THE GAME OF PIG by wuyunyi

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									THE GAME OF PIG

     PROBABILITY
        AND
   EXPECTED VALUE
            THE GAME OF PIG

                              IF YOU
ROLL A
                              ROLL A
SIX SIDED
                              1, THEN
DIE
                              YOUR
                              TURN IS
                              OVER
PIG STRATEGIES




WRITE DOWN THE BEST
     STRATEGY
WAITING FOR A DOUBLE




A DOUBLE MEANS HAVING THE
SAME NUMBER SHOW ON BOTH
           DICE
      GAMBLERS FALLACY


WE WILL CALL THREE
IDENTICAL FLIPS IN A
ROW A TRIPLET
        VOCABULARY
•THEORETICAL PROBABILITY
 – IS PROBABILITY DETERMINED ON
   THE BASIS OF A MODEL
•OBSERVED PROBABILITY
 – IS PROBABILITY BASED ON ACTUAL
   RESULTS OF PAST EVENTS
  WHAT ARE THE CHANCES?

THEORETICAL
    OR
 OBSERVED
         PAULA’S PIZZA

HOW MANY
DIFFERENT
POSSIBILITIES?
        RUG GAMES

DO WE HAVE
EQUAL
REGIONS?
  THE COUNTER’S GAME




PLACE 11     ROLL A PAIR OF
MARKERS      DICE
ROLLIN’ ROLLIN’

            ROLL A PAIR
            OF DICE 50
            TIMES
   THE THEORY OF
   TWO-DICE SUMS




DEVELOP A RUG DIAGRAM
TWO-DICE SUMS AND
    PRODUCTS




DEVELOP ANOTHER RUG
     DIAGRAM
   SPINNER GIVE AND TAKE

MAKE A
SPINNER
                   AND PLAY
                   THE GAME
         MIA’S CARDS
A STANDARD             HEARTS
DECK OF                WORTH 10 PT
CARDS                  CLUB, SPADE
                       DIAMONDS
                       WORTH 5 PTS
      EXPECTED VALUE
•IS THE AVERAGE AMOUNT
 GAINED (OR LOST) PER TURN IN
 THE LONG RUN
      A FAIR RUG GAME?


CRYSTAL            TONY WINS
WINS $5            $3
           ONE-AND-ONE
60%
CHANCE
OF
MAKING
THE FREE
THROW
A SIXTY-PERCENT SOLUTION

               SIMULATION
               40 TIMES
  THE THEORY OF ONE-AND-
           ONE




DEVELOP A RUG DIAGRAM AND FIND
     THE EXPECTED VALUE
STREAK-SHOOTING SHELLY

            EXPECTED
            VALUE
       SPINS AND DRAWS




ARCIBALD   CHARITY
                     BEATRICE
      MARTIAN BASKETBALL

1ST                  80% 2ND
SHOT
                     AND
60%
                     90% 3RD
     THE CARRIER’S PAYMENT
        PLAN QUANDARY
$5
                       AND
OR                     RECEIVE
PICK                   $11
TWO                    OR
BILLS
                       $2
 THE GAME OF LITTLE PIG




RED CUBE = 1 POINT
BLUE CUBE = 4 POINTS
YELLOW CUBE = 0 POINTS
  LITTLE PIG STRATEGIES




•THE TWO POINT STRATEGY

•THE TWO DRAW STRATEGY
  LITTLE PIG STRATEGIES

•THE THREE POINT STRATEGY



•THE THREE DRAW STRATEGY
  LITTLE PIG STRATEGIES




•THE FOUR POINT STRATEGY

•THE FOUR DRAW STRATEGY
  LITTLE PIG STRATEGIES




•THE FIVE POINT STRATEGY

•THE FIVE DRAW STRATEGY
  LITTLE PIG STRATEGIES




•THE SIX POINT STRATEGY

•THE SIX DRAW STRATEGY
         SHOULD I GO ON?

WHICH
STRATEGY IS
BETTER?



       POINT OR DRAW??????
THE BEST LITTLE PIG
        FOR WHAT SCORES
        DOES IT PAY TO
        DRAW AGAIN?


