Re: Some probability questions for you math masters
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As I said in my post, assume it's 3 random hands (although in some of the questions, your hand may not be random, but the hands are random unless stated otherwise) and they all see the showdown.
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I don't think you did say that, but it makes it easier to answer.
In the first question, your best chance is obviously if there are no straight and flush prossibilities, no pairs on the board and your trip is the highest card on the board. Then you can't lose.
For every card on the board that's higher that your trips, the chances that a single player has a pair of them in hand is 1 in 330. If there's a higher pair on the board, the probability that a single player has a match is 43 in 330. If there's a lower pair on the board, the probablity that a single player has quads is 1 in 990. With any single pair on the board, higher or lower than your card, the chance of a full house without a pocket pair is 14 in 990. You'll have to count the straight and flush outs yourself, they depend on the exact structure of the board.
It's not quite correct to add up all the ways to lose and multiply by 2 for two players. It overstates the risk of losing, but not by much if the answer is low. Figuring this one exactly means counting up all the cases and figuring which ones overlap.
Pokerstove will do the calculation for you if you give a specific board and your hand. So you could get exact answers for a few different cases, would that help?
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