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Poker Probability Example Problems

Poker Probability Example Problems - Poker Probability...

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Poker Probability Example Problems: ASSUME THAT THE HANDS ARE 5 CARDS FROM A STANDARD 52 CARD DECK UNLESS OTHERWISE NOTED SOME ANSWERS WILL VARY DEPENDING ON THE DEFINITION OF ALLOWABLE STRAIGHTS: SOME PEOPLE DO NOT INCLUDE THE STRAIGHT FROM ACE TO 5 AS ALLOWABLE. Example 1 Let A be the event that all 5 cards are different with respect to their value (no other restrictions). 13 4 * ^ 5 5 1 ( ) ( ) 52 ( ) 5 N A P A N . The “13 choose 5” represents the number of ways to get 5 different face values from the 13 total face values. The “4 choose 1” represents the number of ways to get a suit of a particular card. This term is raised to the 5 th power since we have 5 cards total and each one has the same number of ways of being “assigned” a suit. P(A) is .5071. Example 2 IMPORTAN T DISTINCTION: Please be aware that event A is not the event of “your best hand is a high card” i.e. the best hand you can put forth is a high card or all one of a kinds. Let B be the event that your best hand is a “high card” or that you have at best all one of a kinds. Event B is different from A since we cannot have straights or flushes in Event B, but they were allowable in Event A. One must be careful in assessing whether or not “better hands” are allowable for our given event. If they are not, we must make sure to exclude them. In this case, we only have to modify the probability of A slightly to get the probability of B.
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5 13 4 # of straights * # of flushes 5 1 ( ) ( ) 52 ( ) 5 N B P B N .
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