Re: odds of FLOPPING 2 pair or better in holdem
If you have two different cards in your hand, you can get two pair or better by flopping two or more of the six matching cards in the deck. There are 15 ways to get two of them, with 44 possibilities for the third flop card, and 20 ways to get three. 15*44 + 20 = 680 of the 19,600 possible flops. That's 1 chance in 29.
If the hand is suited, there are also 11*10*9/(3*2*1) = 165 hands that give you a flush, with no overlap to the other hands.
With KQ there are 128 possible straights, QJ has 192. If these hands are suited 2 of the KQ straights and 3 of the QJ are straight flushes, so you don't want to double count them.
This doesn't count hands where there is a non-matching pair or trips on the flop to give you better than two pair.
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