Blackjack Myths vs. Reality

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```					 Blackjack: Myths vs. Reality

Group K
Andrew Kerr             Andrew Phillips
Sven Skoog              Woj Wrona
Agenda

   Blackjack: The Game
   Assumptions
   Simulation
   Data Findings
   Decision Tree
   Descriptive Analysis
Blackjack: The Game

   Each player is dealt two cards and is then offered the
opportunity to take more.
   The hand with the highest total wins as long as it doesn't
exceed 21; a hand with a higher total than 21 is said to
bust. Cards 2 through 10 are worth their face value, and
face cards (Jack, Queen, King) are also worth 10.
   An ace's value is 11 unless this would cause the player
to bust, in which case it is worth 1. A hand in which an
ace's value is counted as 11 is called a soft hand,
because it cannot be busted if the player draws another
card.
Assumptions

   \$100 bet / hand
   No splitting, double down, insurance
   Samples with blackjack bonus and without bonus
Simulation
Percentage of Blackjack

Assumption: 10,000 Hands   Mean: 0.0454 or 4.5%
Percentage of Bust

Assumption: 10,000 Hands   Mean: 0.2803 or 28.03%
Normality of 1, 2 and 3 Card
Totals                                                                                                                  300
Histogram of 3-Card-Sum
Normal
Mean 19.84
StDev 4.915
N      3333
250

200

Frequency
150

Histogram of 2-Card-Sum
100
Normal
Mean 14.47
500                                                                         50
StDev 4.121
N      5000

400                                                                          0
8   12       16       20   24      28
Frequency
3-Card-Sum

300
Face card probability = 30%
200

Histogram of 1 Card
100
Normal
Mean 7.275
3000                                           StDev 2.952                0
N     10000                     6   9       12      15    18      21   24
2500                                                                                       2-Card-Sum

2000
Frequency

1500

1000

500

0
2   4     6          8   10   12   14
Card

Approaching Normality as Card Count Increases
Why Dealer Stays at 17?

Dealer            16                17                 18
Stays at..
Blackjack         4.7%             4.6%               4.9%

Bust          20.42%            28.23%              37.53%

Dealer         17.74%            27.85%              23.33%
Beats 17
Values derived from 10,000 card simulation
2 Card Total Confidence Interval

Probability of achieving a 2 card total 18 ≤ 2 cards ≤ 21 is 20.9%
3 Card Total Confidence Interval

Probability of achieving a 3 card total 18 ≤ 3 cards ≤ 21 is 37.1%
Regression of Aces vs. Wins
   Do Aces result in Wins?
 Many players assume that an Ace increases the odds of winning
a hand

   Regression model confirms that Aces lead to a very slight player
edge

   Any edge is likely attributable to the flexibility of the Ace (1 or 11)
but not the fact that the Ace gives you an 11 ( no more powerful
that any other pairing, i.e. 8,3 or 7,4 that leads to an 11).
Regression of Aces vs. Wins
Two Card Play                     Four Card Play

Three Card Play
Player=15, Dealer shows 7
7.7%    0.0769
A makes 16
0    -100      A makes 16       7.7%      0.0769
2 makes 17   7.7%    0.0769                           0     -100
100     0
3 makes 18   7.7%    0.0769     2 makes 17       7.7%      0.0769
200    100
100        0
Hit             TRUE       Chance
0       -30.79
3 makes 18       7.7%      0.0769
4 makes 19   7.7%    0.0769
200    100                         200       100
7.7%    0.0769
5 makes 20                            Chance
200    100
6 makes 21   7.7%    0.0769           -30.79
200    100
53.9%   0.5386     4 makes 19       7.7%      0.0769
else BUST
0    -100                        200       100
2-Cards = 15          Hit? (Card 3)
-100         -30.79                                            5 makes 20       7.7%      0.0769
Stay           FALSE          0
0        -100
200       100
A makes 16   7.7%      0
6 makes 21       7.7%      0.0769
0    -200
2 makes 17   7.7%      0                          200       100
200     0
7.7%      0        else BUST       53.9%      0.5386
3 makes 18
400    200                             0     -100
Double         FALSE       Chance
-100      -61.58
4 makes 19   7.7%      0
400    200     Win              Push       Lose
5 makes 20   7.7%      0
400
7.7%
200
0
30.7%            7.7%       61.5%
6 makes 21
400    200
else BUST    53.9%     0
0    -200
Player=17, Dealer shows 8
A makes 18    7.7%    0.077
100    0        A makes 18      7.7%   0.077
7.7%    0.077
2 makes 19
200   100
100     0
7.7%    0.077
3 makes 20
200   100       2 makes 19      7.7%   0.077
4 makes 21    7.7%
200
0.077
100
200    100
5 makes 22    7.7%    0.077
3 makes 20      7.7%   0.077
0   -100
Hit                TRUE        Chance                                        200    100
0       -46.16
6 makes 23    7.7%    0.077
4 makes 21      7.7%   0.077
0   -100
7 makes 24    7.7%    0.077                      200    100
0   -100
8 makes 25    7.7%    0.077     5 makes 22      7.7%   0.077
0   -100
9 makes 26    7.7%    0.077                        0    -100
0   -100
30.8%   0.308
Chance
10 makes 27
0   -100
Decision
-46.16
2 cards = 17
-100           -46.16
7.7%   0.077
Dealer 18                Stay              FALSE           0                         6 makes 23
0        -100                                           0    -100
A makes 18    7.7%    0.000
200    0
7 makes 24      7.7%   0.077
2 makes 19    7.7%    0.000
400   200                          0    -100
3 makes 20    7.7%    0.000
400   200
8 makes 25      7.7%   0.077
4 makes 21    7.7%    0.000
400   200                          0    -100
5 makes 22    7.7%    0.000
Take only one card                     0   -200      9 makes 26      7.7%   0.077
FALSE        Chance
Double
-100      -92.32
0    -100
7.7%    0.000
6 makes 23
0   -200      10 makes 27    30.8%   0.308
7 makes 24    7.7%
0
0.000
-200
0    -100
8 makes 25    7.7%    0.000
0   -200
9 makes 26    7.7%
0
0.000
-200
Win              Push    Lose
10 makes 27   30.8%   0.000
0   -200    23.0%            7.7%    69.2%
Player=11, Dealer shows 7   A makes 13    7.7%    0.000

