1. PROBABILITY AND EXPECTED VALUE
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. WRITE DOWN THE BEST STRATEGY
PIG STRATEGIES
WRITE DOWN THE BEST STRATEGY

4. A DOUBLE MEANS HAVING THE SAME NUMBER SHOW ON BOTH DICE
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 OBSERVED 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. PAULA’S PIZZA
HOW MANY DIFFERENT POSSIBILITIES?

9. RUG GAMES
DO WE HAVE EQUAL REGIONS?

10. THE COUNTER’S GAME
PLACE 11 MARKERS
ROLL A PAIR OF DICE

11. ROLLIN’ ROLLIN’
ROLL A PAIR OF DICE 50 TIMES

12. 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. MIA’S CARDS HEARTS WORTH 10 PTS A STANDARD DECK OF CARDS
CLUB, SPADE, DIAMONDS WORTH 5 PTS
A STANDARD DECK OF CARDS

16. 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 CARRIER’S 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

26. 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

30. LITTLE PIG STRATEGIES
THE SIX POINT STRATEGY
THE SIX DRAW STRATEGY

31. 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 GAMBLER’S FALLACY
WHAT DO YOU THINK ABOUT THE STRATEGY THE PEOPLE USED IN 1913 AT THE CASINO IN MONTE CARLO?

39. THE GAMBLER’S FALLACY FLIP A COIN 25 TIMES AND RECORD EACH FLIP
FIND HOW MANY “SAME’S” AND “DIFFERENT’S” YOU GET

40. 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...

41. THE GAMBLER’S 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. PAULA’S PIZZA WHAT IS THE PROBABILITY SHE WILL GET WHAT SHE ORDERED?
WHAT IS THE PROBABILITY SHE WILL NOT?

47. 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?

48. RUG GAMES
WHAT’S 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. 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?

61. 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?

62. A FAIR RUG GAME? IS THIS A FAIR GAME?
WHAT IS TONY’S EXPECTED VALUE FOR EACH TURN?
WHAT IS CRYSTAL’S?

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 SHELLY’S EXPECTED VALUE PER ONE-AND-ONE SITUTAION?

68. 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

69. SPINS AND DRAWS WHAT IS AL’S EXPECTED VALUE PER SPIN?
WHAT IS BETTY’S EXPECTED VALUE PER SPIN?

70. SPINS AND DRAWS
HOW MIGHT THE PAYMENTS BE CHANGED SO THAT THE GAME IS FAIR?

71. SPINS AND DRAWS ARCHIBALD CHARITY WINS A PENNY IF WINS 20 CENTS 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 CARRIER’S PAYMENT PLAN QUANDARY

74. THE CARRIER’S 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?