1. Oh Craps! 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 HTHT P(H) = 1/2P(T) = 1/2

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

6. 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? ______

7. 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

8. 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

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 23456789101112

12. 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%

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