POKER TOOLS - Poker Odds

[BigOx56]

I think the odds of flopping quads stated above, about 407 to 1, is overstated. Suppose we have 77 and we are playing 9-handed. First we have to make sure that none of our opponents has a 7, because otherwise flopping quads is impossible. So the 16 cards dealt to our opponents must have come from the 48 cards remaining in the deck that are not sevens. (48 choose 16)/(50 choose 16) is (34x33)/(50x49) or about 0.458. Disregarding the order in which the flop cards are chosen, there is only one way to choose both sevens out of the 34 remaining cards in the deck, and the third flop card can be any one of 32. So there are 32/(34x33x32) flops that will give us quads, or 1 in 1056. So we will flop quads with a pocket pair only 13 times in 30,000 hands.