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Oh Craps!

Oh Craps!. An Introduction to Simple Probability in Games. AMATYC Presentation November 2009 Lance Phillips – Tulsa Community College. The Vocabulary of Probability. Experiment – A situation which involves chance or probability the result of which is called an outcome.

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Oh Craps!

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  1. Oh Craps! An Introduction to Simple Probability in Games AMATYC Presentation November 2009 Lance Phillips – Tulsa Community College

  2. 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.

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

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

  5. Coin Toss Tally Sheet Heads Tails Total Study 1 _________ ________ _____ Study 2 _________ ________ _____ Study 3 _________ ________ _____ Total ____ ____ ____ Observed Ratio __/__ __ / __

  6. Advancing the Experiment • Two tosses of the coin 1st Toss 2nd Toss Outcomes H H,H H T H,T H T,H T T T,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? ______

  7. Advancing the Experiment • Three tosses of the coin 1st Toss 2nd Toss 3rd Toss OutcomesH H,H,H H T H,H,TH H H,T,H T T H,T,T H T,H,H H T T,H,TT H T ,T,H T T T,T,T Probability of tossing three tails is 1 in 8. 8 possible outcomes

  8. Advancing the ExperimentFour tosses of a single coin • HHHH • HHHT • HHTH • HHTT • HTHH • HTHT • HTTH • HTTT • THHH • THHT • THTH • THTT • TTHH • TTHT • TTTH • TTTT

  9. 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?

  10. 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

  11. Rolling a Pair of Dice • 36 Different possible outcomes 3 4 5 6 7 8 9 10 11 12 2

  12. Percentage of Dice Totals Appearing Dice Total Likelihood 2, 12 1/36 = 2.78% 3, 11 2/36 = 5.56% 4, 10 3/36 = 8.33% 5, 9 4/36 = 11.11% 6, 8 5/36 = 13.89% 7 6/36 = 16.67%

  13. 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?

  14. Combinations leading to 7

  15. Basic Craps The Playing Field

  16. A Typical Commercial Craps Table

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

  18. 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.

  19. Pass Line Bets

  20. Don’t Pass Bet

  21. The Come Bet

  22. The Don’t Come Bet

  23. Field Bets

  24. Place Bets

  25. 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 – lphillips@tulsacc.edu

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