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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
P(H) = 1/2
T
P(T) = 1/2
Coin Toss Tally Sheet
Study 1
Heads
_________
Tails
________
Total
_____
Study 2
_________
________
_____
Study 3
Total
_________
____
________
____
_____
____
Observed Ratio
__/__
__ / __
Advancing the Experiment
• Two tosses of the coin
1st Toss
2nd Toss
H
Outcomes
H,H
H
T
H
H,T
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
1st Toss 2nd Toss 3rd Toss
Outcomes
H
H,H,H
T
H,H,T
H
H,T,H
T
H,T,T
8 possible
H
T,H,H
outcomes
T
T,H,T
H
T ,T,H
T
T,T,T
H
H
T
H
T
T
Probability of tossing three tails is 1 in 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
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?
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 – [email protected]