[Heisenb3rg]

button clearly has an ace.
facts we know.

1-His stats indicate he's a reasonable agressive player
2-He 3-bet PF, narrowing his range a fair bit. For arguments sake lets go a little loose. KQ, AT+, 77+
3-He's over-calling the flop and the turn, when both have you have shown strength. The bettor, significant strength.
4-He can't have KQ of spades because you have the K of spade

What is the ideal way to play AT-AQ in buttons case? Exactly like this. He doesnt want to scare off KK/QQ into a fold, and doesnt want to get 3-bet by AK.


What do you think could be going through a rational players mind that would have him overcall to the river with QQ?

He would have to think that theres a decent chance that you capped pre-flop with JJ- and that the other opponent is calling down with JJ- as well.
And that's if he even has QQ!

Even if by some small chance he has a lower pocket pair, you have to multiply the chances that the initial raiser has an ace. This is also a decent percentage (although lower).

To me it is pretty obvious that you are not good here 8% of the time.

I would probabily check-fold the river, and possible check-fold the turn depending on how much these guys peel.
By getting called in two places on the turn you've got pretty significant information.