Re: The odds of trips.
Let me answer a simpler question first. Suppose you take 66T out of a deck, then shuffle the remaining 49 cards and deal two cards. What is the chance those two cards will form three of a kind with the 66T board?
The answer is there are Combin(49,2) = 1,176 possible combinations of two cards you can deal from the deck. 1 of them is 66, which gives four of a kind. 3 of them are TT and 6 of them are 6T, both of which give a full houses. 88 of them are 6 paired with a card other than 6 or T, which gives three sixes. Depending on which of these hands you want to count as a set, you can add them up and divide by 1,176 to get the probability.
In a real Hold'em game, it's not so simple. The basic probability is the same, but there is more than one person who can be holding the set. On the other hand, most hands with 6 in them will fold preflop. In a real game you are much more likely to see a set with a AAT flop than a 66T flop.
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