Re: KQo Dominated?
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Oops, pzhon has the answer.
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No, I posted a way of getting an estimate. My estimate (.2645) is good if the dominating hands repel each other perfectly. You posted a way of getting an estimate, too. Your estimate (.2354) is good if the dominating hands don't repel each other at all. The actual value is between the two, and it is messy to work out.
To refine my estimate, we can consider the probability that at least two players have dominating hands. After you have KQ, a pair of players can have (50 choose 2)(48 choose 2) cards. If the first player has one of the 6 AA hands, The second player can have a dominating hand 19 ways (8 choose 2 - 9 ways to have KQ). If the first player has one of the 3 KK or QQ hands, the second player can have a dominating hand 25 ways. If the first player has one of the 12 AK or KQ hands, the second player can have a dominating hand 22 ways. These total 6*19+3*25+3*25+12*22+12*22 = 792. The probability that a pair of players has dominating hands is at most 45*792/(50 choose 2 * 48 choose 2) = .0258.
So, the probability that KQ is dominated at a full table is between .2649 and .2645-.0258 = .2387. It should be much closer to the latter.
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