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[QUOTE="PurgatoryD, post: 1300529, member: 43498"]
Not quite. The probabilities would be correct if all players were drawing from their own decks of cards. But since all players share a deck, what P1 one has in his hand affects what P2 can have in his hand. So, there are dependencies that affect the probabilities.

For a concrete example, consider a deck containing only four cards: A, K, 3, and 2. Each player gets dealt one card and only one card is in the community cards. Thus, each player's hand consists of only two cards. The probability of forming a hand with at least one face card is 5/6 = 83.3%.

For two players, when trying to compute the probability that both players have a hand with at least one face card, if you just multiply 5/6 by 5/6, you get a probability of 69.4%.

However, this "game" only contains 24 different possible hand combinations. If you enumerate them all and see which contain hands in which both players have at least one face card, you will see that 16/24 = 66.7% do.

So, while the multiplication method yields a 69.4% probability, the actual probability is 66.7%. That's a close approximation, but not exact.

As I'm sure we all know from seeing so many different probabilities published for the same events, my numbers could be wrong. If so, please let me know! :)

-Dave
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