[Caballa]

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The "call a standard raise, shove over a 3bet" move almost always screams "I have a mid pair up to JJ at best".
Everyone else in the hand can pretty much play perfectly as a result. For that reason I'd prefer a call, although I think it's better to 3bet yourself in the first place.

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the "call a standard raise, overcall a standard reraise" move almost always screams "I have a mid pair up to JJ at best"

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Yes, but is QQ+ not going to make a continuation bet on a board of 5 8 J against two callers? Given the size of the pot and stacks you're going to be called all-in regardless of how much it screams that you've probably hit a set based on your preflop call.