands.
           Not asking for insurance when having an ace.
           Not turning double cards perpendicular to patrons‟ hands.
           Not calling out change and getting an approval from the Inspector.
           Failure to check limit bets by cutting them down to make sure it doesn‟t exceed limit.
           Picking up money with the same hand as cards.
           Over-shuffling.
           Not heeling mixed denomination bets.
           No name tags.


5.4             Roulette Game Protection
Inspectors on Roulette are required to have learned all the dealers game procedures, all the typical cheat
moves and, in addition, must be very well acquainted with all the following procedures and strategy.

The attitude of the Inspector is most important as a game protection technique. You should always give
the impression that you are totally in control of all your games and that you know exactly what is
happening on them. This can be achieved by saying very little, but by standing at all times so that
players and would-be cheats can see your face and eyes.

The following rules are intended as a guide to your behaviour at the tables, and contain some examples
of specific moves by players to watch for.


5.4.1           General

               Keep moving at all times and watch the layouts continuously.
               While watching one table, listen to the action on the other(s).
               Be aware of the dealers, their attitudes to the players, their control of the game(s), their
                procedures for dealing and most important, are they calling everything to you that they
                should?
               Be aware of the players, their playing styles, what value they are playing at, how much
                they are in for, their attitudes. Are they nervous? Are they trying not to be seen? Are
                they watching your progress?
               In any dispute, do not allow yourself to be totally engrossed in this area. There may be
                trouble elsewhere.
               Establish communication with the dealers. Learn their names, and ensure they know
                yours. If they feel they can relate to you, your task of supervising the game will be
                easier and more effective.
               Check all fills and credits carefully, and make sure all signatures and license numbers
                have been correctly filled in.
               Communicate with your relief Inspector everything he needs to know about the action
                on your table(s), and about what might take place (trouble makers, request for fills to
                come, players‟ progress, etc).
               Watch slow games (one player) and dead games. Both require your full attention as
                well as do heavier games for total security of the operation.
   A suspected cheat move may be no more than a patron making a genuine mistake
    through tiredness or lack of knowledge. A big player making suspected cheat moves
    needs very careful handling. He may respond to humour (“bit early for the next spin,
    Sir”), or he may be abusing his action by openly claiming non existent bets in front of
    other players. Detailed explanation, based on thorough and certain knowledge of the
    procedures, will always be the best approach, but in this situation you may well be
    overruled by the Pit Boss if your decision has to be against him.
   Dealers and Inspector are to agree all payouts. If two different figures are obtained, the
    Inspector should talk to the dealer so that an agreement is reached. A dealer should
    never be in the position of being told what to pay, as this is a security risk.
   Are there players who make it a habit to hover over the layout when the ball is about to
    drop?
   Look for players who stand behind seated players. They could be part of a team, or
    trying to seal chips from the layout or other players.
   Watch for players who drop a large quantity of colour chips on the winning number. He
    may have placed a high value cash chip beneath them.
   Watch for players betting across winning bets.
   Watch for people with score cards, pieces of paper or cigarette packs near the columns
    and even chances.
   Watch for players leaving the table with colour chips.
   Watch for people who knock chips over on the layout as the ball drops, a clever means
    of distraction to cheat on the columns.
   Watch for any kind of distraction or dispute on one end of the table that may be
    intended to distract the dealer‟s and Inspector‟s attention from the other end of the table
    where a cheat move may be taking place.
   Watch for correct handling of the chips by the dealer. Never let a dealer obscure the
    payout, either in its being made or passed out.
   Watch dealers who consistently “accidentally” knock chips off the winning number and
    confidently replace them. They may be replacing more than those they swept off.
   Watch carefully a dealer who frequently “accidentally” pays losing bets on the even
    chance.
   Constantly be aware of the colour values. Have they been changed? Who now has the
    colour? Why didn‟t the dealer announce the transaction?
   Verify the correct number is being paid off.
   Your ears must be tuned in to the dropping of the ball. Instantly watch the layout and
    winning bets. Try to memorise the winning bets before the dealer clears the layout.
   Always check the wheel and the number cleared. Dealers hardly ever realise until it is
    pointed out to them that they have cleared the wrong number.
   Make sure the dealer announces all transactions.
   While scanning the pit, look for such things as:-
    a.       Chips on the floor.
    b.       Is anyone watching you, particularly your eyes?
    c.       How many colour chips and cash chips does the player have in front of him?
             Approximately how many does he lay on every spin?
   Keep up the pace of the games. Competent, personable dealers who help people place their
    bets, create atmosphere that will generate more action.
   Check the colour values constantly. Have they changed since you last looked? If so, why?
    Did the dealer announce it? Is it the same player playing the colour?
   Make sure that all dealers know and adhere to the correct order of payout. It is impossible
    to adequately monitor several games if the dealers are randomly paying the bets.
   When more than one patron is playing cash chips try to become familiar with their bets.
    There are more disputes over cash chips than anything else.
   When the ball is spinning, check for cash chips on the layout and try to identify the players.
   Check for cash chips under colour chips on the layout.
   Check that the cash chips are still on the layout when the ball drops. Some people steal
    cash chips when they are placing colour.
   Beware of high denomination cash chips beneath a solitary colour chip, particularly if it
    happens more than once.
   Disputes must be settled quickly as possible. Lost spins are lost percentage. More money
    an be lost in the lost spins than the amount involved.
   Never let the payout go out unless you are absolutely certain it is correct.
   Make sure the dealer and chipper do not converse unless it is directly related to the game.
   Watch particularly those tables without a chipper.
   Watch especially one dealer dealing to one player. This is a very high risk situation and
    should be observed accordingly. Just because there appears to be little action does not
    mean it is not worthy of the Inspector‟s attention.
   Disputes over cash chips should be handled with discretion. Assess the situation. Who are
    the players involved? Are you familiar with their bets? Their personalities? Resolve the
    dispute as quickly as possible.
   Never pay a claimed bet instantly, even though you may have made the decision to do so.
    Always hear both sides of an argument. Without protracting the dispute, give the
    appearance of considering the outcome – you do not want such claims to become a common
    occurrence.
   In the event of a wrongly-cleared number, and you are in the vicinity of the table and you
    have an approximate idea of the original bet, act affirmatively. Assess the average stake of
    each player and place the bets yourself. Most players do not remember their actual bets.
   Never permit a player to abuse a dealer or conversely allow a dealer to abuse a patron.
   Study the layouts when the ball is spinning. Check for bets exceeding the maximums.
    Check for complicated bets.
   Check that all colours are marked.
   Make sure that “no more bets” is called before the ball drops, not when it drops.
5.4.2           Specific Cheat Moves

1.      Player gives large complicated bet to the dealer as the ball is slowing – he will attempt to place
        it but very likely will lose concentration of the areas of the table to be watched (columns,
        outside chances). This is where the Inspector can ensure complete table security by watching
        the table closely for any large bets or alterations.

2.      Watch for players who apparently, by mistake, bet on the winning area. The dealer may not
        realise that the $25 chips under the stack of colour was also a late bet.

3.      Note cash chips on the layout for several reasons.

        a.      So that two players do not claim one bet (they cannot both be paid – also one of them
                should have been given a colour).
        b.      So that any additional chips after a distraction are obvious (take them off – chances are
                a cheat will not have the nerve to claim it).
        c.      So that if a big player‟s value chip has been removed by another player – or even
                moved by mistake – the situation can be handled.

4.      Watch for players not following normal behaviour patterns who are standing behind other
        players, hiding in badly-lit area just off the table, watching the game rather than playing,
        watching your movements.

5.      If there is some kind of distraction or dispute, see if the dealer can handle it. Keep your
        attention over the whole area of your responsibility – the plan may be to get you involved so
        that cheating can take place elsewhere. If the dealer cannot resolve the problem, be sure
        everything is under control before attending to the matter.

