Just a side note to the main discussion, but if we're looking at this hand and we've got a good enough read to limit his holdings to AA/AK/QQ, AA/AK beating us and QQ losing to our hand, what is the probability of AA/AK vs. QQ?

QQ clearly has 3 possibilities. AA/AK could between 2.4 and 6 possibilities depending on how you look at it.

2.4 comes from the average of the number of hands present assuming all aces and kings are part of AA/AK. I'm not sure if we can look at it like this. To explain, here are the different sets that might lead you to think 2.4:

AA/AA/AA
AA/AK
AA/AK
AA/AK
AK/AK/AK

Taking the averages of these sets (3+3+2+2+2)/5 we get 2.4. This assumes that all aces and the king are only part of these hands though, which isn't necessarily the case. But if any aces or the king aren't part of these hands, then there are fewer AA/AK's possible.

Giving credit for 6 possible hands doesn't seem right because only 3 of the hands are possible at the same time AT MOST. (AA/AA/AA or AK/AK/AK)

Does anyone know what's right on this one?