THE GAME OF PIG

THE GAME OF PIG

PROBABILITY AND

EXPECTED VALUE

THE GAME OF PIG

ROLL A SIX SIDED DIE

IF YOU ROLL A 1, THEN 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 MARKERS

ROLL A PAIR OF 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

AND PLAY THE GAME

MAKE A SPINNER

MIA’S CARDS

A STANDARD DECK OF CARDS

HEARTS WORTH 10 PTS

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 WINS $5

TONY WINS $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 CHARITYBEATRICE

MARTIAN BASKETBALL

1ST SHOT

60%

80% 2ND

AND

90% 3RD

THE CARRIER’S PAYMENT PLAN

QUANDARY$5

OR

PICK TWO BILLS

AND RECEIVE $11

OR

$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


•THE THREE POINT STRATEGY

•THE THREE DRAW STRATEGY


•THE FOUR POINT STRATEGY

•THE FOUR DRAW STRATEGY


•THE FIVE POINT STRATEGY

•THE FIVE DRAW STRATEGY


•THE SIX POINT STRATEGY

•THE SIX DRAW STRATEGY

SHOULD I GO ON?

WHICH STRATEGY IS BETTER?

POINT OR DRAW??????

THE BEST LITTLE PIGFOR 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.


•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?


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


•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?


•FLIP A COIN 25 TIMES AND RECORD EACH FLIP

•FIND HOW MANY “SAME’S” AND “DIFFERENT’S” YOU GET


•WHAT DOES THE GAMBLERS FALLACY SAY ABOUT THE ROULETTE STRATEGY?

•HOW IS THE GAMBLER’S FALLACY RELATED TO STRATEGIES FOR THE GAME OF PIG...


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


•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?


•SNOW FALLING SOMETIME IN JULY IN FLORIDA

•SNOW FALLING SOMETIME IN JULY IN NEW ZEALAND


•GOING TO A STORE AND NOT FINDING A T-SHIRT IN YOUR SIZE.

•A STUDENT IN YOUR MATH CLASS WEARING SNEAKERS.


•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 GAMESWHAT’S THE PROBABILITY OF BEING HIT FOR EACH COLOR?

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


•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.


•WHAT ARE THE POSSIBLE TWO-DICE PRODUCTS?

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


1 2 3 4 5 6

1 1 2 3 4 5 62 2 4 6 8 10 123 3 6 9 12 15 184 4 8 12 16 20 245 5 10 15 20 25 306 6 12 18 24 30 36


•WHICH IS MORE LIKELY--THAT THE TWO-DICE PRODUCT IS AN ODD NUMBER OR THAT THE TWO-DICE PRODUCT IS AN EVEN NUMBER?


•WRITE DOWN WHO YOU PREDICT TO BE THE WINNER OF THIS GAME.

•NOW PLAY THE GAME 25 TIMES AND RECORD YOUR RESULTS.


• 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


• IN WHAT % OF SITUATIONS WILL SHELLY SCORE NO POINTS?

•ONE POINT?•TWO POINTS?


•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–WINS 20 CENTS IF•A JACK IS DRAWN

• BEATRICE–WINS 8 CENTS IF•A HEART IS DRAWN

• CHARITY –WINS A

PENNY IF•NEITHER A JACK OR HEART IS 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

TWO POINT STRATEGY

TWO DRAW STRATEGY

THREE POINT STRATEGY

THREE DRAW STRATEGY

LITTLE PIG POINTS VS DRAWS

1 point 1.61 draw 1.62 point 2.12 draw 2.23 point 2.23 draw 2.24 point 2.2474 draw 1.9755 point 2.3625 draw 1.6466 point 2.3626 draw 1.3177 point 2.325

LITTLE PIG POINTS VS DRAWS

1 point 1.61 draw 1.6 2 point 2.12 draw 2.2 3 point 2.23 draw 2.2 4 point 2.2474 draw 1.975 5 point 2.3625 draw 1.646 6 point 2.3626 draw 1.317 7 point 2.325

THE BEST LITTLE PIG

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

THE GAME OF PIG

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