Simple Probability in Games
Oh Craps!
Oh Craps!
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
Tails
Total
Study 1 _________ ________
_____
Study 2 _________ ________ _____
Study 3 _________ ________ _____
Total ____
____
____
Observed Ratio __/__ __ / __
Advancing the Experiment
•
Two tosses of the coin
1
st
Toss
2
nd
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? ______
Advancing the Experiment
•
Three tosses of the coin
1
st
Toss
2
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
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
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%
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 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
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
Welcome – My Name is Lance Phillips and this session explores simple probability through the play of some familiar games, a toss of a coin, roll of a die, and will include a turn at craps, so shooters, get your arm ready.
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.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
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
