Re: KK vs. AA
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Not quite. The odds of getting a specific pair dealt to you, like AA, is 1/221 or 220 to 1. There's one chance in 13 (4 in 52) of getting an Ace on the first card, and if you do, one chance in 17 (3 in 51) on the second. 13*17 = 221.
Once you have KK, or any other two non-Aces, the chances of another player getting AA increases to 4/50 * 3/49 = 12/2,450 or about 1/204. That's the appropriate number to use for this problem.
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wouldn't that be heads up?
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He's talking about the chance of one particular player having AA when you have KK. That's the same whether it's heads-up or a full table. Then if you want the chance that any of your N opponents have it, you would multiply that number by N for a very good approximation. To be exact, you would then have to subtract the probability that 2 opponents have it, which is C(N,2)/C(50,4), but this is a small number.
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