Re: trips to full houses
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Do you have a pocket pair?
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no.
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I am implying, however, that my opponent has a pocket pair.
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Why? What if you have 23 and your opponent has 34 on a board of
3347J
edit: by my count, there are 9 ways your opponent could have 3x for a boat, and 9 ways (s)he could have a pocket pair for a boat, so there are 18 possible hands he could hold. Since you are looking at 7 of the 52 cards in the deck (your hand and the board), there are only 45 cards left to deal your opponent's hand with => 990 possible hands he could have.
18/990 = 2/110, or about 0.0181818 or 1.8%
So, IF YOU ARE HEADS UP, the probability that your opponent has a full house when you have trips is 1.8%
The probability one of 9 players have it can be approximated by 1-(972/990)^9, which is approximately 0.152 or 15.2% However, this over counts times when 2 or more opponents have boats, so you'd want to use inclusion-exclusion to get an exact answer.
If I had to guess, though, I'd say around 14% if you assume that everyone goes to show down. A computer simulation would give a much better approximation, but I'm not feelin' it tonight. Sorry [img]/images/graemlins/smile.gif[/img]
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