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This is an interesting spot. Betting the turn allows us to control the pot size a bit more efficiently, and checking really disguises our hand if we hit our draw. If our implied odds don't change on the river regardless of whether we bet or check the turn, betting seems to be the better option as we get to dictate the bet sizing. But are we bet-folding, or bet-calling? If he flats are we check calling a J on the river, or leading out (i'm guessing c/c)? What about a King?
I think regardless, if we hit our flush we're shoving the river.
As played I'm not sure how much of his range he gets to the river with and folds if you shove, but i think it's a good portion.
He pretty much can't call with the bulk of his non-set, non-two pair holdings (except as pointed out earlier maybe KQ/QJ). I mean what's our range to shove the river, it's EXTREMELY polarized and heavily weighted towards nut hands. You probably can't have TT because you would've checked TT on the turn, so 22,77,88,JJ+,AQ. Your range seems heavily slanted to sets and overpairs than AK. What else are you raising with under the gun that you would lead two streets OOP and shove the river. He'd have to put you on a missed backdoor flush draw (what you have) way too much of the time for him to call profitably with the bulk of his non-monster hands.
I'm definitely a novice in a lot of respects, but I'm still a huge fan of making big bluffs in spots where you almost never have anything but a monster, because you'll inherently increase the frequency with which your monsters get paid off. I could be wrong about that though.
I think ISF Theory (and this is a really good example of it) would dictate that shoving can't be that bad, as your range is way way way ahead of his for making 3 aggressive actions OOP (starting with a raise UTG) and shoving the river on this board.
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