[Cobra]

I think we sometimes underestimate the probability of a set over set. What we really need to think about is how wide is the range of hands that our opponent played and how does the flop fit into that range. An example might help.

At a full ring table the UTG raises to 3x the BB. He is straight forward TAG and you put his range at AA-TT, AJ's+, AQ'o+, KQ's. This is around 70 combination of hands. The button calls. He is a player that is reasonably tight and understands position you put him on the same range as the UTG plus all pairs, except AA and KK, and some small suited connectors. His range will be about 130 combos. You look down in the big blind and see 22. You and all your opponents have >200 BB so you decide to close out the action and call for set value.

The Flop comes T 6 2, rainbow. You have your set and now you are trying to figure out it anyone has a higher set.

The UTG could only have a set of Tens, the Button could have a set of Tens or sixes. How often did this occur. Because of card removal both opponents ranges have changed slightly after the flop. We will say that UTG has a new range of about 66 combinations and the button has a new range of 120 combinations.

Probability that UTG or button has you beat is,

3/66 + 3/120 + 3/120 = 9.5% or 1 in 10.5 times.

This is meant to just be an estimate, what I am really trying to say is that the wider a persons range is the less likely he is to have a set. If a person has a very tight range and you have bottom set, and both other cards fit his range then there is a 6 in (whatever his range is) chance you are beat.

Cobra