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Hypothetical question

You have QQ and raise after one limper. Button 3-bets, limper (fish) calls...say u just call. Flop is AKx rainbow...what do u do?

2. Same thing except u cap preflop.

I dont know how well I handle these situations where the 3-bet is legitamate. HPFAP mentions c/f the flop w/ a A or K in it and c/c down a favorable board.

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First lets define what a legitimate 3 bet is. If the raiser would only 3 bet you with JJ+ and AK, than you are a 5-2 underdog to have the best hand over the raiser, And if he would 3 bet here with TT+ and AK, than you are a 5-4 underdog to the raiser. When you combine the fact that you are a significant underdog to the raiser and you stil have another opponent you have to worry about, I would understand if someone checked and folded everytime in this spot. That said, if you just call the 3 bet there will be 10.5 sb in the pot. It may be worthwile to bet into the raiser assuming he will fold JJ or TT. If you do bet the flop you will be getting 10.5 to 1 on your bet so the question you have to ask yourself before you bet this flop is, are you a greater than 10.5-1 underdog for both the raiser to have JJ or TT and the other guy to also not have an Ace or a King in his hand. This would be a classic desperation bet, since theres a small chance you have the best hand but if youre raised youre going to fold and if youre called youre also usually done with the hand. So its either check and fold or invest one small bet hoping that both your opponents fold out. Of course if the raiser folds and the other guy calls you may have to bet again in case the limper is on a gutshot draw or another weak draw like a pocket pair draw. In a capped pot youre getting 13.5-1 on your desperation bet so there is a little more incentive to try this. Overall its close between checking and folding and trying a flop desperation bet.

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Desperation bet after you called the 3bet preflop looks so very ultra suspicious- opp must think "why didnt you checkraise?" If you capped, then at least it looks natural. Even then it feels pretty dubious. I'd only desperation-bet after calling the 3bet if I had a very specific read/reason to. Especially given that the limper could have you beat with Ax or Kx as well and we know he's not going anywhere if he got a piece.

2nd

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Your points are valid, naturally if you dont think a desperation bet will accomplish anything then its time to check and fold, I wasnt really advocating betting the flop here, i was just giving the hero something to consider. And vs the right opponents, a desperation bet may be worthwhile.