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What range of hands limp/reraises preflop and checks the flop? Do you think betting is the best way to maximize my EV here, generally speaking?

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Well, if you bet the flop. And Villian calls or raises then you can be confident he has AA, and can get away from the hand cheaply. I'm very much learning this game myself so take my advice with a pinch of salt, but that's my opinions anyway.

I suppose the more you think about it, the more clearcut he has AA, and just played it all wrong. But in the heat of the moment you don't have all the time in the world to think about it.