Poker Strategy

The aces are still ahead, but the the 76h now has a pair of sixes with a straight draw and a flush draw. He has 20 outs: any heart for flush (9) a seven for two-pair (3) a six for trips (2) a five for straight (3) a ten for straight (3).

The next two cards can not contain any of these 20 cards in order for the aces to hold up. We therefore must choose the last two cards from only 25 cards (45-20=25). 25C2 = 300 times while the total possible combinations are 45C2 = 990.

There are 29 exceptions where one of the 20 cards will fall and the aces will still win by making two pair or a full house. The 29 exceptions follow:

aces up vs. two-pair	aces up vs. two-pair	aces full vs. flush	aces full vs. trips and/or flush
7c8c 7c8d 7c8s 7d8c 7d8d 7d8s 7s8c 7s8d 7s8s	7c9c 7c9d 7c9s 7d9c 7d9d 7d9s 7s9c 7s9d 7s9s	Ah8c Ah8d Ah8s Ah9c Ah9d Ah9s	6dAh 6dAs 6sAh 6sAs

The aces will then win 300 + 29 = 329 of the times and the 76h will win the rest of the time 990 - 329 = 661. the 76h is favored to win on the flop by 67% (661/990=.667).