6.      Paying a claimed bet without considering the case at all may appear magnanimous but will lead
        to further claims, and investigation of your own inspecting technique and motivation by the Pit
        Boss. Hear the player‟s story and the dealer‟s. Consult the chipper but without protracting the
        dispute make your decision known (you may have done it already), and inform your Pit Boss.

5.5             Building Extraordinary Casino Patron Service
5.5.1           The Competitive Edge

Large and small hotel Casinos alike have begun to realise that trying to compete solely on marketing
strategies and give-away programs is not good business. Competing on the
basis of Casino differentiation is becoming increasingly difficult. What builds a solid patron base is the
ability to make the guest feel comfortable and eager to return. That can only be accomplished by every
employee having an attitude that the patron is supremely important and being committed to make that
patron feel as comfortable as possible. Every bartender, maid, cashier, Casino dealer or any other
patron contact employee, must create an environment in which each decision and action is designed to
make the patrons‟
experience better than it would have been, had the guest been dealing with the competition. The
Casino hotel must focus on the quality of the patrons experience at every level in the organisation.

SERVICE is not A competitive edge, it is becoming THE competitive edge.

“I found that when I took care of patrons extremely well, and made them a focal point, profit inevitably
flowed from that”
Stanley Marcus

“Perfection is not attainable. But if we chase perfection, we can catch excellence”
Vince Lambardi

5.5.2           Startling Statistics

Why patrons stop doing business with a particular hotel or establishment:-
1%    die
3%    move away
5%    develop other friendships
9%    leave for competitive reasons
14% are dissatisfied with the product
68% quit because of an attitude of indifference toward the patron by an employee (Source Michael
LeBoeuf‟s How to Win Customers and Keep them for Life).

The average business never hears from 96% of its unhappy patrons. (But 90% or more of them will not
visit or buy from that business again)

For every complaint received, the average company in fact has 26 patrons with problems.

Complainers are more likely than non-complainers to do business again with the company that upset
them, even if the problem was not satisfactorily resolved.

Of the patrons who register a complaint, between 54% and 70% will do business with you again if you
resolved their complaint. That figure jumps to a staggering 95% if the patron feels the problem was
resolved quickly.

The average patron who has had a problem with a hotel tells 9 or 10 people about it. One in five, or
13% of people who have had a problem with an organisation recount the incident to more than 20
people.

Patrons who have complained to an organisation and had their complaints satisfactorily resolved tell an
average of 5 people about the treatment they received. (Source: A survey conducted by Technical
Assistance Research Programs, Inc., located in Washington D.C.)

A study by Cambridge Reports, a Massachusetts‟s based research firm, found that 44% of the 1,500
patrons surveyed chose “ease of doing business with” as the principle reason for choosing a financial
institution. “Quality of personal service” was the second most important reason at 28%. In other
words, being easy to do business with, being treated well and having a choice of products outranked
location, interest rates, and other “traditional wisdom” factors that we‟d predict as reasons people would
choose a bank. Heres the bottom line –
Those organisations gaining most in market share were those rated highest in service quality by
their patrons.

Why bother keeping a grocery store patron happy?

Because over a ten year period, that patron will do $50,000 worth of business with you. Here‟s how
that figure is calculated. The average grocery store patron spends $100 a week at that store. Given 50
weeks a year, to allow 2 weeks vacation, that‟s $5,000 per year, over a ten year period, that adds up to
$50,000.
(Tom Peters, Thriving on Chaos)

The influence of each patron contact person

If a patron frequents a good restaurant twice a month for a six-person business dinner she is worth
$75,000 to that restaurant over the course of 10 years, and that‟s just the beginning. A repeat patron is
any firms principal vehicle of powerful word-of-mouth advertising. If one happy lifelong patron sells
just one other patron to you, she is worth $150,000. Now say you are a waiter who waits on 5 tables a
night. You are catering 5 x $150,000 or $750,000 worth of potential Business.

Sentences that drive Casino patrons away

1.   “I don‟t have anything to do with your problem. You‟ll have to find a Casino host”
2.   “I can‟t comp that for you. You don‟t play enough money”
3.   “I don‟t know. We‟ve always done it that way”
4.   “There‟s nothing I can do about it – that‟s company policy”
5.   “That‟s not the way we do it here”
6.   “I can‟t help you with that. You‟ll have to go back to the pit where you were playing”
7.   “I just came in – could you check back in about 15 to 20 minutes?”
8.   “I can‟t find the shift boss right now. You‟ll have to come back later”

5.5.3            Player Contact

It is terribly important for the Casino player to feel comfortable with the Casino atmosphere and feel
welcome in approaching a table game to try his luck. Looks of indifference or aloofness do not
encourage players to “belly up” to a game. Dealers and supervisors must try to remove as much of the
natural intimidation that players feel from their gaming experience as possible. I have outlined some
suggestions below:

Initiating Patron Contact

A. When
       Live Table
       1. Shift change.
       2. When new player arrives…..give at least acknowledgement.
       3. When relieving.
       4. When leaving table for break, for shift.
B. Dead game
       1. Be aware of patrons passing by table.
       2. Respond to eye contact.

C. During shuffle or break in action.

What to say

A.       Live game
         1. A simple “hello”.
         2. “Good Morning/Afternoon/Evening.
         3. A simple head or nod of acknowledgement.
         4. Direct eye contact and a smile go a long way.

B.       Dead game
         1. Make eye contact.
         2. Reach out with a greeting towards players.

C.       During shuffle or break in action
         1. Make note of hotel/Casino events, activities.
         2. Make positive statements…..“Hope you are enjoying your visit”

How to say it

A.       With sincerity
         Note: Any greeting or acknowledgement cannot be effective and may even be perceived
         negatively if not said or executed with sincerity.

Contact with patrons who are losing

A.       What to say
         1. Generally agree with their concerns …see it their way without insulting any other patron.
         2. Stay in a positive mind set. In Craps, the entire crew must be of a positive mind set.
         3. Empathise with the player‟s problem.
         4. Provide hope and encourage player.

B.       What not to say
         1. Don‟t agree with players when they are criticising fellow players.
         2. Don‟t emit negative body language. Don‟t sigh with poor or mistaken play.
         3. Don‟t take sides when players are interacting among themselves.

Disagreements at game

1.     Never take the game personally. It is not player against dealer. Don‟t feel as though you are in
       competition.
2.     Never feel as though you were made to look bad. Sometimes a patron relations decision needs
       to be made without regard to whether the dealer was correct or incorrect.
3. Respond honestly when asked about a player disagreement or conflict:
            either you saw and the player is right
            you saw and the player is wrong
            you did not see

5.5.4            Building Rapport

Specific gestures and vocal patterns that build rapport with patrons:

We tend to like people who are like us. One way to build rapport with a patron is to be like them by
using the gestures, words, and vocal patterns they use. For example, if the patron talks slowly, you
likewise should slow down your talking speed. If the patron doesn‟t use many gestures, tone down your
own gestures. In short, you are trying to be like them by mirroring their body and voice patterns. Don‟t
do this to the point of mimicking them, of course, but most of this behaviour will be subtle. The patron
won‟t be as aware of what your doing, but he‟ll instinctively begin to like you and feel comfortable with
you.

IF THE PATRON IS:                                  YOUR RESPONSE IS:
           Friendly                                Cheerful
           Natural                                 Natural
           Angry                                   Concern
           Overburdened                            Sympathy
           Emergencey                              Urgency

Smile training

Basic Casino patron service training has really been dealt with lightly over the years. Simple “smiles,
thank-you‟s and good lucks” are rare in our industry. So often, we have adopted adversarial roles of us,
the Casino, versus them, the players. I honestly believe this kind of non-service attitude is really
counter-productive in retaining repeat player business. Teaching your dealers, and indeed yourself, the
value of “warm fuzzies” that is, smiles and thank-you‟s can be the most valuable tools you can use to
make each and every player feel warm and welcome, stay longer and come back sooner.

