Wednesday, April 4, 2007

Odds of being dealt a straight flush

A straight flush can be determined by the suit of the flush and the highest card of the straight. The ace is usually the highest card in the deck, and can be given rank 14 (king is 13, queen is 12, jack is 11). You can choose to use the ace as a low card instead. The ace can be given the rank 1 if you so desire. The only time you'd want to do this, is if it can be used in small straight. 5432A is the smallest possible straight, and is called a 5-high straight. AKQJT is the biggest possible straight ("14-high") and is called an ace-high straight. There are 10 different ranks that can be the highest rank of a straight, so there are 10 different "straight combos" in each suit.

n(straight flushes) = suit combos * straight combos = 4 suits * 10 straight flushes pr. suit = 40 straight flushes

You can find the odds of being dealt a straight flush by dividing the number of straight flushes you can be dealt by the total number of hands you can be dealt (2 598 960).

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