THE GAME OF PIG

1
THE GAME OF PIG

• PROBABILITY
• AND
• EXPECTED VALUE

2
THE GAME OF PIG
IF YOU ROLL A 1, THEN YOUR TURN IS OVER
ROLL A SIX SIDED DIE
3
PIG STRATEGIES
WRITE DOWN THE BEST STRATEGY
4
WAITING FOR A DOUBLE
A DOUBLE MEANS HAVING THE SAME NUMBER SHOW ON
BOTH DICE
5
GAMBLERS FALLACY
WE WILL CALL THREE IDENTICAL FLIPS IN A ROW A
TRIPLET
6
VOCABULARY

• THEORETICAL PROBABILITY
• IS PROBABILITY DETERMINED ON THE BASIS OF A MODEL
• OBSERVED PROBABILITY
• IS PROBABILITY BASED ON ACTUAL RESULTS OF PAST
  EVENTS

7
WHAT ARE THE CHANCES?
THEORETICAL OR OBSERVED
8
PAULAS PIZZA
HOW MANY DIFFERENT POSSIBILITIES?
9
RUG GAMES
DO WE HAVE EQUAL REGIONS?
10
THE COUNTERS GAME
PLACE 11 MARKERS
ROLL A PAIR OF DICE
11
ROLLIN ROLLIN
ROLL A PAIR OF DICE 50 TIMES
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THE THEORY OF TWO-DICE SUMS
DEVELOP A RUG DIAGRAM
13
TWO-DICE SUMS AND PRODUCTS
DEVELOP ANOTHER RUG DIAGRAM
14
SPINNER GIVE AND TAKE
MAKE A SPINNER
AND PLAY THE GAME
15
MIAS CARDS
HEARTS WORTH 10 PTS CLUB, SPADE, DIAMONDS WORTH 5
PTS
A STANDARD DECK OF CARDS
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EXPECTED VALUE

• IS THE AVERAGE AMOUNT GAINED (OR LOST) PER TURN
  IN THE LONG RUN

17
A FAIR RUG GAME?
CRYSTAL WINS 5
TONY WINS 3
18
ONE-AND-ONE
60 CHANCE OF MAKING THE FREE THROW
19
A SIXTY-PERCENT SOLUTION
SIMULATION 40 TIMES
20
THE THEORY OF ONE-AND-ONE
DEVELOP A RUG DIAGRAM AND FIND THE EXPECTED VALUE
21
STREAK-SHOOTING SHELLY
EXPECTED VALUE
22
SPINS AND DRAWS
CHARITY
ARCIBALD
BEATRICE
23
MARTIAN BASKETBALL
1ST SHOT 60
80 2ND AND 90 3RD
24
THE CARRIERS PAYMENT PLAN QUANDARY
5 OR PICK TWO BILLS
AND RECEIVE 11 OR 2
25
THE GAME OF LITTLE PIG
RED CUBE 1 POINT BLUE CUBE 4 POINTS YELLOW
CUBE 0 POINTS
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LITTLE PIG STRATEGIES

• THE TWO POINT STRATEGY
• THE TWO DRAW STRATEGY

27
LITTLE PIG STRATEGIES

• THE THREE POINT STRATEGY
• THE THREE DRAW STRATEGY

28
LITTLE PIG STRATEGIES

• THE FOUR POINT STRATEGY
• THE FOUR DRAW STRATEGY

29
LITTLE PIG STRATEGIES

• THE FIVE POINT STRATEGY
• THE FIVE DRAW STRATEGY

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LITTLE PIG STRATEGIES

• THE SIX POINT STRATEGY
• THE SIX DRAW STRATEGY

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SHOULD I GO ON?
WHICH STRATEGY IS BETTER?
POINT OR DRAW??????
32
THE BEST LITTLE PIG
FOR WHAT SCORES DOES IT PAY TO DRAW AGAIN?
FOR WHAT SCORES DOES IT PAY TO STOP?
33
BIG PIG MEETS LITTLE PIG
AFTER HOW MANY POINTS SHOULD WE STOP ROLLING THE
DIE?
34
SOLVING THE UNIT PROBLEM
SUMMARIZE WHAT YOU HAVE LEARNED ABOUT THE BEST
POSSIBLE STRATEGY FOR PIG.
35
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?

36
WAITING FOR A DOUBLE

• HOW CLOSE IS YOUR PREDICTED AVERAGE TO THE YOUR
  EXPERIMENTS AVERAGE?

37
WAITING FOR A DOUBLE

• MAKE A FREQUENCY BAR GRAPH OF THE CLASSES DATA

38
THE GAMBLERS FALLACY

• WHAT DO YOU THINK ABOUT THE STRATEGY THE PEOPLE
  USED IN 1913 AT THE CASINO IN MONTE CARLO?