Work miracles with a smile

A real, sincere smile works almost like a “magic switch” that turns on a friendly feeling in the other
person instantly. A few pointers are:

1. What a smile says

                It can say so many things. Frequently a smile implies …..
                I like you – I come as a friend.
                I assume you are going to like me.
                I am confident you are a good guy and that you like me.
                You are worth smiling at.

2. Smile from way down deep
        Voice teachers tell their pupils to “breath deep” and let their voices come from “way down
        deep”. If your smile is going to be a friend-maker, you‟ll have to smile “down deep” too – from
        the heart. A smile that goes no further than the lips is no good.

        Learn to smile on the inside. It is your feeling that gets across to our guests subconscious ….
        not just your facial expression.

3. Let go and smile.

        One simple reason many of us do not smile more often – or more sincerely – is the habit we
        have of always holding in our true feelings. We have been taught not to show the world our
        feelings. Practice “letting go” …..don‟t be ashamed or self-conscious about letting your face
        say, “Am I glad to see you”.

4. How to use mirror magic

        You got it …. a daily practice session in front of the mirror. When was the last time you really
        looked at your smile in the mirror?

5. Develop a genuine smile

        Everyone can recognise a real smile when they see one. Practice the genuine thing. A phoney
        smile says just that….baloney.

A smile is the million dollar asset in your human relations inventory – use it

                                                 SO GOOD TO SEE YOU
                                                 MAY I HELP YOU?
                                                 I APPRECIATE THAT. THANK YOU.
                                                 LET ME FIND OUT FOR YOU
                                                 ENJOY YOUR STAY……AND GOOD LUCK

“It is not even whether or not the guests desired service can be fulfilled that is most important … what
really counts is the attitude with which the guest is treated”

Peter G Demos, Jr

P.S. Take a chance he is friendly. The odds are in your favour.

5.5.5           Six Rules for Saying “Thank You”

Those two little words, “thank you” can be magic words in human relations if they are used correctly.
Memorise these six rules. They have been tested and proved.

1. Thanks should be sincere
      Say it as if you mean it. Put some feeling and life into it. Don‟t let it sound routine, but
      “special”.
2. Say it – don’t mumble it
      Come right out with it. Don‟t act as if you were halfway ashamed for the other person to know
      you want to thank him.

3. Thank people by name
      Personalise your thanks by naming the person thanked. If there are several people in a group to
      be thanked, don‟t just say “thanks everybody”, but name them.

4. Look at the person you are thanking
      If he is worth being thanked, he is worth being looked at and noticed.

5. Work at thanking people
     Consciously and deliberately begin to look for things to thank other people for. Don‟t just wait
     until it occurs to you. Do it deliberately until it becomes a habit. Gratitude does not seem to be
     a natural trait of human nature.

6. Thank people when they least expect it
      A “thank you” is even more powerful when the other person does not expect it, or necessarily
      feel that he deserves it. Think back to some time when you got a nice “thank you” from
      someone where it never occurred to you that any “thanks” were in order and you‟ll see what we
      mean.

5.5.6           The Patron’s Top Ten

Does the Casino Hotel Property …….?

1.      Express CARE and CONCERN for patrons.
2.      Provide TIMELY (quick) responses to requests.
3.      Provide ASSISTANCE without a patron request.
4.      Express SINCERE APPRECIATION to the patron.
5.      Provide FLEXIBLE, PERSONALISED treatment for each patron.
6.      Recover from lapses in service in ways that IMPRESS the patron.
7.      EDUCATE the patron.
8.      Have PATRON FRIENDLY policies and procedures.
9.      Have USER FRIENDLY policies and facilities.


“Our business is serving the entertainment and gaming needs of the public. If we can do that better than
other (Casinos), we‟ll get the business. If we can‟t, we won‟t get the business and we don‟t deserve to”.


Donald Trump
5.5.7            Casino Patrons

           are the most important people who will ever be in the facility.
           are those special VIP‟s who call on the phone.
           are not interruptions of work …. They are the reason for it.
           are individuals with names and feelings.
           are not people I argue with.
           are the reasons I have a job.
           are not always right, but they are always ……….

Service Quotes

           It takes months to find a patron, seconds to lose one.
           The goal of patron service is to make people want to do business with us.
           Patron complaints are the school books from which we learn.
           Patron service means “doing” what you say you will.
           Patron service means getting to the cause of patron problems rather than symptoms.
           Companies give excellent service by rewarding employees for providing it.
           Patron service is training people how to serve clients in an outstanding fashion.
           Patron service means “anticipating” patron needs.
           Patron service means hiring people-sensitive employees.
           Always exceed the patron‟s expectations.
           Patron service is listening …… and hearing ……what patrons say and don‟t say.
           The best way to evaluate patron service? Ask them.
           Patron service is “application” of our knowledge and philosophy. Slogans without action
            won‟t work.
           A patron that “complains” is doing you a great service.
           Patron service is awareness of needs, problems, fears and aspirations.
           Patron service, above all, is an attitude that the patron is our purpose for being.
           Make it a “joy” for people to do business with you.
           Ask everyone for service improvement ideas.
           Patron service is a smile and a pleasant voice.
           Patron service must be measured.
           Patron service is a commitment.
           Patron service makes every client feel like “the most important.”
           The patron‟s evaluation of service is more important than your own.
           Patron service must be consistent.
           Tell patrons you appreciate their business.
           “The patron that doesn‟t complain but doesn‟t come back is the one that hurts us.
           Patron service means an organised integrated effort.
           Everyone in the organisation must serve the patron … or support someone who does.
           Patron service means that every employee knows that “no one is more important than the
            patron”.
           Never let a patron problem go unresolved.
           “Thank” patrons for bringing problems to you.
           Empathise with patron‟s problems.
           Look your patrons in the eye.
           Patron service means quick response.
           The patron is our reason for being here.
           Always be courteous and polite during each patron contact.
           Never promise more than we can deliver.
           Nothing is ever gained by winning an argument and losing a patron.
           Patron service is patience.
           Never be “the reason” a patron doesn‟t come back.

5.6             Casino Supervision – A Basic Guide
           The satisfied patron is our best business strategy.
           Correct patron service problems immediately.
           Respect complaints.
           Patron service is a combination of little things.
           You never get a second chance to make the good first impression.
           Nobody ever won an argument with a patron.
           Hold discussion groups on service.
           Patron service must be breathing in every employee.
           Look at your business through your patron‟s eyes.
           Satisfied patrons multiply and come back.
           Service is not a competitive edge; it is becoming the only competitive edge!
           96% of unhappy patrons never complain about rude or discourteous treatment … they
            simply don‟t come back!
           It is not even whether or not the guest‟s desired service can be fulfilled that is most
            important … what really counts is the attitude with which the guest is treated.
           It is not the Casino who pays wages… it only handles the money. It is our guests who pay
            the wages.

5.7            I am Your Guest
I am your guest, satisfy my needs and wants, add personal attention and a friendly touch and I will
become a walking advertisement for your Casino. Ignore my wants, show carelessness, inattention and
poor manners, and I will simply cease to exist – as far as you are concerned.

I am sophisticated, much more so than I was a few years ago. My needs are more complex. I have
grown accustomed to better things, I have more money to spend.

I am an egotist. I am sensitive. I am proud. My ego needs the nourishment of a friendly, personal
greeting from you. It is important to me that you appreciate my business. After all, when I come to
your Casino my money is feeding you.
I am a perfectionist. I want the best I can get for the money I spend. When I criticise your food,
beverage or service – and I will, to anyone who will listen, when I am dissatisfied – then take heed. The
source of my discontent lies in something you have failed to do. Find that source and eliminate it, or
you will lose my business and that of my friends.

