Probability of flopping a pair or better for two people HU

[kurosh]

It's HU, one guy has AK, the other has T9. What's the probability of one guy flopping a pair? Both flopping a pair? If one flops a pair, what's the probability the other one will hit a pair by the river?

[pokerlaw]

Either flopping a pair:

12 cards will do that (3 aces, K, 10, 9). so roughly 36/48 or 75%.

Both flopping a pair: one person hitting a pair = roughly 18/48, or 40%. square that to see odds of both hitting, so 16%.

3rd situation: If one flops a pair, 40%. Chance of getting pair by river = 6 outs 4 times, since one card is a pair for opponent. 24/45 about, or 55%. 40% * 55% or about 22%. NOTE - if in this secerio you are specifying that villan does not also flop a pair, but instead gets on on turn or river, this gfoes down to I would guess 8% or so.

[Cobra]

There are some errors in your computation. You can't just figure the odds of getting a pair on the next card and multiply be three for the flop. This creates many double counts.

Probability of one person getting a pair is:

=12*(36 c 2)/(48 c 3) = 43.7%

The Probability of both getting a pair is:

=6*6*36/(48 c 3) = 7.5%

The probability that you hit a pair on the turn or river given the opponent has already paired is:

=(6*34+15)/(45 c 2) = 22.1% this is actually the probability you hit one or two of your cards and your opponent does not hit his card on the turn or river.

Cobra