Poker Hands: Frequency of.

Poker Hands, Frequency of
There are 2,598,960 possible different poker hands, the number of different sets of 5 cards in 52 cards. [5!/(52 -5)! x 5!, or (52,5.)] The 2,598,960 comprise the following numbers of the various possible hands:

40 Straight Flushes
624 hands with four-of-a-kind
3,744 Full Houses
5,105 Flushes
10,200 Straights
54,912 hands with three-of-a-kind
123.552 hands with two pair
1,098,240 hands with one pair
1,302,540 hands with nothing (‘garbage’)

That makes 2,598,960. If you divide 1,302,540 by 2,598,960, you get the percentage of all hands that are ‘garbage,’ 50.1177%. Thus, less than half, 49.8823%, of all possible hands are of value as a poker hand. The deck is 50.1177 to 49.8823 against, to begin with. So don’t feel bad if you get nothing in straight poker--that will happen slightly more than half the time. And note that a high pair in straight poker isn’t a bad hand. But don’t bet the farm...