[W. Deranged]

I think a flop check raise for value is in order here.

A good thing to notice about the flop play on this hand is that you cannot protect your hand, really. Most opponent's three-betting standards include hands already beating you (the big pairs and maybe AJ or a hand like 88), hands with basically very few outs (like 99 or TT), or hands with two overcards (like AK). Therefore, there are basically no hands villain could have that have multiple live outs that he would simply fold to a single flop bet. Missing the flop sucks for value reasons, but it's not a total disaster like some missed check-raises are which have a high likelihood of causing you to lose a hand you would've won had you bet.

I also think a flop check-raise will make the rest of the hand much easier to play. I don't necessarily want to commit to having to three-bet the flop here. Without at least a flop check-raise or a flop three-bet, I don't feel we can define villain's range of hands with enough precision to be confident in many later folds.

As played, I'm calling the river too just because the action is so bizarre that I can't confidently say villain isn't bluffing. His line here is basically inconsistent with most all logical hands, and I'm not ruling out a river bluff with missed AK or something like that.