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I play it the same. If you're going to bet the turn, you're playing this hand for your stack. By checking you keep things manageable.

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I agree with this. You only have $80 left after the flop and the pot is over $80. If you bet the turn, I think you have to bet at least half the pot. So a $40 turn bet leaves you with only $40 left. I don't think I'm going to fold there if I get raised with those odds, but I don't really like playing for my whole stack in this situation. So I like the check behind on the turn, call reasonable bet on the river line. That's actually pretty standard for me in this particular situation.