I am fickle. Other Casinos continually beckon to me with offers of “more” for my money. To keep my
business, you must offer something better than they. I am your guest now, but you must prove to me
again and again that I have made a wise choice in selecting your Casino, your Casino and your services
above all others


5.8             Extract from the Pit Boss Training Manual
Personnel
A Pit Boss must set and lead by example:-

1.      With a professional and positive attitude.

2.      In dealing with the patron.

3.      In dealing with staff.
        A.      Must be able to motivate.
        B.      Must encourage not discourage.
        C.      Reward good work (“thank you”).
        D.      Speak to people as you wish to be spoken to.
        E.      Always be approachable.
        F.      When instructing given the reason “why”.
        G.      Be able to discipline (fair but firm).
        H.      Teach the aspects of the job.
        I.      Help employees to improve.

4.      A good working relationship is paramount. Listen with understanding, offer advice, and try to
        develop a promotable talent.

5.      If delegating, monitor the work issued.

Patrons

Above all, the main objective is to satisfy patrons, without whom we cannot survive. We must
encourage repeat business and create new business, by offering good, efficient and friendly service.

1.      HANDLE PATRON REQUEST

A.      Comps:- In this area information on patrons must be accurate, so as to utilise its benefits
        correctly.
B.      Drinks:- Light refreshment (alcohol VIP?) served at tables by waitress.
C.      Information:- Possess a knowledge of the facility and all it offers, as well as the Casino area.
2.   PATRON COMPLAINTS

A.   Gather the facts.
B.   Make decisions within the bounds of your authority and consistent with policies and procedures.
C.   Remember there are two sides to every story.
D.   Always be prepared to resolve a dispute but know the limit of your authority.
E.   Remain objective.
F.   Support your staff when necessary.

THE ARBITRATION OF PATRON COMPLAINTS OR DISCREPANCIES SHOULD BE
HANDLED QUICKLY AND COURTEOUSLY.

A.   GAMING TABLES

1.   All equipment is present.
2.   Relevant procedures for dealing are adhered to.
3.   Games are run efficiently.
4.   Damaged equipment is replaced quickly such as cards.
5.   Games security.
6.   Awareness of limits in your pit.

B.   PERSONNEL

1.   Ensuring that staff are qualified for the position they are given.
2.   To ensure follow up training of staff when and where it is deemed necessary.
3.   Motivation of staff.
4.   Decisiveness where necessary.
5.   Promoting a climate of enthusiasm and teamwork.

C.   GOVERNMENT REGULATIONS

1.   Sound knowledge of Government regulations.
2.   Supervision of all staff to achieve this.
3.   Ensuring Inspectors instruct dealers on procedures where necessary and that this is followed up
     with positive reinforcement.

D.   INTER-DEPARTMENT CO-OPERATION

1.   Always be polite when asking for assistance.
2.   Recognising the importance of working as a team.
3.   A working knowledge of what employees responsibilities are in other departments.

E.   PATRON AND EMPLOYEE RELATIONS

1.   Motivations of staff through example, information teaching, guidance and the ability to listen.
2.   Accountable for your own work.
3.      Required to evaluate others.
4.      Patron complaints.
5.      Creating new business.
6.      Seeing to patron requests.
7.      Communication.

To the pit employee, the Pit Boss is a symbol of authority, able to motivate, facilitate and coordinate and
importantly a source of knowledge.
Chapter 6 Setting Table Maximum
Bet Limits                    _




Risk and volume dependence in relation to
determining maximum betting limits for
independent trial, negative expectation table
games.
CHAPTER 6         Setting Table Maximum Bet Limits
     6.1    Background………………………………………………                   153
     6.2    Key Principles……………………………………………                153
     6.3    Setting proper table limits………………………………        154
     6.4    Maximum Loss Point……………………………………               158
     6.5    Effect of Variable Bet Distributions……………………   159
     6.6    Non High-End Casino Operation……………………...       162
     6.7    Conclusion……………………………………………….                  166
Background
Interesting theories abound in the Casino industry on how table maximum bet limits should be set.

One expert at a recent World Gaming Congress and Expo seminar in Las Vegas wisely stated that in
well-managed Casinos, limit spreads should not exceed a “four times double-up spread in small Casinos
and maybe up to a seven time double-up spread in large Casinos”. So what does this mean? A $5
minimum limit table game should not then allow a bet of greater than $80 ($5, $10, $20, $40, $80.) in a
small Casino and $640 in a large Casino. To show this more mathematically, if you would like to
calculate for other numbers then the formula is:

Maximum = $.2n
where         $ = the minimum bet limit and,
              n = the number of double ups to which you wish to limit.
For n = 4 then Maximum = 16.$
and n = 7 then Maximum = 128.$
Several questions, however, arise from this hypothesis. Firstly, how does one define a small and large
Casino? Secondly, does this mean that many Casinos in Las Vegas such as The Mirage, M.G.M. Grand
etc. are poorly managed as they certainly do not appear to follow this sage‟s formula? Thirdly, what on
earth have bet spreads and double-ups got to do with anything in negative expectation games? Fourthly
and finally is there a more logical, mathematically correct and sensible business principle upon which
this often confusing and confused issue can be based?

6.1                 Key Principles
Let‟s first establish some key principles.

1.      “Money management systems are a bunch of junk!” ref 1 There is no system in a fixed negative
expectation game which changes the Casino advantage. Theoretical win equals turnover ref 2 multiplied
by edge (notice that in this well known and often used formula there is no mention of decreasing
theoretical win by dividing by a “system” factor.).

2.       In independent trial games sequences of results have no relationship between each other. The
Roulette wheel, dice, coins etc. have no memory and the results are distinct. Sequences or lists of
results may be a good road map of where you‟ve been but are useless in trying to determine where
you‟re going. The next result has the same probability as the last.

Particularly with this second key principle in mind, let‟s debunk our “expert‟s” theory of limiting table
maximums by a double-up factor. Consider two table games sitting right next to each other in a small
Casino. One, a $5 minimum table and the other, a $25 minimum table, both playing the same
independent trial game. On the first we have a minimum bet to maximum bet range of $5 to $80 and on
the second $25 to $400. Our intrepid gambler in this well managed “small” Casino starts her double-up
system with a $5 bet on Table One. The bet loses and so the system player then bets $10. This also
loses and so the bet is increased to $20, loses again. $40, loses again. $80, surely not but loses again
and because the Casino is “protected” by its limit spread the player is of course doomed, as a bet of
$160 is not permitted on Table One. But, the player then moves to Table Two and starts off with a bet
of $160, which loses and then bets $320. The game has no memory, right, so what‟s the difference if
she finishes the betting sequence on Table Two? Table One was “hot” or on a “streak” you say, but so
what? The map shows where you have been, not where you are going. So did the small, “well-
managed”
__________________________
ref 1
        Mason Malmuth.
ref 2
        the term turnover relates to total amount wagered throughout this document.
Casino, with a four time double-up philosophy suddenly become bigger, less “well-managed” or should

someone have barred the player‟s action or stuck an indelible sign on her forehead, “$5 to $80 player

only”? Clearly ridiculous, but an often argued point. “The limits are too loose.” “A system player will

take advantage of the spread.” “When they get ahead they are playing with our money and are more

dangerous if you give them higher limits.” “A $5 to $5000 table limit on Baccarat is ridiculous.” The

list goes on and on, with many opting for the conventional wisdom of either sixteen times or one

hundred and twenty eight times the table minimum. Notice also, the cavern here between small and

large, sixteen and one hundred and twenty eight!



6.2             Setting proper table limits

Enough of this, how should table limits be set properly?



