by Felonius_Monk » Tue Nov 30, 2004 8:21 am
I think you're underestimating there, ice. You hit a pair or better with 2 cards of different ranks by the river nearly half the time (this is why AK vs 22 is a coinflip; if you only caught two times in three then the 22 would be a big favourite). If you're talking about pairing up on the flop, the odds are 1-(44/50 x 43/49 x 32/48) which is roughly 1/3 (I assume that's what you're talking about with your 1 in 3). So, the odds that two random hands with 2 cards of different ranks will make at LEAST one pair by the river are around 3/4 (75%, or slightly under), whilst the odds that at least one will pair up on the flop are 1-(2/3 x 2/3) = 45% or so. This all assumes that you don't know any dead cards, and that both cards in each hand are different (i.e. NOT AQ vs A8 etc).
Monk
xxxxx