Understanding Simple Probability in Games
Introduction to basic probability concepts in games, such as experiments, outcomes, events, and the likelihood of specific results. Covers examples like coin tosses, card draws, and multiple toss scenarios to illustrate the principles. This informative content is a helpful resource for grasping foundational probability ideas in a gaming context.
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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. 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.
Setting up a Simple Experiment The Coin Toss Call it! > Heads > Tails P(event) = number of favorable outcomes ______ total number of equally likely outcomes
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
Coin Toss Tally Sheet Heads Study 1 _________ ________ Tails _____ Total Study 2 _________ ________ _____ Study 3 _________ ________ _____ Total ____ ____ ____ Observed Ratio __/__ __ / __
Advancing the Experiment Two tosses of the coin 1st Toss H 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? ______ 2nd Toss Outcomes H H,H T H T H,T T,H T,T
Advancing the Experiment Three tosses of the coin 1st Toss H T Probability of tossing three tails is 1 in 8. 2nd Toss 3rd Toss H Outcomes H,H,H H T H,H,T T H H H,T,H 8 possible outcomes T H,T,T H T,H,H T T,H,T T H T ,T,H T T,T,T
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
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?
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
Rolling a Pair of Dice 36 Different possible outcomes 2 3 4 5 6 7 8 9 10 11 12
Percentage of Dice Totals Appearing Dice Total 2, 12 3, 11 4, 10 5, 9 6, 8 7 Likelihood 1/36 = 2.78% 2/36 = 5.56% 3/36 = 8.33% 4/36 = 11.11% 5/36 = 13.89% 6/36 = 16.67%
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?
Basic Craps The Playing Field
Basic Craps Vocabulary: Shooter - Come Out Roll The Point - A Natural - Craps Come - Don t Come - The Field -
Regular Craps Rules Game begins by Stickman passing dice to next player in clockwise rotation. First roll 7 or 11 Wins First roll 2, 3, or 12 Loses 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. P=2/9 P=1/9
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