Firstly, establish what the capital reserves of the company are. What are the shareholders‟ expectations

from the operation? Are they risk-averse and therefore averse to using capital reserves to pay losses or

fixed expenses? What are the longest and shortest periods that you must analyse? Can the shareholders

look to one month but no longer than one year, or can you fix longer term strategies with comfort?

What turnover volumes are experienced or forecast? What does the market expect in maximum betting

limits and what effect will not meeting these have on turnover? What profile of games are on offer, or

are expected to be on offer? What are the fixed and variable expenses associated with the operation?

Many other questions could be asked but essentially these are the most pertinent.



Bottom line safety is often intuitively linked to offering the lesser of two maximum bet limits.

However, this is volume dependent and market driven. For example it may, in fact, be safer to offer a

$250,000 table maximum, in comparison to a $50,000 table maximum. Why, because the market you

are attempting to attract may not respond to your offer under the $50,000 scenario, but if offered

$250,000 as a maximum would generate significantly greater turnover. Based then on the following,

you could calculate at what point this would be true:
Win percentage

Game variance

Variable expense percentages

Fixed expenses

Taxes, fees etc.

As an example consider the following game with equal-sized bets :-

Game:                                 Baccarat

Win percentage:                       1.25% ref 3

Variance:                             0.97 ref 4

Variable expenses:                    0.7% of turnover (indicative example only)

Fixed expenses:                       $500,000 per annum (example only)

Tax:                                  13.75% of win (example only)

Fees:                                 13.5% of after tax and expense profit. (example only)

The expected return of 1.25% is based on a mix where approximately 60% of the bets are placed on

Banker and 40% of the bets are on Player. It is assumed that N hands of equal bet size are played. The



__________________________
ref 3
        relative edge at the game of Baccarat based on relative probabilities of 0.5068 (bank) and 0.4932

(player) and a 60:40 mix of bets
ref 4
        average sum of squares for the game of Baccarat at a 60:40 mix of Bank and Player bets



standard deviation of a sample is equal to the standard deviation of the population (square root of the

population variance) divided by the square root of the sample size. Therefore the standard deviation of

the expected percentage return is

                    =  (97%) /  N

                    = 98.5% /  N

The expected percentage return represents a random variable which is normally distributed with mean

1.25 and standard deviation 98.5 /  (N). Then the quantity Z where
                Z = (y – 1.25) / s.d.

has approximately the standard normal distribution ie. the probabilities for the Z values are

approximately equal to the areas under the standard normal curve. Therefore the probability that the

return (Y) is negative ie. that the player wins after N equal-bet size games is

                Prob (Y  0)      = Prob (Z  (0 – 1.25) / s.d.)

                                  = Prob (Z  -1.25 N/98.5).

Therefore the unfavourable end of the 90% probability interval is obtained by solving for the percentage

return y where -1.645 represents the Z-score or number of standard deviations that y is to the left of the

mean

                (y – 1.25) N / 98.5 = -1.645 ref 5

Thus for N hands

                Y = N * 0.0125 – N * 1.645 * 0.985/ N

For example if N = 1000 then –38.7 units is the lower limit on loss in terms of a uniform bet size.



Prior to fixed expenses and fees, the following table is produced for the lower end of a 90% probability

interval (1 in 20 chance of the displayed result or worse occurring).



Table 1

Number of                Win              90% lower                         Win net of tax
Hands N                                   probability limit                 & commission

  1000                    12.5             -38.7                             -40.4

  5500                   68.8              -51.4                             -82.8

 10500                   131.3             -30.0                            -106.4

 15500                   193.8               -7.9                           -115.4

 20500                   256.3               24.3                           -122.5

 25500                   318.8               60.1                           -126.7

 50500                   631.3             267.2                            -123.0

100500                   1256.3            742.7                             -62.3

150500                   1881.3           1252.8                              27.0
The maximum loss point occurs at:

  34500               431.3            130.4                            -129.1

To calculate the effect of any table maximum bet limit merely requires the multiplication of the limit by

the numbers shown. Fixed expenses and fees can then be included to determine the net profit effect of




__________________________
ref 5
        normal distribution table value for a standard deviation that provides a 5% tail at either end of the

distribution



providing the limit as a “poor”, not “worst” case scenario for the shareholders to evaluate. More

extreme cases may also be demonstrated by altering the confidence interval to a 95% level (one chance

in forty of the result or worse occurring) or a 98% confidence interval (one chance in one hundred of the

result or worse occuring.) The determinant in which option to evaluate, is dependent on the

shareholders‟ risk-aversion, other income sources, capital reserves, long term strategic planning issues

and the expected period of business.

Mathematics

Hands = N                                      Win percentage = E%

Variance = V                                   Tax = T%

Commission = C%                                Fixed expenses = F

Fees = M%                                      Bet size = B

90% confidence limit = 1.645 ref 5                     (95% = 1.96, 98% = 2.33)

Win = N.E%

Lower confidence limit = (N.E%)-(1.645. (N.V))

Win net of tax and commission = (((N.E%)-(1.645. (N.V))).(1-T%)-(N.C%))

Net Profit = ((((N.E%)-(1.645. (N.V))).(1-T%)-(N.C%))-F).(1-M%).
From the calculation of the maximum loss point (net of tax and commission) it is possible to

calculate, based on the maximum loss net of all costs which the company is prepared to accept, the

maximum bet which could be offered.



From Table 1 (for the specific example provided) we have a maximum loss point of –129.1. If we

consider the maximum the company is prepared to lose as a positive number then:



(129.1B + F).(1-M%) = Maximum Loss

therefore B = ((Max.loss/(1-M%))-F)/129.1

A more general formula for determining maximum bet size is:

B = ((Max.loss/(1-M%))-F)/(Maximum loss point prior to fixed expenses and fees)



Fixed costs would be determined based on annual costs and an evaluation of the period required to

achieve the number of hands at the maximum loss point.



If, as an example, the maximum loss the company were prepared to accept was $10 million and fixed

costs equalled $500,000, then the maximum bet calculated would be $85,695.



It is important to remember that “Maximum loss” actually represents a probability of one in twenty of

this loss or greater occurring. More conservative numbers may be calculated by increasing the

confidence limit.



Of course not all bets occur at the maximum limit and therefore some degree of judgement needs to be

made as to the average bet size or preferably the forecast distribution of bet sizes. Thus $100,000 table

maximum may equate to average bets of $75,000 or a range of bets from $1 to $100,000 with the same

average but a different variance. But these are only estimates and the increased accuracy produced by

estimating bet distributions is easily lost. In most cases, it is more appropriate to keep it simple,

however, for those interested this will be expanded later.
In the above, what has been shown is a thinly-disguised evaluation of how to calculate what table

maximums should be provided for high level junket players. With limited cash reserves and low

turnover volumes, a strategy of offering $250,000 table maximums would be suicidal, or the Casino

would be gambling, if one also includes the other expense considerations. Even if the Casino could

generate 10,500 hands per annum, all at this level, then while turnover would be $2.625 billion, there

would exist a one in twenty chance that prior to fixed expenses and fees, the Casino would lose $26.6

million. Further, the maximum loss point would occur at 34,500 hands or $8.625 billion in turnover,

with a one in twenty chance of losing $32.275 million or more. If a single visit produced 1,000 hands,

then turnover would be $250 million and a one in twenty chance of losing $10.1 million or more would

exist. Clearly, extremes at this level of business exist, which suggest the need for large capital reserves,

and major shareholders who understand the complexity of the issues, and their long term vision of

growth. The other issue, implicit in this calculation is market demand, as while a $250,000 table

maximum does impart high risk, a lesser maximum limit may produce less short-term risk but higher

long-term risk after all costs are included, as well as depriving the company of market penetration and

growth. If, in the above example, hands played were increased to 20,500, yet with a $50,000 table

maximum, only 5,500 hands could be anticipated, then the following ten year scenario is of interest

(after fixed expenses and fees.)