7.7%
0   -100
0.000     A makes 12     7.7%    0.077
2 makes 13

7.7%
0   -100
0.000
0    -200
3 makes 14

7.7%
0   -100
0.000     2 makes 13     7.7%    0.077
4 makes 15
0   -100
0    -200
5 makes 16    7.7%    0.000
0   -100
3 makes 14     7.7%    0.077
Hit               FALSE        Chance
0        15.39                                         0    -200
6 makes 17    7.7%    0.000
100    0
4 makes 15     7.7%    0.077
7 makes 18    7.7%    0.000
200   100                         0    -200
8 makes 19    7.7%    0.000
200   100
5 makes 16     7.7%    0.077
9 makes 20    7.7%    0.000
200   100                         0    -200
10 makes 21   30.8%   0.000
200   100           Chance
2 cards = 11                 Decision
-100            30.79                                                    30.79
Stay              FALSE           0
0        -100
6 makes 17     7.7%    0.077
A makes 13    7.7%    0.077
0   -200                      200     0
2 makes 13    7.7%    0.077
0   -200
7 makes 18     7.7%    0.077
3 makes 14    7.7%    0.077
0   -200                      400    200
4 makes 15    7.7%    0.077
0   -200
8 makes 19     7.7%    0.077
5 makes 16    7.7%    0.077
Take only one card                     0   -200                      400    200
Double             TRUE        Chance
-100       30.79                       9 makes 20     7.7%    0.077
6 makes 17    7.7%    0.077
200    0                        400    200
7 makes 18    7.7%    0.077
400   200       10 makes 21   30.8%    0.308
8 makes 19    7.7%    0.077
400   200                       400    200
9 makes 20    7.7%    0.077
400   200
10 makes 21   30.8%   0.308   Win             Push    Lose
400   200

53.8%           7.7%    38.4%
Player=15, Dealer shows 7                                                                                                            7.7%    0.00591361

18                                                                                                                                                                               16
A makes 17

7.7%     0                                                                                                                100       0
A makes 17    7.7%        0.00591361
A makes 19                                                                                                              2 makes 18   7.7%
200
0.00591361
100

200   100                                                                                                3 makes 19   7.7%    0.00591361                                            100           0
200      100
Hit            TRUE       Chance
2 makes 18    7.7%        0.00591361
2 makes 20   7.7%     0                                                                                             0       -30.79
7.7%    0.00591361
4 makes 20
200      100                                                200          100
200   100                                                                                                5 makes 21   7.7%
200
0.00591361
100
7.7%        0.00591361
else BUST    61.6%   0.04733195                            3 makes 19
Hit         FALSE        Chance                                                                  A makes 16    7.7%    Hit? (Card 4)
0      -100
200          100
0         -30.79

0       -53.86                                                                                        Stay           FALSE
0
0
-100                           Hit            TRUE        Chance
A makes 18   7.7%        0

