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I'm trying to figure out why you shouldn't raise.

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Whether he should raise the turn or not is close, since he can always 3 bet the turn and go for the free showdown if he misses his boat draw, so he would lose the same when ahead and win more when he improves. In this situation I would still call the turn however. On the river, raising would just be bad poker since calling makes the same amount of money without the risk of being 3 bet by a better hand.