Table 2

90% Probability interval lower limits.

Year             $250K max.                        $50K max.

1                -$26.9M                           -$4.0M

2                -$28.5M                           -$5.4M

3                -$25.9M                           -$6.4M

4                -$21.2M                           -$7.1M

5                -$15.1M                           -$7.7M

6                -$8.0M                            -$8.2M

7                -$0.1M                            -$8.6M

8                $8.3M                             -$8.9M

9                $17.2M                            -$9.2M
10              $26.5M                            -$9.5M



These cumulative totals demonstrate the volume dependence and demand matching elements of

establishing appropriate limits for a business segment. Incorporating cash reserves and income streams

(positive net cash flows) provides for a determination of whether or not the table maximums have been

appropriately set. If, in the above scenarios, both companies had large cash reserves and net profit

income streams from core business in excess of say $40 million per annum, then offering a $250,00

table limit is clearly the preferred option. On the other hand, if cash reserves are minimal and income

streams from core business is only $4 million to $5 million per annum, then either the $50,000 table

limit or not even entering the market would be preferred. Theoretical profit after all costs is only $0.47

million per annum as opposed to the substantial risk of totally eroding profit. Other factors such as

whether or not the company is publicly listed and the effect of profit fluctuations on market valuation

need also to be considered.



Once determined, however, the maximum limits should drive all other game limits within the Casino,

provided the maximum bet limits were based on these premises and the maximum loss points used, not

the annualised projected figures. A high-limit scenario for the junket segment in conjunction with a

low-limit grind philosophy for the core business is nonsensical. While management may segment

business into grind, premium and junket for internal reporting, it would only sub-optimise the

performance of the entire operation if, on the main gaming tables for example, limits were restricted to

$5 to $200 bet spreads, while in the premium room bets of $250,000 per hand could be made. Of course

this is still market driven, and if the $5 to $200 limit entirely meets market demands and no greater

action could be derived by increasing the maximum limit then so be it, but if the opportunity existed to

increase turnover, then the fact that a $250,000 table limit is provided elsewhere in the Casino should

drive the other maximum bet limits.



While these principles have been established here to act as a guide for setting Baccarat table limits for

junkets, the same methodology can be used for any size or style of Casino operation. Again, it is

necessary to understand the company‟s internal position and cash flows, the market demands, fixed and
variable expenses, taxes, fees and game profiles. Armed with this information, it is possible to

calculate the maximum bet levels which the company can reasonably be expected to accept, without

sending the operation bankrupt. This may be more difficult than our “expert‟s” strategy of setting limits

in relation to double-up spreads, however, why use something simple if it is basically wrong, illogical

and only enforces incorrect assertions? The only instance where bet spreads should be considered as

relating both the lower and upper values, would be dependent trial games where a player may gain an

advantage (ie. card counting at Blackjack.). In this case, depending on the rules and regulations in

place, limiting bet spreads can negate the overall advantage of the player.



In fixed negative expectation games, however, consideration need only be given to the elements

described previously.



Calculations such as the above should be a pre-requisite from any well-managed Casino‟s point of view,

and should obviously be coupled with market research to determine whether the demand exists to reach

the number of hands forecast at the maximum loss point within a reasonable time period.



Expansion of several of the issues raised above is provided for the more interested reader. These issues

relate to the calculation of the maximum loss point, the effect of bet distributions, and how this theory

may actually be applied in a Casino that doesn‟t market to high bet limit players.



6.3     Maximum Loss Point

Firstly, the maximum loss point, of the left tail of a probability interval for win net of tax (and

commission if applicable), can be determined by establishing the relevant number of hands that will

minimise the loss. The loss is minimised at the turning point in the curve which can be established by

differentiating the function of the curve. The only variable in the equation for determining win net of

tax is the number of hands. Therefore, by differentiating with respect to the number of hands, it is

possible to calculate that number of hands which will minimise the loss.

Let:

Number of Hands = N
Tax = T%

Commission = C%

Win percentage = E%

Variance of a single game = V

Probability limit = Z (1.645 for 90% limit, 1.96 for 95% limit etc.)

Profit net of tax and commission = P

Then:

P = (E%.N-Z. (N.V)).(1-T%)-N.C%

P = N.(E%.(1-T%)-C%)-Z.(1-T%). (N.V)

dP/dN = E%.(1-T%)-C%-1/2.Z.(1-T%). (V/N)

The turning point occurs where the differential equals zero.

0 = E%.(1-T%)-C%-1/2.Z.(1-T%).(V/N)

Z/2.(1-T%)(V/N) = E%.(1-T%)-C%

(N) = {Z.(1-T%)/(2.(E%.(1-T%)-C%))}.(V)

N = ((Z.(1-T%))/(2.(E%.(1-T%)-C%)))2.V

The following is provided by way of example:-

Game:                            Baccarat

Win percentage:                  1.25% (see ref3)

Variance:                        0.97 (see ref4)

Commission:                      0.7% of turnover (indicative example only)

Tax:                             13.75% of win (example only)

Probability interval:            90% therefore Z = 1.645

Then:

N = ((Z.(1-T%))/(2.(E%.(1-T%)-C%)))2V.

N = ((1.645.(1-13.75%))/(2.(1.25%.(1-13.75%)-0.7%)))2.0.97.

N = 34,136.

and,

P = N.(E%.(1-T%)-C%)-Z.(1-T%).(N.V)
P = 34,136.(1.25%.(1-13.75%)-0.7%)-1.645(1-13.75%).((34,136).(0.97))

P = -129.1

This compares to the result shown in Table 1 on Page 5 of:

The maximum loss point occurs at:

Number of                Win              90% confidence                   Win net of tax
hands N                                   lower limit                      & commission

34500                    431.3            130.4                            -129.1



Calculation in the above manner represents a more efficient method than tabling a series of results and

establishing the maximum loss point from that listing. As the number of hands required is generally

relatively low this is a technique which is more readily applicable in high limit junket operations.

Otherwise the establishment of the forecast number of hands (decisions) in the minimum period under

consideration should over-ride this where that result is greater than the number of hands at the

maximum loss point.



Secondly, let us consider how to take into consideration the effect of various bet distributions on what

table maximum bet limit can be set with comfort. Clearly, the simple method would be to assume that

all bets occurred at the maximum bet limit and thus adopt whatever maximum limit had been calculated

based on the maximum loss which the shareholders would accept. This, however, would be a highly

conservative approach as it would be extraordinarily rare for all bets to occur at the maximum limit.

Indeed, such an approach, while simple, could lead to the adoption of a table maximum bet limit that

sub-optimised the overall Casino‟s performance by inhibiting turnover. To address this the following is

provided:
6.5     Effect of Variable Bet Distributions

Consider how a variation in bet distribution will affect the variance of the expected return to player.

Assume that the average bet size is $100,000 with the following distribution.