7.7%     0                                                                                                                200      100                           0       -30.79
3 makes 21                                                                                                              2 makes 19   7.7%        0
200      100
4 makes 20    7.7%        0.00591361
200   100                                                                         Hit            FALSE
0
Chance
-38.48
3 makes 20   7.7%        0                                                 200          100
else BUST    76.9%    0                                                                                                                200
7.7%
100
0
4 makes 21
200      100
5 makes 21    7.7%        0.00591361
0   -100                                                                                               else BUST    69.2%
0
0
-100
200          100
2 makes 17    7.7%    Hit? (Card 4)

Hit? (Card 4)                                                                                                      0
Stay
0
TRUE       0.0769
else BUST     61.6%       0.04733195
100         0

100                                                                                                                                     A makes 19   7.7%
200
0
100
0          -100
2 makes 20   7.7%        0

TRUE         0.0769                                                                                                                              200      100        Hit? (Card 4)
Stay                                                                                                                   Hit            FALSE      Chance
0       -53.86
-30.79
200        100                                                                                                                3 makes 21   7.7%
200
0
100
else BUST    76.9%       0
Stay           FALSE          0
0      -100

19                                                                                                                                                                                                   0        -100
3 makes 18    7.7%    Hit? (Card 4)

A makes 20   7.7%     0                                                                      0
Stay
100
TRUE       0.0769
200        100

200   100                           Hit             TRUE
0
Chance
-25.467751

17
A makes 20   7.7%        0

Hit         FALSE        Chance                                                                                        Hit            FALSE      Chance
200      100
A makes 18     7.7%                0
0       -69.24

0       -69.24                                                                                                               2 makes 21   7.7%
200
0
100
200             100
84.6%       0

7.7%     0
else BUST
0      -100
2 makes 19     7.7%                0
2 makes 21                                                                 4 makes 19    7.7%    Hit? (Card 4)
0          100
200             100
200   100                                                                         Stay           TRUE
200
0.0769
100
A makes 21   7.7%        0
Hit            FALSE        Chance
else BUST    84.6%    0                                                                                         FALSE      Chance
200      100
Hit
0       -84.62                                            0         -38.48
0   -100                                                                                               else BUST    92.3%       0

5 makes 20    7.7%    Hit? (Card 4)
0      -100
3 makes 20     7.7%                0
Hit? (Card 4)                                                                                                      0
Stay
100
TRUE       0.0769                                                                    200             100
200        100

100                                                                                        6 makes 21    7.7%          0.0769
7.7%                0
else BUST
200
53.9%
100
0.5386
4 makes 21
Stay        TRUE         0.0769                    2-Cards = 15          Hit? (Card 3)
0          -100
200             100
-100    -25.467751

200        100                                           Stay       FALSE
0
0
-100                                                                                                 else BUST     69.2%                0
7.7%            0
A makes 16
0          -200                                                                                             0           -100
7.7%            0

A makes 21   7.7%     0                                                    2 makes 17
200           0
Hit? (Card 4)
20                                    200   100                           Double     FALSE
-100
3 makes 18

Chance
-61.58
7.7%
400

7.7%
0
200

0
0

Hit         FALSE        Chance                                                                  4 makes 19
400          200
Stay            TRUE         0.0769
5 makes 20    7.7%            0

0       -84.62                                                                  6 makes 21
400
7.7%
200
0
100             0
400          200
53.9%           0

else BUST    92.3%    0                                                    else BUST
0          -200

0   -100
6 makes 21                                     7.7%                                              0.0769
Hit? (Card 4)
100                                                                                             200                                                  100
Stay        TRUE         0.0769                   else BUST                                      53.9%                                             0.5386
200        100                                                                                 0                                         -100
House Edge (and Sensitivity)
…many complicating factors…

   Play on Hunches (ex: “stop on 17”), no Split, no Double      5%-15%
   „Educated Hunches‟ (modified basic strat.), Split + Double   3%-5%
   Basic Strategy (perfect play), 8-decks, blackjack pays 3:2   0.5%
   Basic Strategy (perfect play), 1-deck, blackjack pays 3:2    ≈ 0%
(not typical)

   Basic Strategy (perfect play), 1-deck, blackjack pays 6:5      ≈ 1.4%
   Basic Strategy plus variable-bet card counting                 ≈ 1.0%
(plus broken kneecaps)

   How much difference does splitting/doubling-down make?        ± 3.5%
   How much difference does blackjack payoff make?               ± 1.3%
   How much difference does surrender make?                      ± 0.8%
   How much difference from deviations/slip-ups?          1 slip/hr ≈ 1%
(basic strategy becomes hunch)
Two, Three, and Four Card Game
Payout Over Time
   House has distinct advantage over the player as additional cards are
played.

Player           45.70%          40.47%          21.16%
Dealer           47.48%          55.90%          77.92%
Push             6.82%           3.63%           0.92%

   The house edge results from the fact that the player acts first and risks
busting before the dealer.
Two, Three, and Four Card Game
Payout Over Time
The End

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