Re: Omaha math - chance AA is out
Not quite.
Your first computation is approximately correct if you're the only one at the table playing Omaha, everyone else is playing hold'em. But since they each have four cards, there's a much better chance that one has AA.
For a single hand, there are C(48,4) = 194,580 possible hands. There are 6*C(44,2) = 5,676 ways to hold AA and two non-Aces (so this does not count AAA7 but does count AA77). 5,676/194,580 = 2.92% or about 1 in 34.
The exact number with 9 players is a little more complicated, but multiplying by 9 is approximately correct.
With a lone Ace it's approximately correct that the chance is cut in half, since there are now only 3 pairs of Aces available, not 6. However, there are more available combinatinos of cards to fill out the hand, 990 instead of 946. So the probability really goes down by 48% instead of 50%.
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