39
THE GAMBLERS FALLACY

• FLIP A COIN 25 TIMES AND RECORD EACH FLIP
• FIND HOW MANY SAMES AND DIFFERENTS YOU GET

40
THE GAMBLERS FALLACY

• WHAT DOES THE GAMBLERS FALLACY SAY ABOUT THE
  ROULETTE STRATEGY?
• HOW IS THE GAMBLERS FALLACY RELATED TO
  STRATEGIES FOR THE GAME OF PIG...

41
THE GAMBLERS FALLACY

• DID YOU SOMETIMES STOP ROLLING BECAUSE YOU
  THOUGHT THERE WAS NOW A GREATER CHANCE OF ROLLING
  A 1?

42
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?

43
WHAT ARE THE CHANCES?

• SNOW FALLING SOMETIME IN JULY IN FLORIDA
• SNOW FALLING SOMETIME IN JULY IN NEW ZEALAND

44
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.

45
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.

46
PAULAS PIZZA

• WHAT IS THE PROBABILITY SHE WILL GET WHAT SHE
  ORDERED?
• WHAT IS THE PROBABILITY SHE WILL NOT?

47
PAULAS PIZZA

• PAULA ACTUALLY LIKES SAUSAGE AND PEPPERONI TOO.
  WHAT IS THE PROBABILITY SHE WILL GET A PIZZA SHE
  LIKES?
• AND THE PROBABILITY SHE DOESNT?

48
RUG GAMES
WHATS THE PROBABILITY OF BEING HIT FOR EACH
COLOR?
49
RUG GAMES
50
RUG GAMES
51
ROLLIN, ROLLIN, ROLLIN

• ROLL A PAIR OF DICE 50 TIMES AND RECORD THE SUMS
• DRAW A GRAPH OF THE DATA YOU GATHERED

52
ROLLIN, ROLLIN, ROLLIN

• WHAT NEW THOUGHTS DOES THIS EXPERIMENT GIVE YOU
  ABOUT HOW TO PLAY THE COUNTERS GAME?

53
THEORY OF TWO DICE SUMS
54
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.

55
TWO-DICE SUMS AND PRODUCTS

• WHAT ARE THE POSSIBLE TWO-DICE PRODUCTS?
• WHAT IS THE PROBABILITY OF GETTING EACH OF THE
  TWO-DICE PRODUCTS?

56
TWO-DICE SUMS AND PRODUCTS
57
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?

58
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.

59
SPINNER GIVE AND TAKE

• IF AL AND BETTY PLAY 100 GAMES, HOW FAR AHEAD IS
  THE EXPECTED WINNER LIKELY TO BE?

60
MIAS CARDS

• IF MIA PICKS A CARD MANY TIMES, WHAT WILL BE HER
  AVERAGE NUMBER OF POINTS FOR EACH TIME SHE PICKS
  A CARD?

61
MIAS 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?

62
A FAIR RUG GAME?

• IS THIS A FAIR GAME?
• WHAT IS TONYS EXPECTED VALUE FOR EACH TURN?
• WHAT IS CRYSTALS?

63
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.

64
A SIXTY-PERCENT SOLUTION

• DO THE SIMULATION 40 TIMES
• WHAT WAS THE MOST FREQUENT OUTCOME?
• WHAT WAS THE AVERAGE SCORE?

65
THE THEORY OF ONE-AND-ONE
66
STREAK-SHOOTING SHELLY

• IN WHAT OF SITUATIONS WILL SHELLY SCORE NO
  POINTS?
• ONE POINT?
• TWO POINTS?

67
STREAK-SHOOTING SHELLY

• WHAT IS SHELLYS EXPECTED VALUE PER ONE-AND-ONE
  SITUTAION?

68
SPINS AND DRAWS

• ALS WINS 1/5 OF THE TIME
• BETTYS WINS 4/5 OF THE TIME
• AL WINS 1.25
• BETTY WINS 30 CENTS

69
SPINS AND DRAWS

• WHAT IS ALS EXPECTED VALUE PER SPIN?
• WHAT IS BETTYS EXPECTED VALUE PER SPIN?

70
SPINS AND DRAWS

• HOW MIGHT THE PAYMENTS BE CHANGED SO THAT THE
  GAME IS FAIR?

71
SPINS AND DRAWS

• CHARITY
• WINS A PENNY IF
• NEITHER A JACK OR HEART IS DRAWN

• ARCHIBALD
• WINS 20 CENTS IF
• A JACK IS DRAWN
• BEATRICE
• WINS 8 CENTS IF
• A HEART IS DRAWN

72
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
73
THE CARRIERS PAYMENT PLAN QUANDARY
74
THE CARRIERS PAYMENT PLAN QUANDARY
75
TWO POINT STRATEGY
76
TWO DRAW STRATEGY
77
THREE POINT STRATEGY
78
THREE DRAW STRATEGY
79
LITTLE PIG POINTS VS DRAWS
80
LITTLE PIG POINTS VS DRAWS
81
THE BEST LITTLE PIG

• BASED ON YOUR FINDINGS, WHAT STRATEGY WILL GIVE
  THE HIGHEST POSSIBLE EXPECTED VALUE PER TURN?