  Bet size = x            Frequency = f                       x.f                       (x)2.f

      150,000                        15%                   22,500             3,375,000,000

      125,000                        20%                   25,000             3,125,000,000

      100,000                        35%                   35,000             3,500,000,000

        75,000                       15%                   11,250               843,750,000

        50,000                       10%                    5,000               250,000,000

        25,000                        5%                    1,250                31,250,000

SUM                                  100%                 100,000           11,125,000,000

When the bet size is represented as a relative frequency as illustrated above the standard deviation is as

follows :



Standard deviation       = (sum (x2.f) – (sum (x.f))2)

                         = (11,125,000,000 – 100,0002)

                         =  (11,125,000,000 – 10,000,000,000)

                         = 33,541



One can assume that the variance of the expected return when all bets are fixed at some value B is

approximately equal to V.N, where V is a constant close to 1 and relates to the variance of the game in

question (ref 4) and N is the number of hands dealt. Then the standard deviation of the expected return

when there is a bet distribution with a mean bet size of B is approximately equal to:

            B.(V.N.(1 + (SB/B)2))

Where SB is the standard deviation of the variable bet distribution.
Consider the win W net of tax and variable expenses assuming N hands of equal bet size B

          W = [ (NE – 1.645(NV)) (1-T) –NC] B

where     N =Number of Hands

          E = Expected Win Percentage

          V = Variance of Baccarat Hand with Constant Bet Size

          T = Tax Rate

          C = Commission Rate



Then the win for a variable bet distribution with a mean bet size Bav and a variance of VN (1 + (SB/Bav)2

is

          W = [ (NE –1.645NV(1 + (SB/Bav)2 ))(1-T) – NC] Bav



If Bmax is the maximum fixed bet size which will produce an acceptable risk profile then by equating the

win net of tax and variable expenses of N hands at bet size Bmax to N variable bets with a mean Bav it is

possible to determine a limiting factor on the variance of the variable distribution such that the

maximum allowable risk is not exceeded.



Let F be the factor which accounts for the increased variance of the variable bet distribution. Then

solving for F in the following equation

[(NE –1.645(NVF))(1-T – NC] Bav = [(NE –1.645(NV) )(1-T) – NC] Bmax

                           -1.645(NVF) = [NE –1.645(NV) – NC/(1-T)] Bmax/Bav – NE

                                                                                 + NC/(1-T)

                                          F = {1/1.645(NV))(NE – NC/(1-T))(1 - Bmax/ Bav)

                                                                               + Bmax/ Bav }2

Therefore, provided 1 + (SB/ Bmax)2 = F is less than the right hand side of the above equation, the overall

bet distribution will satisfy the risk constraints.
Thus in relation to the maximum bet size that may be offered, based on the shareholders

acceptance of a loss point, the bet limit represents a bet distribution with mean, x.f (Bav), and variance,

SB, where the mean bet multiplied by one plus the square of the standard deviation of the bet

distribution divided by the mean bet is equal to what may be referred to as the effective bet limit.



Effective Bet Limit = Bav (1 + (SB/ Bmax)2).



The effective bet limit used then to calculate a maximum loss point would be greater than the mean but

less than the maximum bet on offer, if bet sizes had some range. This is an appropriate methodology if

bet sizes and frequencies can be predicted with some degree of accuracy, however, it is vulnerable to a

situation where the bet distribution actually achieved is skewed towards much higher bet levels than

anticipated. Then the shareholders may experience greater fluctuations in profits than desired or losses

which they were not prepared for. The other potential use for this is to determine whether or not based

on known bet distributions the actual results fall with an acceptable range.



As an example of how this information may be used, let us consider the following:



Maximum bet = $85,695 (refer to page 156 example) to incur a maximum potential loss of $10 million

after all costs.



An average bet of $80,000 with the following range and distribution could be applied and still produce a

lesser maximum loss point than the shareholders accepted.



The limiting value F when the average bet size Bav is $80,000 and the maximum bet size Bmax is $85,695

is as follows

 F= (1/(1.645(NV))(NE – NC/(1-T))(1 - Bmax/ Bav) + Bmax/ Bav }2

   = {1/(1.645(34,500.0.97))(34,500.0.0125-34,500.0.007/(.08625)).

      (1-85,695/80,000)=85,695/80,000}2
  = 1.07207

  Bet size = x            Frequency = f                      x.f                       (x)2.f

      120,000                        2.5%                  3,000               360,000,000

      100,000                      35.0%                  35,000             3,500,000,000

        80,000                     32.5%                  26,000             2,080,000,000

        60,000                     22.5%                  13,500               810,000,000

        40,000                       5.0%                  2,000                 80,000,000

        20,000                       2.5%                   500                  10,000,000

SUM                                 100%                  80,000             6,840,000,000



Standard deviation     = (sum (x2.f) – (sum (x.f))2)

                       = (6,840,000,000 –80,0002)

                       = 20,976.

Effective Bet Limit    = Bav . (1 + (SB/ Bav)2).

                       = 80,000. (1 + (20,976/80,000)2)

                       = 80,000. (1.06875)

                       = 85,500.



Note that the actual value of 1 + (SB/ Bav)2 equals 1.06875 for the above distribution which is less than

the allowable maximum calculated at 1.07207.



Therefore the game will behave as if there were 0.933N hands of size $85,000 rather than N hands with

equal bet size $80,000. Based on 0.933N hands of fixed bet size $85,500 there is a one in twenty

chance that the company will lose $9.98M which falls within the acceptable risk profile.



The effective bet limit at $85,500 is less than $85,695 and therefore implies that it should be appropriate

to allow a table maximum bet limit of $120,000 on the assumption that the distribution of bets actually

experienced will reflect the above. Clearly, a reasonably accurate assessment of how the market will
respond to this range of limits is required, however, if this sort of distribution is achieved then

there is only a one in twenty chance that the company will lose $10 million or more based on the

assumptions regarding fixed and variable expenses also being accurate.



It is important to recognise that this must be market driven or historical and cannot be derived a priori.

Of interest is that if a priori determination were attempted, a higher table maximum bet limit could be

provided, but at the cost inevitably of deriving a lower average bet and thus reduced profitability, if the

shareholders‟ maximum loss point is not otherwise increased. This would be a direct result of possibly

falsely attempting to increase the bet range and therefore, implicitly, increasing the variance of the bet

distribution.



To finally evaluate how all the above may be applied practically in a Casino operation that does not

market to high-end players, the following is provided.



6.6              Non High-End Casino Operation

To calculate the bet level that may reasonably be offered requires the following in this case :

1. Ignore fixed expenses and project all costs at a variable percentage based on fixed and variable

levels, and represent this in place of a commission percentage. This removes the interdependence that

would otherwise link the level of fixed expenses to the period under consideration.

2. Calculate the number of decisions achieved per day based on the average table hours, and decision

rates per hour per table.

3. Determine the length of the period which is to be evaluated. 1 day, 1 week, 1 month, or 1 year.

4. Estimate the maximum loss that the shareholders will accept for the period under consideration.

5. Calculate the maximum bet on the above basis taking into account bet distributions and market

matching.



As an example of this the following is provided:

Average table operating hours                      = 25 tables x 18 hours
                                                 = 450

Average decisions per hour per table             = 50

Total decisions per day                          = 22,500

Total decisions per week                         = 157,500



Win net of tax and variables expenses and fees are

              W = (((N.E%)-(1.64.(N.V.SB))).(1-T%)-(N.C%)).(1-M%)

For simplicity if the game considered is totally Baccarat with no opposing bets and,

if T          =13.75%

N             = 157,500

V             = 0.97

E%            = 1.25%

C%            = 0.7%

M%            = 13.5%

Consider the scenario where the shareholders were prepared to experience a loss of $350,000 or greater

in any one week with a probability of occurrence of one in twenty. Based on market research and past

experience an assessment can be made regarding probable bet distributions in this operation. The

following three betting scenarios highlight the effect that high limit betting has on the weekly risk

profile.



                          Bet Distribution 1

    Bet size = x           Frequency = f                      x.f                        x2.f

           7000                     1.5%                 105.00                     735,000

           2500                     2.5%                   62.50                    156,250

            500                   10.0%                    50.00                      25,000

            100                   26.0%                    26.00                       2,600

             50                   35.0%                    17.50                         875

             25                   25.0%                     6.25                         156

SUM                                100%                  267.25                     919,881
Standard deviation          = (sum (x2.f) – (sum (x.f))2)

                            = (919,881 -2672)

                            = 921.

Equivalent Bet Limit        = Bav (1 + (SB/ Bav)2).

