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Pre-flop: I like the call.

Flop: I'd push. There is is t270 in the pot. Any reasonable re-raise is going to commit you to the pot anyway, and you really would hate to get called and have an A/K/Q come on the turn.

If he has AA/KK/QQ that sucks, you'll just have to hit your J on the turn/river. His ~pot size bet on the flop with a relatively safe flop makes me think a higher pair than yours is less likely anyway.

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Bang on. Can you hope for a better flop with JJ (besides a set of course)? He could very likely be semibluffing with a big Ace or a heart draw here.