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Probability and Casino Games Maximilian Mohr. Gamblers Fallacy Roulette Wheel Shooting Craps Permutations and Combinations Poker Hands Overview.

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Presentation on theme: "Probability and Casino Games Maximilian Mohr. Gamblers Fallacy Roulette Wheel Shooting Craps Permutations and Combinations Poker Hands Overview."— Presentation transcript:

1 Probability and Casino Games Maximilian Mohr

2 Gamblers Fallacy Roulette Wheel Shooting Craps Permutations and Combinations Poker Hands Overview

3 The error of thinking that the probability of a particular outcome increases with the successive number of opposite outcomes Gamblers Fallacy

4 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 Gamblers Fallacy

5 Probability of one toss heads = ½ Probability of 10 tosses being heads = 1/(2^10) = 1/1024 So the probability of the 10 th toss being heads = 1/1024, right? Gamblers Fallacy

6 NOPE!!! Gamblers Fallacy

7 The tenth toss has just as much of a chance to be heads as tales. Its 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 Gamblers Fallacy

8 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

9 Roulette

10 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

11 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

12 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

13 Craps

14 Craps is a game where gamblers wager of the outcome of rolls of dice. All possible rolls: Craps Basics

15 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

16 If the roll is 2, 3, or 12, the shooter loses Probability of losing? Pass Line Bet

17 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

18 Texas Holdem

19 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 Holdem

20 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

21 Combination Lock?

22 Permutation Formula Where n is the number of items to choose from, and r is how many youre picking out

23 ___n!___ r!(n-r)! You divide out r! from the permutation formula because combinations of the same items in different orders dont count as separate sets. Combination Formula

24 How many possible poker hands in all? Out of 52 possible cards, choose a combination of 5

25 52 choose 5 = 2,598,960 How Many Hands?

26 Getting 10-J-Q-K-A all of the same suit Royal Flush

27 Discounting the possibility of getting a royal flush 5 cards in numerical order, all in the same suit % Straight Flush

28 4 of one value of any card, the same value from each suit 0.024% 4 of a Kind

29 3 cards of a kind + a pair 0.144% Full House

30 5 cards of any value, all from the same suit Discounting straight flushes 0.197% Flush

31 5 cards in rank order from any suit Discount royal flush and straight flush 0.392% Straight

32 3 of the same rank, other two cards can be anything 2.11% 3 of a kind

33 4.75% 2 Pair

34 42.3% Pair

35 50.1% No Pair/High Card

36 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 were both all in? Homework

37 ons-permutations.html ons-permutations.html +fallacy +fallacy Sources


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