Number of different hands after Flop, Turn, River

[Jamper]

Couldn't find this in search, so thought I'd put the Q to the math gurus -

169 for the hole cards. What about any 2 hole cards and those on the board - how many possible hands at each stage?

-thanks

[Zapped]

You might need to refine your question a bit. There are actually 52C2 = 1326 possible two-card combinations in the pocket. The number 169 refers one way of categorizing those combinations: 169 is the sum of the 78 unsuited non-pairs, the 78 suited non-pairs, and the 13 pairs (unsuited of course). Clearly 169 doesn't mean 'the number of two-card poker hands', because then there would only be 13 pairs and 78 non-pairs.

By the time we get to the flop, for example, you could say there are just 9 possible poker hands - straight flush, 4 of a kind, full house, flush, straight, trips, two of a kind, pair, no-pair.

So what exactly are you looking for?

[Jamper]

The number of unique hands, with the same rank or potential-rank. For example, at the River I count roughly 330k. This is the easiest stage to calculate because there are no potential hands. About half of the total comes from the High Card hands:

13*12*11*10*9 - 11 (less the straights) = ~ 150k

It's the potential straights & flushes at the flop/turn that make the problem more difficult. Not to mention the 6-card hands at the Turn. Instead of toling over it, I thought someone might know. But it's no biggie - don't sweat it if you don't already know the answer.

-jamp