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

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 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?

Combinations leading to 7

Basic Craps

The Playing Field

A Typical Commercial Craps Table

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.

Pass Line Bets

Don’t Pass Bet

The Come Bet

The Don’t Come Bet

Field Bets

Place Bets

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