Probability and Casino Games Maximilian Mohr. Gamblers Fallacy Roulette Wheel Shooting Craps...
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Transcript of Probability and Casino Games Maximilian Mohr. Gamblers Fallacy Roulette Wheel Shooting Craps...
![Page 1: Probability and Casino Games Maximilian Mohr. Gamblers Fallacy Roulette Wheel Shooting Craps Permutations and Combinations Poker Hands Overview.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5519c103550346695e8b4721/html5/thumbnails/1.jpg)
Probability and Casino Games
Maximilian Mohr
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Gambler’s Fallacy Roulette Wheel Shooting Craps Permutations and Combinations Poker Hands
Overview
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The error of thinking that the probability of a particular outcome increases with the successive number of opposite outcomes
Gambler’s Fallacy
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Coin Toss If you toss a coin ten times, and the
first nine results are heads, you might think that the probability of the fifth coin being heads is very low
Gambler’s Fallacy
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Probability of one toss heads = ½ Probability of 10 tosses being heads =
1/(2^10) = 1/1024 So the probability of the 10th toss
being heads = 1/1024, right?
Gambler’s Fallacy
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NOPE!!!
Gambler’s Fallacy
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The tenth toss has just as much of a chance to be heads as tales. It’s 1/2
At the point of your contemplation, the coin has already flipped 9 times, and each individual coin flip is not affected by the previous flip
The universe is not keeping a memory of what has happened and what should come next
Gambler’s Fallacy
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The probability of getting 10 heads in a row OR 9 heads then 1 tail both have the same odds.
Each is an exact combination of 10 outcomes
H H H H H H H H H H H H H H H H H H H T There are two possibilities for each outcome,
and compounded ten times, both sets have a probability of 1/1024
Additionally
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Roulette
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Roulette is a game in which a small ball is spun around a rotating wheel with 38 different pockets
In American roulette, the pockets are numbered 00, 0, 1-36
Gamblers bet on the outcome of the pockets into which the ball will fall
Each number is also colored either red or black
Roulette
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Single bet – a bet on one exact outcome Split – a bet placed on two adjoining squares Betting on three numbers in a horizontal line Square – marker placed at the intersection of
four numbers
Types of Inside Roulette Bets
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Manque (1-18) Passe (19-36) Red or Black Bets Even or Odd Bets Column Bet – All 12 numbers in any vertical
line
Types of Outside Roulette Bets
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Craps
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Craps is a game where gamblers wager of the outcome of rolls of dice.
All possible rolls:
Craps Basics
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
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The most basic bet, a bet for the shooter to win
If the roll is 7 or 11, shooter wins Probability of winning this way?
Pass Line Bet
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If the roll is 2, 3, or 12, the shooter loses Probability of losing?
Pass Line Bet
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If the roll is any other value, the player establishes a point. If the player rolls that point again before a 7,
he/she wins If the player rolls a 7 before that point, he/she
loses. Example: Rolling a 4
Pass Line Bet
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Texas Hold’em
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The basics Two cards dealt to each player, 5 cards turned
over in succession from the deck Player with the best hand using his cards and
“the flop” is the winner
Texas Hold’em
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Which applies to poker hands?? Permutation: a specific set of items in a
particular order Combination: a specific set of items in no
particular order
Combinations & Permutations
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Combination Lock?
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Permutation Formula
Where n is the number of items to choose from, and r is how many you’re picking out
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___n!___r!(n-r)!
You divide out r! from the permutation formula because combinations of the same items in
different orders don’t count as separate sets.
Combination Formula
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How many possible poker hands in all?
Out of 52 possible cards, choose a combination of 5
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52 choose 5 = 2,598,960
How Many Hands?
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Getting 10-J-Q-K-A all of the same suit
Royal Flush
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Discounting the possibility of getting a royal flush
5 cards in numerical order, all in the same suit
0.00139%
Straight Flush
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4 of one value of any card, the same value from each suit
0.024%
4 of a Kind
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3 cards of a kind + a pair 0.144%
Full House
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5 cards of any value, all from the same suit
Discounting straight flushes 0.197%
Flush
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5 cards in rank order from any suit Discount royal flush and straight flush 0.392%
Straight
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3 of the same rank, other two cards can be anything
2.11%
3 of a kind
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4.75%
2 Pair
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42.3%
Pair
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50.1%
No Pair/High Card
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If I am playing a pass line bet in craps, and I roll a 9, how much more likely am I to lose than win?
What percent chance do I have of beating a player with a regular flush in poker, if we’re both all in?
Homework
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http://www.mathsisfun.com/combinatorics/combinations-permutations.html
http://en.wikipedia.org/wiki/Poker_probability http://dictionary.reference.com/browse/mont
e+carlo+fallacy
http://en.wikipedia.org/wiki/Craps
Sources