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Reraiseallin
04-13-2005, 07:00 PM
I am a fish. Just wanted to ask a quick couple of questions: What are the chances (assuming 5000 runners) of a set being beaten by a higher set? Secondly, given 9 per table, what are the chances of AA and KK being out there preflop? Cheers, yours sincerely, a fish.

closer2313
04-13-2005, 08:03 PM
Im not sure what you mean by your second question, do you mean if you have KK what are the chances someone has AA?

If you do, this is the solution

Example 1

This is the simplest non-trivial poker example. If you hold KK before the flop, what is the probability that at least one of your 9 opponents holds AA?

Note that at most 2 opponents can have AA. The probability that any particular player holds AA is 6/C(50,2). So the first term in inclusion-exclusion is simply 9*6/C(50,2). That is the sum of the 9 probabilities of each player having AA. This alone is very close to the exact answer, but it double counts the times that 2 players hold AA. For the second term, we take the probability of 2 particular players having aces, 1/C(50,4), and multiply by the number of ways to pick the two players, which is C(9,2). So the final answer is:

P(KK vs. AA) = 9*6/C(50,2) - C(9,2)/C(50,4)
or about 4.39%

Found here http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&amp;Board=&amp;Number=417383&amp;page=&amp;v iew=&amp;sb=5&amp;o=&amp;fpart=