Question

In Texas Hold em, each player initially gets two cards, and then five community cards are dealt in the center of the table. Each player makes his or her best five-card hand from the 3.31 seven cards. a. How many initial two-card starting hands are there? b. Many starting hands play the same way. For example, suits do not matter for a pair of Aces. Each pair of Aces plays the same (on average) as any other pair of Aces. The starting hands can be divided into three playing groups: both cards have the same rank (a pair), both cards are in the same suit (suited),or neither (off-suit). How many differently playing starting hands are in each group? How many differently playing starting hands are there in total? (Note that this answer is only about 1/8th the answer to the question above.) c. How many initial two-card hands correspond to each differently playing starting hand in the question above? Add them up, and show they total the number in the first question.

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