Re: probabilty of ATC opponent flopping flush draw
Call the event that he has two spades A, and the event that the flop contains two spades B. The probability of A, given that B has occured, is different from the probability of B given that A has occured.
Maybe it would be a little easier to think of a more extreme example.
Suppose on the board there a 4 card straight flush - say, 5s6s7s8s. What is the probability that he has a straight flush if he has random cards? Not too bad, since he only needs the 9s or the 4s. It actually works out to be 8.5%.
Now, if we know that he has the 9s or 4s preflop, what is the probability of him hitting a straight flush? I won't bother calculating it, but I think you'll agree it should be much less than 8.5%.
You can see that the same concept applies in your flush draw example. If you want to see some math on the subject, look up Baye's Theorem.
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