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THE GAME OF PIG. PROBABILITY AND EXPECTED VALUE. THE GAME OF PIG. IF YOU ROLL A 1, THEN YOUR TURN IS OVER. ROLL A SIX SIDED DIE. PIG STRATEGIES. WRITE DOWN THE BEST STRATEGY. WAITING FOR A DOUBLE. A DOUBLE MEANS HAVING THE SAME NUMBER SHOW ON BOTH DICE. GAMBLERS FALLACY.

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THE GAME OF PIG


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    Presentation Transcript
    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. 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 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