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Oh Craps! AMATYC Presentation November 2009 Lance Phillips – Tulsa Community College

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The Vocabulary of Probability Experiment – A situation which involves chance or probability the result of which is called an outcome. Outcome – The result of a single trial of an experiment. Event – One or more outcomes of an experiment. Probability – The measure of how likely an event is.

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Setting up a Simple Experiment – The Coin Toss Call it! Heads Tails P(event) = number of favorable outcomes ______ total number of equally likely outcomes

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Coin Toss Outcome Heads – One (1) possibility Tails – One (1) possibility Using a Tree Diagram to Illustrate Outcomes HTHT P(H) = 1/2P(T) = 1/2

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Coin Toss Tally Sheet Heads TailsTotal Study 1 _________ _____________ Study 2 _________ ________ _____ Study 3 _________ ________ _____ Total ____ ____ ____ Observed Ratio __/__ __ / __

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Advancing the Experiment Two tosses of the coin 1 st Toss2 nd Toss Outcomes HH,H H TH,T HT,H T TT,T Probability of tossing two tails is 1 in 4. What then is the probability of a tail and a head, in no specific order? ______

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Advancing the Experiment Three tosses of the coin 1 st Toss2 nd Toss 3 rd Toss Outcomes H H,H,H H T H,H,T H H H,T,H T T H,T,T H T,H,H H T T,H,T T H T,T,H T T T,T,T Probability of tossing three tails is 1 in 8. 8 possible outcomes

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Advancing the Experiment Four tosses of a single coin HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT

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Playing Cards How many cards in a deck? Probability of drawing the ace of hearts? Probability of drawing an ace? Probability of drawing a heart?

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Rolling a Die Possible outcomes: –1, 2, 3, 4, 5, 6 Probability of rolling a 4 is 1 in 6 Probability of rolling a 2 is 1 in 6 Probability of rolling an even number 3 in 6 which we simplify to 1 in 2

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Rolling a Pair of Dice 36 Different possible outcomes

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Percentage of Dice Totals Appearing Dice Total Likelihood 2, 121/36 = 2.78% 3, 112/36 = 5.56% 4, 103/36 = 8.33% 5, 94/36 = 11.11% 6, 85/36 = 13.89% 76/36 = 16.67%

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Probability Versus Odds Probability : Favorable outcomes to possible outcomes – probability of rolling a nine is 4 in 36 or 1 in 9. Odds: Wrong outcomes to right outcomes (or opposite) – Odds of rolling a nine are 8 to 1 against. What is the probability of rolling a four? What are the odds of rolling a four?

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Combinations leading to 7

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Basic Craps The Playing Field

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A Typical Commercial Craps Table

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Basic Craps Vocabulary: Shooter - Come Out Roll – The Point - A Natural - Craps – Come - Don’t Come - The Field -

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Regular Craps Rules Game begins by “Stickman” passing dice to next player in clockwise rotation. First roll 7 or 11 Wins P=2/9 First roll 2, 3, or 12 Loses P=1/9 On first roll a roll of 4, 5, 6, 8, 9, or 10 establishes the “point” number. Win on subsequent rolls if “point” appears before a 7.

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Pass Line Bets

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Don’t Pass Bet

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The Come Bet

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The Don’t Come Bet

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Field Bets

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Place Bets

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Resources Felts available on Ebay or Amazon ranging in price from $5 - $40, Foldable table tops from $45 - $150. Pucks around $10. Dice anywhere. Lance Phillips –

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