Re: A tough spot.
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4 betting does have value if BB is in fact raising with just two pair(because I bet the flop he may not put me on the straight necessarily) which he may fold and saves us at least half the pot those times we are chopping. If he has a set we make him pay for the draw but I am sure he wouldn't fold here.
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You'd actually rather let BB draw to his 4 outs since when he hits them you're usually just chopping the pot. The value of protecting your hand goes down when you're unlikely to have the whole pot.
The reason to 4-bet IMO would be if there's any chance of getting BB to fold a straight.
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