*Originally posted by maniac*

is this 839,028,960 the numer of boards possible?

839,028,960 is the number of boards analyzed by PokerStove when you calculate the equity of 7

5

against the range.

__48 choose 5 __ do you mean deck +flop?

48 choose 5 means the number of ways of choosing 5 objects out of 48. Once you select a hand for yourself and your opponent, there are 48 more cards, and the number of possible flops+turns+rivers (when you don't care about the order) is 48 choose 5 = 1,712,304.

For each combination in the calling range, there are 48 choose 5 boards, so to count the combinations you can divide the 839,028,960 (reported by PokerStove) by 1,712,304 to get 490 combinations. This is a faster way to count the calling combinations than saying

6 combinations of AA

6 combinatiosn of KK

...

3 combinations of 77 since you have a 7

6 combinations of 66

3 combinations of 55 since you have a 5

...

12 combinations of A8o

9 combinations of A7o since you have a 7

etc.

You can verify that this method, dividing the number of reported games by 1,712,304, gives the same count of combinations in some simpler situations, like AK vs. QQ+.

I hope this helps.