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This deep is it really a good idea to make a 3-bet with QQ on this flop? Certainly 4-flush hands (and pair+draw hands) are in his range, but the best result we can really hope for after a 3-bet is a fold, because whether he calls or shoves we'll be in a pretty sick spot, out of position, and it's much easier for him to put us on mostly overpairs than it is for us to figure out what percentage of his range we have good equity against.
Basically, QQ is just not that strong on this board and raising this flop heavily this deep just turns our hand into a bluff in my opinion. We may have the best hand on the flop, but we are also out of position and this is a pretty bad RIO situation. I don't like it as a default play without a read.
That said, every option is tough so I'm not sure I can really advocate just folding to the flop raise. Just calling and getting it on a blank turn might be a decent compromise (bet/call).
Certainly as played you have to get it in on a blank turn. When you raised the flop you basically already decided that, and you shouldn't have raised the flop unless you intended to do so.
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QFT, spot on.
OP, check out
www.holdemranger.com for a PokerStove type tool that allows you to weight ranges without having to go through all the maths yourself.