Re: The odds of trips.
The probability that someone at your table was dealt one or more sixes after the flop is relatively easy to determine. The usefulness of this information is suspect because you don't know wether that person stayed to see the flop. That put aside the probability that one or more people at your table was dealt at least one six assuming you were not is:
9 opponents 1-(combin(45,18)/combin(47,18)) = 62.4%
4 opponents 1-(combin(45,8)/combin(47,8) = 31.5%
Now in trying to answer the question: is that player still there after the flop lets come up with some reasonable hand selections they may have played and determine the probability someone was dealt that hand. This is called inclusion - exclusion. Lets say your opponenet would stay with 66, A6 suited, 76, 65. And lets assume you do not have a A, 7, 6, 5.
Total combo's 19.
Hand possibility 1081
Opponents 9
Probability on one or more hands:
= 9*18/1081 - (9c2)*146/(47c2)/(45c2) = 15.8%.
Obviously the probability that someone would have three of a kind depends on how many playable combinations of hand that card makes.
A 6 makes few combo's
A 10 makes more
A ace makes a lot.
Cobra
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