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Min-raising sucks.

I'd fold unless I had an actual reason to think he might bluff here.

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I agree, time to fold. Yeah he might be buying it, but then again he might have JT and planned on stringing you along until the river where his all-in might seem desperate to you. It might not be what you or I would do with JT here, but I see that sort of slowplaying at the 11s-33s a lot.

Granted, it's bad for business to imagine monsters everywhere, especially HU, but his calls--especially on the turn--tell me he likes his hand. Not sure if I'm being weak-tight here, but after he called my flop bet I'm probably shutting it down and check-folding future streets. Like you said, the blinds are low and there's plenty of time to find better spots. Also note that if he is on a draw, your betting 500 on the turn is almost giving him the right odds to call his 8- or 9-outer.