View Full Version : Odds of a pair on the flop

Jon Shoreman
10-13-2003, 06:26 PM
I know the odds of the flop containing one pair only (i.e. not trips, two pair, or quads) is 42.34% (got it from Super System)

Can anyone tell me how to perform the calculation?
And also, how I would calculate for at least a pair (i.e. one pair, trips, two pair or quads)?


10-13-2003, 09:08 PM
the total number of boards is C(52,5).

as far as figuring out at least a pair, find the number of unpaired boards, which is 52*48*44*40*36/5!, and divide this by C(52,5) to find out the probability of an unpaired board.

this simplifies to 44*40*36/(51*50*49), which is right about 50% of boards being unpaired, meaning roughly 50% will contain at least one pair.