[ QUOTE ]
[ QUOTE ]
Assuming you don't have a pair in your hand to start with:
You will flop exactly 2 pair:
(44/50*6/49*3/48)*3 = 99/4600 = 0.0215
[/ QUOTE ]
What do these numbers represent? I was trying to figure this out using the poker odds calculator and subtracting out trips and full houses and came up with a different number.
This appears simpler and more precise anyway, so I would like to know how to construct this type of formula for 2 pair, trips, and full house.
[/ QUOTE ]
Suppose that we hold QJ (the calculation is the same for any non-pair). There are 3 Jacks, 3 Queens, and 44 other cards out of the 50 cards remaining. The probability that the flop comes xJQ or xQJ is the probability that the first card is one of the x other cards (44/50), times the probability that the second card is a J or Q (6/49), times the probability that the last card makes 2-pair (Q when 2nd card was J, or J when 2nd card was Q, 3/48). Then multiply all of this by 3 since the x can come in any of 3 positions.
See
this post and its links for more on trips, full house, etc.