400nl AK turn decision vs. deep opponent

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I think when you flat call and keep the pot 'small', you have a better chance of getting to a showdown for a reasonable pot size.

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Yeah, if he has a worse hand than you on the river

You think he's slows down on the river with 2 pair + ? Also, if you call, the pot on the river is $340, so a decent bet from him is $200-$300, whereas a turn raise from you can be $150-$200 more. So I say that raising the turn is cheaper when you are behind