        FOR WHAT
        SCORES DOES
        IT PAY TO
        STOP?
  BIG PIG MEETS LITTLE PIG
AFTER HOW
MANY
POINTS
SHOULD WE
STOP
ROLLING THE
DIE?
SOLVING THE UNIT PROBLEM
               SUMMARIZE
               WHAT YOU HAVE
               LEARNED
               ABOUT THE
               BEST POSSIBLE
               STRATEGY FOR
               PIG.
  WAITING FOR A DOUBLE
•MAKE A PREDICTION
•DO THE EXPERIMENT 10 TIMES
 – WHAT WAS THE LARGEST # OF
   ROLLS TO GET A DOUBLE?
 – WHAT WAS THE AVG OF THE TEN
   EXPERIMENTS?
  WAITING FOR A DOUBLE
•HOW CLOSE IS YOUR PREDICTED
 AVERAGE TO THE YOUR
 EXPERIMENTS AVERAGE?
  WAITING FOR A DOUBLE
• MAKE A FREQUENCY BAR GRAPH
  OF THE CLASSES DATA
 THE GAMBLER’S FALLACY
•WHAT DO YOU THINK ABOUT THE
 STRATEGY THE PEOPLE USED IN
 1913 AT THE CASINO IN MONTE
 CARLO?
 THE GAMBLER’S FALLACY
•FLIP A COIN 25 TIMES AND
 RECORD EACH FLIP
•FIND HOW MANY “SAME’S” AND
 “DIFFERENT’S” YOU GET
 THE GAMBLER’S FALLACY
•WHAT DOES THE GAMBLERS
 FALLACY SAY ABOUT THE
 ROULETTE STRATEGY?
•HOW IS THE GAMBLER’S FALLACY
 RELATED TO STRATEGIES FOR
 THE GAME OF PIG...
  THE GAMBLER’S FALLACY
…DID YOU SOMETIMES STOP
 ROLLING BECAUSE YOU THOUGHT
 THERE WAS NOW A GREATER
 CHANCE OF ROLLING A 1?
 WHAT ARE THE CHANCES?
•REACHING INTO A BAG WITH 3
 RED, 2 BLUE, AND 4 BLACK GUM
 BALLS AND PULLING OUT A BLUE?
•FLIPPING A COIN TWICE AND
 GETTING DIFFERENT RESULTS?
 WHAT ARE THE CHANCES?
•SNOW FALLING SOMETIME IN JULY
 IN FLORIDA

•SNOW FALLING SOMETIME IN JULY
 IN NEW ZEALAND
 WHAT ARE THE CHANCES?
•GOING TO A STORE AND NOT
 FINDING A T-SHIRT IN YOUR SIZE.
•A STUDENT IN YOUR MATH CLASS
 WEARING SNEAKERS.
 WHAT ARE THE CHANCES?
•ROLLING A DIE AND GETTING A
 PRIME NUMBER.
•ROLLING 2 DICE AND GETTING
 DOUBLES.
•ROLLING A PAIR OF DICE AND
 GETTING DOULBES BY THE 3RD
 ROLL.
       PAULA’S PIZZA
•WHAT IS THE PROBABILITY SHE
 WILL GET WHAT SHE ORDERED?
•WHAT IS THE PROBABILITY SHE
 WILL NOT?
       PAULA’S PIZZA
•PAULA ACTUALLY LIKES
 SAUSAGE AND PEPPERONI TOO.
 WHAT IS THE PROBABILITY SHE
 WILL GET A PIZZA SHE LIKES?
•AND THE PROBABILITY SHE
 DOESN’T?
RUG GAMES
      WHAT’S THE
      PROBABILITY OF
      BEING HIT FOR
      EACH COLOR?
RUG GAMES
RUG GAMES
  ROLLIN’, ROLLIN’, ROLLIN’
•ROLL A PAIR OF DICE 50 TIMES
 AND RECORD THE SUMS

