I wonder what the math is, if we knew that villain's range is AKo/AKs/QQ+, and would only fire 1 street, and shut down when unimproved if our call(s) are still +EV.

Theres no need for anyone to playback at people when players like hero will level themselves into making bad calls.

Almost assuredly not worth a call pre because of the odds that A or K spike on you when they do have AK. Is worth it on the flop, as shown above if you make those assumptions.

What about when the flop comes AJx?

Board: Ac Js 4h
Dead:

equity win tie pots won pots tied
Hand 0: 77.811% 77.81% 00.00% 34665 0.00 { JJ }
Hand 1: 22.189% 22.19% 00.00% 9885 0.00 { AA, AKs, AKo }

Or when the flop comes AKJ

Board: Ac Js Kh
Dead:

equity win tie pots won pots tied
Hand 0: 51.215% 50.41% 00.80% 22458 358.50 { JJ }
Hand 1: 48.785% 47.98% 00.80% 21375 358.50 { KK+, AKs, AKo }


Or when it comes KJ2

Board: 2c Js Kh
Dead:

equity win tie pots won pots tied
Hand 0: 81.150% 81.15% 00.00% 50613 0.00 { JJ }
Hand 1: 18.850% 18.85% 00.00% 11757 0.00 { KK+, AKs, AKo }

Or when it comes KQJ

Board: Qc Js Kh
Dead:

equity win tie pots won pots tied
Hand 0: 63.092% 62.28% 00.81% 44396 576.00 { JJ }
Hand 1: 36.908% 36.10% 00.81% 25732 576.00 { QQ+, AKs, AKo }

No offense, but this is pretty bad work, put it in pokerstove versus their range and assign percentages preflop. Of course it looks good if you flop a set, but that doesn't really tell us if preflop is a good idea.

There's no way you have 40% equity pre in all likelihood.

You don't have 40% equity pre. You have 36.2%

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 36.190% 35.98% 00.21% 125683776 731868.00 { JJ }
Hand 1: 63.810% 63.60% 00.21% 222162504 731868.00 { QQ+, AKs, AKo }

He tends not to double/triple barrel. I didn't think about that while I was writing his description, but in the pots where he raised to his standard 12, he usually cbets 100 percent (OOP and IP) of flops but does bet again on the turn maybe only 10-20 percent of hands and usually folds to aggresion if he is not IP. I must admit though that I haven't seen him do that in 3bet pots and I have not based my call in a hand on this that much. Looking back though I think I can expect him to fire AK or even AQ only on the flop (and I can see him 3betting AQ sometimes for sure after playing longer with him).

This might be true and I wasn't sure what to do. That's why I have posted the hand. With new information from seeing more of his play, I probably play against the same or put a 4bet there. But I didn't have that much info as I do now while the hand was played, so I should have fold pre and lose 10 and play better spots.