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At this limit a 3 bet often means aces or kings. Keep that in mind.
So here is a possible range taking into account the flop cards but not flop play.
Hands that beat you
AA.....3 combos
KK.....6 combos
QQ.....1 combo
Total = 10
Hands you beat
AK.....12 combos
JJ ......6 combos
Total = 18
Mathematically AK and JJ account for a lot of the hands, but they aren't particularly consistent with how he has played the hand. He 3 bet PF. Postflop, he is playing the hand tricky aggressive, consistent with having a monster hand. AK and JJ are totally inconsistent with how he is playing this hand. Thus, I would weight the hands that beat you category more strongly than the hands that beat you. I don't like the way he is playing the hand.
---Play of the hand + Combos probability estimates---
Hands that beat you 75%
Hands you beat 25%
I would play this hand cautiously postflop. I'd prefer bets in the 1/2 to 2/3 areas. Your very large turn bet has put you in a tough spot, as you are now forced to play a big pot with hand that might be in very bad shape.
It looks to me like he wants to play for stacks. I'd be inclined to fold. Calling isn't terrible, but be aware that you are likely to get sucked in here, get pot committed and lose your stack if he indeed has AA, KK or QQ.
He's claiming to have a monster hand. I believe him.
If you fold and he shows you AK, JJ or something trashier -- make a note of it and try to play more pots with this joker.
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