Re: Flop the nuts and get check-raised
 

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In short, we have to give villain the chance to make a mind-bogglingly bad mistake on the flop because he clearly doesn't like being popped OOP.

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...and because he's way more likely to get it in with a draw/worse hands than if you cold call and he doesn't improve on the turn. Obviously you get it in good close to 100% if he does improve on the turn; however, this will generally not outweigh the chance of him getting it in bad on the flop.

Re: Flop the nuts and get check-raised
 

999 is indeed the right 3bet size here btw.

Just assume he has 2pair always and go from there.

Re: Flop the nuts and get check-raised
 

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So many turn cards kill our action and there are tons of hands he'll be happy to get in on the flop with just 3-bet

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Yea agreed, there are plenty of cards that shut him down and your average donk can put you on plenty of hands his TP beats. 3 bet please.