oh craps! amatyc presentation november 2009 lance phillips – tulsa community college
TRANSCRIPT
Oh Craps!An Introduction to
Simple Probability in Games
AMATYC Presentation November 2009Lance 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
TP(H) = 1/2
P(T) = 1/2
Coin Toss Tally Sheet Heads Tails
TotalStudy 1 _________ ________ _____
Study 2 _________ ________ _____
Study 3 _________ ________ _____Total ____ ____
____
Observed Ratio __/__ __ / __
Advancing the Experiment• Two tosses of the coin
1st Toss 2nd Toss Outcomes
H H,HH
T H,TH T,H
TT 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? ______
Advancing the Experiment• Three tosses of the coin
1st Toss 2nd Toss 3rd Toss OutcomesH H,H,H
HT H,H,T
HH H,T,H
TT H,T,T
H T,H,H
HT T,H,T
TH T ,T,H
TT T,T,T
Probability of tossing three tails is 1 in 8.
8 possible outcomes
Advancing the ExperimentFour 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
Percentage of Dice Totals Appearing
Dice Total Likelihood2, 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%
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 CrapsVocabulary:
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 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.
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 – [email protected]