Too Passive with KK?

[MATT111]

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My thinking behind raising the turn:

a) Fold a 5 outer, probably not worth it since as you said the pot is small and he's probably putting 1BB in on the river. Do you find a river value bet if he checks?

b) Maybe get an ace to fold. When this happens it's huge, but I'm thinking it doesn't happen often at 2/4.

c) Charge a semibluff. Does a semi bluff usually fire another barrel on the river when they miss here?

As far as just folding out a bluff, I think if we're ahead villain is more likely to have a piece than be flat out bluffing, still a factor though.

To sum it up, if he'll bet the busted draws on the river, and he's paying off 1BB on the river with a 5 outer, then it makes no sense to raise if he's not folding an ace, since we just give up the chance to spike a king when 3 bet, or even make an incorrect fold if he has something like 34.

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I do not think this is a good situation for the turn-raise play against an unknown.
If he has a strong hand or is aggressive he may 3-bet so we won`t be able to see if we hit our 2-outer on the river although we invest 2BB.
If he has a weak ace - assuming he doesn`t fold - we invest the same amount as if we just call down.
If he is bluffing we want him to do so on the river as well.