My question was aimed at AbstraktPB. Since no one will fold anything when I shove AA, clearly checking back the flop and shoving the turn is by far the best play with that hand.
And I'm not saying that sarcastically. I actually think this play makes a buttload of sense with AA in a 3-bet pot on a rag flop, because what's their range? Usually AK, AQ and medium PPs. Sometimes KK trying to trap, sometimes a smaller PP that probably should have folded preflop but thinks they had set mining odds
. A free card costs very little in terms of equity on a flop like this, and we're apparently not repping anything when we check beck flop and shove turn.
So why wouldn't we?
Edited to add:
I do think this requires you to stack off occasionally when opponents show all signs that you're beat because you've under-repped your hand on the flop. (Stacking off with AA in a three-bet pot is usually never wrong).
We definitely need to stack off if we get played back at on the turn after checking the flop. But like you said, we don't really have much choice in the matter after the preflop 3-bet.
I also wanted to say that I really don't like checking AA out of position on a flop like this, because we have nothing to balance it with. I'd never check AK, because I really want them to fold small pairs and I'd rather keep momentum up and make a bluff on the turn rather than check/folding. I mean, let's say I get called by 77 after betting AK OOP on this flop, and the turn is a J, and I shove. Is a decent player going to call with 77?
Checking AA OOP after 3-betting preflop on this board is not a sign of weakness to me. I prefer to always bet OOP.