•DRAW A GRAPH OF THE DATA
 YOU GATHERED
  ROLLIN’, ROLLIN’, ROLLIN’
•WHAT NEW THOUGHTS DOES THIS
 EXPERIMENT GIVE YOU ABOUT
 HOW TO PLAY THE COUNTERS
 GAME?
THEORY OF TWO DICE SUMS
    TWO-DICE SUMS AND
        PRODUCTS
•WHICH IS MORE LIKELY--THAT THE
 SUM IS AN ODD NUMBER OR THAT
 THE SUM IS AN EVEN NUMBER?
•MAKE UP TWO PROBABILITY
 QUESTIONS ABOUT 2 DICE SUMS.
    TWO-DICE SUMS AND
        PRODUCTS
•WHAT ARE THE POSSIBLE TWO-
 DICE PRODUCTS?
•WHAT IS THE PROBABILITY OF
 GETTING EACH OF THE TWO-DICE
 PRODUCTS?
TWO-DICE SUMS AND
    PRODUCTS
    TWO-DICE SUMS AND
        PRODUCTS
•WHICH IS MORE LIKELY--THAT THE
 TWO-DICE PRODUCT IS AN ODD
 NUMBER OR THAT THE TWO-DICE
 PRODUCT IS AN EVEN NUMBER?
  SPINNER GIVE AND TAKE
•WRITE DOWN WHO YOU PREDICT
 TO BE THE WINNER OF THIS GAME.
•NOW PLAY THE GAME 25 TIMES
 AND RECORD YOUR RESULTS.
  SPINNER GIVE AND TAKE
•IF AL AND BETTY PLAY 100
 GAMES, HOW FAR AHEAD IS THE
 EXPECTED WINNER LIKELY TO BE?
        MIA’S CARDS
•IF MIA PICKS A CARD MANY
 TIMES, WHAT WILL BE HER
 AVERAGE NUMBER OF POINTS FOR
 EACH TIME SHE PICKS A CARD?
        MIA’S CARDS
•ON FEB. 14TH, SHE CHANGES THE
 GAME.
 – 20 PTS FOR A HEART
 – 15 PTS FOR A DIAMOND
 – 0 PTS FOR A CLUB OR SPADE

•WHAT WOULD HER AVERAGE
 SCORE PER CARD BE?
     A FAIR RUG GAME?
•IS THIS A FAIR GAME?

•WHAT IS TONY’S EXPECTED
 VALUE FOR EACH TURN?

•WHAT IS CRYSTAL’S?
     A FAIR RUG GAME?
•IF YOU THINK THE GAME IS NOT
 FAIR, CHANGE THE AMOUNT OF
 MONEY THEY EACH WIN IN ORDER
 TO MAKE IT A FAIR GAME.
A SIXTY-PERCENT SOLUTION
•DO THE SIMULATION 40 TIMES
•WHAT WAS THE MOST FREQUENT
 OUTCOME?
•WHAT WAS THE AVERAGE SCORE?
THE THEORY OF ONE-AND-
         ONE
 STREAK-SHOOTING SHELLY
•IN WHAT % OF SITUATIONS WILL
 SHELLY SCORE NO POINTS?
•ONE POINT?
•TWO POINTS?
 STREAK-SHOOTING SHELLY

•WHAT IS SHELLY’S EXPECTED
 VALUE PER ONE-AND-ONE
 SITUTAION?
      SPINS AND DRAWS
•AL’S WINS 1/5 OF THE TIME
•BETTY’S WINS 4/5 OF THE TIME

•AL WINS $1.25
•BETTY WINS 30 CENTS
     SPINS AND DRAWS
•WHAT IS AL’S EXPECTED VALUE
 PER SPIN?

•WHAT IS BETTY’S EXPECTED
 VALUE PER SPIN?
     SPINS AND DRAWS
•HOW MIGHT THE PAYMENTS BE
 CHANGED SO THAT THE GAME IS
 FAIR?
        SPINS AND DRAWS
•ARCHIBALD               • CHARITY
                           – WINS A
  – WINS 20 CENTS IF
                            PENNY IF
     •A JACK IS DRAWN
                             •NEITHER A
• BEATRICE                    JACK OR
  – WINS 8 CENTS IF           HEART IS
     •A HEART IS DRAWN        DRAWN
  MARTIAN BASKETBALL
•HOW MANY POINTS IS SHE MOST
 LIKELY TO SCORE IN A ONE-AND-
 ONE SITUATION?
      1ST SHOT 60 %
      2ND SHOT 80%
      3RD SHOT 90%
THE CARRIER’S PAYMENT
   PLAN QUANDARY
THE CARRIER’S PAYMENT
   PLAN QUANDARY
TWO POINT STRATEGY
TWO DRAW STRATEGY
THREE POINT STRATEGY
THREE DRAW STRATEGY
   LITTLE PIG
POINTS VS DRAWS
   LITTLE PIG
POINTS VS DRAWS
    THE BEST LITTLE PIG
•BASED ON YOUR FINDINGS, WHAT
 STRATEGY WILL GIVE THE
 HIGHEST POSSIBLE EXPECTED
 VALUE PER TURN?

								
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