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Number of players

How are cards dealt

Who is the first player

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very weak actually :) –  Selim Ghazouani Mar 21 '12 at 18:33
What kind of poker? Texas Hold-em? Seven-card stud? Five-card draw? Etc? Or maybe that is what you mean by "how are cards dealt". Also, do you want to factor in behavior? For instance, in Hold-em, if player A's down cards are 2,3 hearts, they would likely fold right off. Yet there's a chance they could have followed it out to a straight flush. These kinds of considerations make the question intractable. That's why most poker calculations stick to a random hand of five cards. –  alex.jordan Mar 21 '12 at 18:50
Since it's revived, want to add this link: List of poker hand | Wikipedia. –  FrenzY DT. Dec 4 '12 at 16:37
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2 Answers

up vote 2 down vote accepted

If you are dealt five cards, there are $4\times10 =40$ possible straight flushes ($4\times 9 =36$ if you exclude royal flushes) out of the ${52 \choose 5}= 2598960$ possible hands. So the probability is $\dfrac{40}{2598960} = \dfrac{1}{64974} \approx 0.00001539\ldots$.

The probability will increase if you can have more than five cards to choose from. The probability that somebody will have a straight flush will increase if the number of players increases. It may reduce if you might drop out of the betting before seeing all five cards.

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Try the book, mathematics of poker by bill chen. Decent read.

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