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paulish
10-03-2005, 06:48 PM
If you hold pocket sevens,
Q1 what are the chances of flopping one card higher than seven, and two cards lower than 7?
Q2 What are the chances of flopping two overcards, and one card under 7?
Q3 What are the chances of your one opponent flopping a higher pair (or better), when he holds two unpaired cards higher than 7, when two overcards come on the flop, and you don't improve?

LetYouDown
10-03-2005, 06:59 PM
Running out, just have time to do this part:

Two unders, one over:
[28 * C(20,2)]/C(50,3) = 27.14%

Two overs, one under:
[C(28,2) * 20]/C(50,3) = 38.57%

Three overs:
C(28,3)/C(50,3) = 16.71%

Three unders:
C(20,3)/C(50,3) = 5.82%

Edit:
Assuming you're limited to two overs and an under for Q3:

378 combinations of overcards...undercard is irrelevant.

Of those, I believe 190 won't improve him.

So I come up with a 49.74% chance that he'll improve to at least a pair.

This does not include drawing hands and rules out flushes. Flopped straights are obviously impossible.