Re: odds of set over set
If you have a pair of Kings in a ten player game, there is a 4.4% chance that another player has a pair of Aces. If you have a pair of Queens the odds are almost twice as high that another player has a higher pair (it's not quite twice as high due to the probability of more than one player having higher pocket pairs, but for this problem it's a good approximation to assume the odds are proportional to the number of pairs that beat your pair).
Given that two players have different pairs, the odds that the board will contain exactly one of each card is 3.1%. Some of these boards will make straights or flushes, or have three of a kind on the board.
Multiplying the two together gives 0.14% times the number of cards that beat your pair.
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