[Hince]

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I guess, my biggest problem with this hand is that Villain should never have AJ or better here, right?

So he's most likely on a draw but at the same time this is a great flop to float on right?

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This is probably the reason I don't think it matters if you bet or check to an unknown. It's probably really close whether he folds to you bet or you are WB. That turn is really ugly to a lot of hands, but it's also great for many that are in his range. In terms of EV, they are about even... so I would go with the option that helps my overall gameplan the most.