Does not Compute! Trouble w/ Combinatorics
I've tried to break down the total number of all possible 5-card poker hands into their categories and get a complete count. I'm a bit short on the total count. Here's what I have:
One Pair: C(13,1)*C(4,2)*C(12,3)*[C(4,1)^3] = 1,098,240
Two Pair: C(13,2)*[C(4,2)^2]*C(11,1)*(4,1) = 123,552
3 of a Kind: C(13,1)*C(4,3)*C(12,2)*[C(4,1)^2] = 24,960
Straight: 10*(4^5-4) = 10,200
Flush: C(4,1)*[C(13,5)-10] = 5,108
Full House: C(13,1)*C(4,3)*C(12,1)*C(4,2) = 3,744
4 of a Kind: C(13,1)*C(4,4)*C(12,1)*C(4,1) = 624
Straight Flush: 4*(10-1) = 36
Royal Flush: 4
High Card: C(13,5)(4^5-4) - 10*(4^5-4) = 1,302,540
where (4^5-4) is all combinations of non-flush hands if there are 5 unique ranks, and 10*(4^5-4) is the number of straights made.
Total = 2,569,008
C(52,5) = 2,598,960 [img]/images/graemlins/frown.gif[/img]
If anyone can spot the error and point it out it would be awesome. The part I had the most trouble with was calculating the number of high card hands, so at least part of the error may lie in here.
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