Can Villain Get Away Here with AK?

PondyPondy Red Chipper Posts: 150 ✭✭
I am analyzing this hand from villain's point of view to see how I would have played it. And I am surprised to see how poorly TPTK performs in this 3bet pot.

10NL full ring on Pokerstars. Effective stacks 100BB

Hero opens from UTG to $0.3. Fish in SB calls.
Villain has :As:Ks in the BB and 3bets to $1. Hero calls. Fish folds. Hero's range here is 77-KK, AT+, KQ, JTs, T9s, which is fairly wide because he might expect the fish to call as well and also because Villain might just squeeze with air.

Flop comes:
:Ad:Jc:8h

Pot $2.30
Villain cbets $1.23. Hero calls. Hero's range here is AT+, 88, JJ, and probably still QQ, KK, T9s and KQ, maybe JTs.

Pot $4.76
Turn is :8s
Villain bets $2.23. Hero calls. Hero's range here is 88, JJ, AK, AJ. Maybe AQ, but not AT. Some chances that T9s doesn't go away.

Pot is $9.22
River is Qh
Villain shoves. Hero calls and shows :Ah:Jh to win the pot.

If I had been villain, I would definitely not have gone for 3 streets of value, but I wonder if villain could have gotten away from the hand. When I did my analysis, I saw that the only possible weaker hand that would call 2 streets here would possibly be AQ and even that would beat AK by the river.

But then I hear coaches recommend to stack off TPTK in smallish spr pots (this was just under 4). So can someone really get away with AK here? Can you fire a cbet and then check-fold? Or would you check-call twice? Three times? I was really surprised to see how poorly AK performs in something that seems a dream flop for this hand.

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