Giving it a try, not sure if I got correctly all the cases. I'll give you only the probabilities of each winning case, leaving to you the final tally.
Say that your pick is A23. I also assume that you make the pick before seeing your hole cards. Also, I'm gonna neglect any poker consideration. It is well known, for instance, that an Ace appears on the flop slightly less than its "uniform" share, since people tend to get involved in a hand and see flops with high cards.
Giving these assumptions, you have C(52,3) = 22100 possible flops.
Quote:
Originally Posted by PTLou
If Flop comes any 3 of a Kind. Pays 100:1
Guessing that here you win here with also, say, 444 and not only with AAA/222/333. If so, you win 13 * 4 times (13 ranks and for each rank you have 4 different 3 of a kind). So, the probability is:
13*4/22100 = 0.0023529411764706
Quote:
If Flop comes any combination of their three cards. Pays 75:1
So, you win with A23, but also with AA2 or similar. We need to remove AAA/222/333 because case #1. We got:
(C(12,3)-3*4) / 22100 = 0.0094117647058824
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If Flop comes any flush. Pays 10:1
We need here to remove A23 suited, because case #2.
(4*C(13,3)-4) / 22100 = 0.05158371040724
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Any pair on flop. Pays 1.5: 1
We need to remove AA2 flop types because case #2.
(6*13*4*12 - 6*3*4*2) / 22100 = 0.16289592760181
I might have made mistakes in counting.