[BruceZ]

[ QUOTE ]
I haven't looked hard at the other numbers, but my guess is that they're at least slightly off. I believe you overlooked the Inclusion/Exclusion principle (sticky, for the love of GOD, lol). So you're double/triple counting times when more than one person has the hand in question.

[/ QUOTE ]

Double/triple counting would happen if he just multiplied by the number of opponents, assuming mutual exclusivity. He's not doing that. He is using the approximation of independence, which should actually give an answer that is less than the actual value. This is because each opponent who does not have it makes it more likely for the next opponent to have it. We are approximating all of the probabilities of not having it as equal, which gives a result that is too high, and then we subtract from 1, which makes it too low. This should give a lower bound, and mutual exclusivity should give an upper bound, so we can see how accurate it is, and whether we need to use inclusion-exclusion.