[sweetjazz]

How many taggy villains would semi-bluff check-raise with a gutshot on the flop (and obviously they will peel the flop 3-bet) but fold UI on the turn?

I'm not sure that happens nearly enough to make the turn semi-bluff profitable, and I actually I am pretty sure it doesn't.

So I still think the turn check-behind is probably best. Ideally, you have 9 flush outs, 3 more straight outs, and 6 pair outs. In which case, you still lose 28/46 = 61% of the time. And those times when he check-raises you on the turn, you only have 13 - 15 outs. (Even worse if he will check-raise with Qsxs here.)

You don't need much folding equity at all to make this semibluff profitable, but is there even a 5% chance that villain will fold here?

Maybe villain would smooth call with AK/AJ preflop and play it this way, and fold on the turn. Or maybe he would play 33 - 55 this way and fold on the turn (though why wouldn't he just fold the flop then?). I don't know, it's hard to detect something that would happen that infrequently. But I just don't think it happens.

So I still think the turn continuation bet is still fairly -EV. If you had an OESD instead of a gutterball, then it is close enough that this might be one of those "loose bets" analogous to Mason's "loose calls" that could be worthwhile for meta-game reasons, namely getting more value out of made hands in the future.

Personally, I find it psychologically discomforting to check behind on the turn, because it feels like I just gave up on my attempt to take the pot. But the only possible justification for betting this turn is for metagame reasons.

Finally, I agree with Josh that you should fire the final barrel on the river against an unknown. It doesn't have to work very often, and it might get someone to call you down with A high later, having noticed that you will bluff all three streets with just a draw. If it's the end of a session and you have any kind of a read that the player goes to showdown a lot, then save your bet as the bluff is hopeless and there is no metagame benefit. [It would be a much greater metagame benefit if you could check behind the river with your draw to set up a future bluff with a future missed draw. But you cannot, of course, count on anyone being that observant. On the other hand, it is quite easy to manipulate people into calling down, increasing the value of your made hands.]