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These kind of spots, we kinda need to play our entire range the same on the flop otherwise we're face up when we have AK. I think here I just check everything. On most flops I'll cbet everything, but this is a flop where I'm probably just going to check. I want to control the pot when I have QQ+, I have all the flop when I have JJ, and I want to see a free turn when I have AQ+.
I'm calling reasonable turn bets.
As played, definitely check now. If he bets river, I guess it depends on the river and his sizing. I can sometimes hero call AK high, but villain has to be capable of floating flop light for AK to be good here. This does seem like a more common spot to float though, so if he's floating sometimes, chances are he's floating now. AK is still a strongish hand on this board, any 9 or lower, or a jack, on the river and it still has decent showdown value.
btw I think you're expecting him to fold way too much on the flop if you think he's throwing away his 55-TT. I'm not folding a pair to one bet on this flop. I'll have some ace high too, probably with a backdoor flush draw. I'm also check/calling Jx and 44 obviously, so I have a fairly balanced check/call range.
Given stacks and pre flop 3bet size, pre flop I'm calling 22+ JTs+ AJo+ A2s-A5s ATs+. I can float all of this range except my ace highs where I don't have a backdoor flush draw.
This would make AK an excellent value bet on the flop, and the flop bet probably isn't bad in terms of ev, but if we're betting the flop with all of our range then it gets tricky to play the turn and river with everything except our JJ and any other Jx we might have. It's easier for villain to bluff us off our premiums.
When we check this flop, we can get to showdown with just two calls. That makes it really hard for Jx to stack us when we have AA.
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