A BayesTheorem Question...Hand Likelihood...

[thirddan]

I asked a question in a SS thread last night but now it is long buried and i don't want to bump a long thread to ask this question, which may be a simple one...

In the hand the Hero figured that on the turn the villain was equally likely to have AA or KK (50% each)...On the river a K fell...Is the villain more likely to have AA now that Hero can see that AA can be made 6 ways and KK only 3 ways?

MicroBob (sorry if you didn't want your name mentioned) commented that this logic might not make sense since it doesn't work as logically in other situations, for example If I put my opponent on AK or AQ preflop and a K flops is it now more likely that he has AQ? This case is not as drastic since it doesn't cut down the likelihood as much as the previous example.

I understand that this works preflop because if my opponent could have AA or KK and I have AQ then KK is more likely for him...

Can we make these kind of adjustments postflop and do they make sense to do? Any comments are much appreciated.

[laja]

Lets take this to the extreme to illustrate a point: Before the flop your opponent caps it and you know this particular player would only do so with k/k or a/a. The flop now comes a/a/a, we now know he obviously has the k/k.

The chance of them having a hand is the number of ways, had the flop camep a/a/x he would have 1 way of having a/a and 6 ways of making k/k, so 1/7 chance of having the a/a.

If you further played this hand like there was still a 50% chance he had the quads you would be losing potential money.

I think it is somewhat useful but it is nothing special as our minds already take these things into consideration without even thinking about it. If somone raises preflop we believe there is good chance he has an ace but if the flop comes a/a/x we narrow that chance a lot but are still a little weary.

[axioma]

the short answer is yes, the K on the flop does make it less likely your opponent has pocket K's.