determining the chances you are ahead in the hand

[bighead9]

Here is a very hypothetical situation that I am curious about. If you have AK and you specifically put your opponent on AA, KK or QQ, on a K82 rainbow board, the chances you have the best hand (if your hand were to be shown down right there on the flop) would be 1.5 to 1 right? I calculated this the following way: The only hands I lose to that my opponent could have are AA and KK (remember, I put my opponent on only AA, KK or QQ). Normally, these hands can be dealt 6 ways each, however, since I already have an ace in my hand (leaving only 3 left in the deck), aces can be dealt to my opponent only 3 ways, not the 6 ways that would normally be the case when all 4 aces are left in the deck. Kings can only be dealt 1 way, because I have a king in my hand and there is a king on board, so this leaves only two kings left in the deck that my opponent can have, and these two kings of course can only be dealt one way. So if aces are dealt 3 ways, and kings can only be dealt 1 way, this makes 4 total hands that beat me. The only other hand my opponent could have is QQ (remember, I put my opponent on either AA, KK or QQ), which can be dealt 6 ways, as there is no queen on board or in my hand, so all 4 queens are left in the deck. So with 6 ways QQ can be dealt and 4 ways aces and kings can be dealt, there is a 6 to 4 chance, or 1.5 to 1 that my opponent has QQ as opposed to aces or kings. Does this math work or is it inaccurate to something I am overlooking?

[pzhon]

What you said is essentially correct. One missing component is whether it is just as likely for your opponent to play AA as QQ in the way you observed. If you think someone with AA would alwys play that way, but someone with QQ would take another line 30% of the time, then you need to dicount the 6 QQ combinations by 30% to get 4.2 QQ combinations.

[bighead9]

true and well explained. i've been figuring out some poker situations in this fashion and was wondering if i was overlooking something as far as the math. thanks for the tip.