KK, top set and I'm bet into by EP...wait for turn to raise?

[SocialWelfareIV]

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I was not refering to the hand themselves, but to the "passing a small edge to exploit a bigger one on the turn"-thought.

And I do think that this is "remotely" close.

A save turncard won't make our edge much bigger and we have everyone trapped right NOW.
This is not a SMALL edge on the flop.

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Calling here and raising the turn has nothing to do with our edge and everything to do with value. We would prefer to get 2 BBs in from each player on the turn and 1 SB on the flop over 2SBs on the flop and 1 BB on the turn.

The relevant questions here are:
how likely is BB to bet out on the turn?
how likely is BB to 3-bet the flop?
how likely are UTG, MP1, MP2 to call raises, 3-bets, and a cap on the flop? on the turn?

If we think BB is very likely to 3-bet the flop, then it's an easy raise.

If BB is unlikely to 3-bet the flop, but is likely to bet the turn (or even UTG), then go ahead and slowplay.

So how likely is the BB to hold a hand here, what is he likely to do if he does?