                            = 267.(1 + (921/267)2)

                            = 3,442



In other words, instead of behaving like N hands with equal bet size $267, this will behave like 0.0777N

hands with equal bet size $3,442. If N = 157,500 which implies that 0.0777N = 12,229 then the win net

of tax etc. is

W =((12,229 x 0.0125 – 1.645(0.97x12,229)) x (1 - 0.1375) – 12,229 x 0.007).(1-0.135)

   = -93.7



As the size of the bets are now assumed to be $3,442 instead of $267 this implies a 90% lower

probability limit of

   = -93.7 x 3,442

   = -$322,365



                        Bet Distribution 2

   Bet size = x          Frequency = f                        x.f                     x2.f

           5000                       2%               100.00                    500,000

           2500                       3%                 75.00                   187,500

             500                  9.5%                   47.50                     23,750

             100                 21.5%                   21.50                      2,150

                 50              29.0%                   14.50                        725

                 25              35.0%                       8.75                     281

SUM                               100%                 267.25                    714,344
Standard deviation           = (sum (x2.f) – (sum (x.f))2)

                             = (714,344 -2672)

                             = 802

Equivalent Bet Limit         = Bav (1 + (SB/ Bav)2).

                             = 267.(1 + (802/267)2)

                             = 2,673

This behaves like 0.10N hands with equal bet size $2,673 and the win net of tax etc. is

W =((15,748 x 00125 – 1.645.(0.97x15,748).

      (1 - 0.1375) – 15,748 x 0.007).(1-.135))x2,673

   = -267,725



                        Bet Distribution 3

   Bet size = x          Frequency = f                        x.f                         x2.f

          10000                        1%               100.00                  1,000,000

          5000                         2%               100.00                    500,000

           500                         5%                 25.00                    12,500

           100                       15%                  15.00                      1,500

            50                       32%                  16.00                           800

            25                       45%                  11.25                           281

SUM                               100%                  267.25                  1,515,081

Standard deviation           = (sum (x2.f) – (sum (x.f))2)

                             = (1,515,081 -2672)

                             =1202

Equivalent Bet Limit         = Bav (1 + (SB/ Bav)2).

                             = 267.(1 + (1202/267)2)

                             = 5,669

This bet distribution will behave like 0.047N hands with equal bet size $5,669 and the win net of tax

etc. is
W =((7,425 x 00125 – 1.645.(0.97x7,425)).

     (1 - 0.1375) – 7,425 x 0.007).(1-0.135))x5,669

   =-452,727



Whilst bet distributions 1 and 2 fall within what is deemed as an acceptable level of risk (in this case a

one in twenty chance of losing $350,000) the large variance of the bet sizes in bet distribution 3 cause

the risk to increase to above $450,000.



Therefore if a very high degree of confidence could be placed in the assessment of the bet distribution,

then it would not be inappropriate to offer a $7,000 table maximum bet in this Casino, based on what

the shareholders have indicated that they are prepared to lose on a weekly basis. If, however, a player or

players come into the Casino and bet substantially more than recognised in the market analysis, there is

a real danger of experiencing losses at a much greater level as demonstrated by distribution 3. Thus, if

that is not acceptable at all, then a much more conservative bet range should be provided for, with

maybe a $5,000 table maximum bet being allowed, or if the shareholders were totally intolerant of any

greater loss within the probability allowance, a maximum limit of $3,500 could be provided depending

on a re-assessment in both cases of the bet distribution and frequency of bets. Once established, this

then would form the upper limit available on any of the games with lower limits, stratified if required, to

allow egos and social groupings as the market requires. Of course not all games are the same within the

Casino and different game profiles would exist. However, this would be a reasonable framework for

establishing table maximum limits within the operation, as we have used a “base case style” game with

low house edge and low game variance. This bet limit would then provide the even money bet

maximum for all games with higher pay-off bets being discounted appropriately. Alternatively, it

would be possible to build the entire Casino profile based on an assessment of the individual games on

offer and the markets for each. To establish box or player maximum limits from the calculated table

maximum limits merely requires a division by the number of boxes on offer and the rules pertaining to

the number of players per box. Otherwise what has been calculated is a maximum bet per table per

round, or what is commonly referred to as a table differential.
Another use of this particular information would be to assess daily, weekly, monthly and yearly

performance and determine whether or not the actual results fell within an acceptable range, based on

probabilistic considerations.



From the above example the following may be calculated as the range of Casino win (prior to expenses

and fees) which would be achieved, with a probability of results falling outside these parameters, being

likely to occur on one occasion in twenty :

Win = BavN.E%

Lower probability limit = BavN.E%-1.645. Bav.(V.N.(1 + (SB/B)2))

                                 Lower limit                   Average               Upper limit

Daily                               -157,897                     75,164                   308,225

Weekly                                -90,474                  526,128                  1,142,770

Monthly                              978,393                  2,254,922                 3,531,451

Yearly                            22,844,142                27,284,555                 31,724,967



Taking into account taxes, expenses and fees the following net profit forecasts may be presented.



                                 Lower limit                   Average               Upper limit

Daily                               -154,211                     19,668                   193,546

Weekly                              -322,365                   137,673                    597,712

Monthly                             -362,342                   590,028                  1,542,399

Yearly                             3,826,519                  7,139,345                10,452,170



Clearly this type of information is essential in establishing possible cash flow discrepancies and whether

or not monthly and yearly statements of profit and loss are reasonable. For example, once displayed in

this manner, the shareholders may either accept the risk implied, based on the assumptions made and the

table maximum bet limits offered, or request a review of those limits to establish tighter, more
consistent returns. It should be noted, at this point, that what has been assessed is a situation

where all bets made at a table are non-cancelling. That is, that bets have been made by the players on

the table on the same proposition and not on opposing bets where the Casino essentially takes no risk.

At Baccarat, for example, if one player has $5 on “Player”, and another player has $5 on “Banker”, the

Casino either draws or wins. If “Player” wins, one bet pays the other; but if “Banker” wins, the Casino

takes 5%. In reality the Casino takes a risk only on non-cancelling bets, but must be prepared to accept

the risk associated by allowing non-cancelling bets at the bet limits provided. When assessing actual

results, in relation to the probability of occurrence based on bet distribution information, it is critical

that this be understood.



Another piece of information that may be of use is the calculation of the probability of ruin, from the

Casino‟s perspective, if all bets were made at the table maximum and all bets were non-cancelling.



If the table maximum were $7,000 and the Casino had capital of $5,000,000 then the effective number

of units (a) which the Casino possesses is : $5,000,000/$7,000 which equals 714. If the game under

consideration is Baccarat, with a probability of the house winning (p) of 0.50625 and a probability of

losing (q) of 0.49375, then based on the following formularef6 we have :

risk = (q/p)a

risk = (0.49375/0.50625)714

risk = 0.00000002



The Casino is not taking much of a chance of going to ruin, and starting with such a large amount of

capital, in relation to the maximum bet allowed, would steadily get richer if that capital could

accumulate.




ref6
       Allan N. Wilson, The Casino Gambler‟s Guide: Enlarged edition page 264.
6.7             Conclusion

The above information has hopefully assisted the reader in understanding how table maximum bet limits

can be established on sensible business principles and how knowledge or forecasts of bet distributions

can be put to effective use. Armed with this type of information, it is possible to explain to shareholders

their risk expectation from the Casino‟s activities and account for actual results by relating to a

probability of occurrence. I would hope that analysts and managers would use this to their best

advantage and that this article has been of some value.



Dated 30/11/94 14:30



Acknowledgements :

Pryna Ypma for reviewing and providing some of the mathematics.

Peter Burrage for proof reading and correcting the article.

Bill Eadington, Peter Griffin, and Jim Kilby for their support.

								
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