Re: ODDs math question
You got an excellent reply to your specific question. I'll try to address your general one.
Expected values add. The expected number of matching cards to your pocket pair on the first flop card is 2/50, or 0.04. Before any flop cards are dealt, the expected value is the same for your second and third flop card as well. The 2/49 figure for the second flop card assumes that you didn't hit on the first one.
So on an average hand you will get 0.04 + 0.04 + 0.04 = 0.12 matches to your pocket pair in the flop. You can't get three matches (if you do, run for the door before you get shot), so the only possibilities are zero matches, one match and two matches.
It's pretty easy to compute the probability of zero matches, (48/50)*(47/49)*(46/48) = 0.8824. That means the chance of any matches is 0.1176. 0.0024 of the time we must get two matches, so that our average number of matches is 0.1200. Therefore, 0.1152 of the time we get exactly one match, trips but not quads (actually, it's 0.1151 due to rounding).
The 10.9% figure you cite also subtracts off full houses.
|