Tricky spot. I would not be surprised if this is a check back for ICM reasons. I think that last bet might need to go in on a 65-70%+ edge depending on payout structure and other stacks. He has 5-8 flush combos undiscounted, unless he's making some ambitious preflop calls.

Ex.

Stack if shove, called, win = 696k

Stack if shove, called, lose = 0

Stack if check, win = 476k

Stack if check, lose = 220k

EVshove = %fold(EVof476k) + %call[(equityvscall)(EVof696k) + (1-equityvscall)(EVof0k)]

EVcheck = %fold(EVof476k) + %call[(equityvscall)(EVof476k) + (1-equityvscall)(EVof220k)]

Equate EVshove and EVcheck to solve for minimum equity you need vs a call range, 'equityvscall'. Other values provided by an icm calculator.

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Doubtful he's c/r/flatting with less than a set, maybe KQ. I think c/r-ing with a low flush is not that much different than c/r-ing with a set considering most players cbet their flushdraws. Not sure if people c/r those sets in practice tho.

Flop can go either way, imo.

Turn, I'd bet bigger as a default with my range and as played I'd just flat the c/r.

I like the flop check back against a good player, we have a lot of deception and we can peel with our Ahi if he leads on further streets (not bad to induce bluffs when we have such heavy equity and the nut draw).

Turn I agree with Yoren, I'd absolutely bet way bigger than 11K, as there is more than 35K in the middle (right?). I'd bet at least 20K, probably more. I mean we check back flop for deception, now that we hit we have to build the pot, as we'll be called light and he'll be willing to make moves. When we bet tiny and then 3b this turn, we actually lose all the deception value of the check back flop, as we're now faced up as having a flush, and maybe a few bluffs with the Ac, but how many Ac with no pair do you play this way?

For those reasons, I don't think we can profitably bet river with ICM, as we're now beat by a decent chunk of his range that XR and peel turn, and we certainly rep a big flush, making it tough to be called by worse (I still expect vilain to have a hard time folding a flush considering his aggro image, but we do give him all the reasons to opt for a hero fold... and he can't have better than a Thi flush).

Hard To Speak On ICM Without Knowing The Other Stacks At The TaBle.  WhaT Is Your Plan With Your Turn Raise Besides, Win The Pot Right Now?  WhaT Hands Do We Think We Are Representing With Our Raise On The Turn?  Which, If Any River Cards, Are We Piling It In?

I think you can eliminate a lot of small flushes from his range. The type of player that wants to run over the FT won't just peel small suited connectors from the SB.

Thinking more about his preflop range I would assume QQ and KK are going to be 3b by him almost every time. Just 44 and a small % of slowplayed QQ and KK make sense for his boats OTR. 

bet call for value

Definitely betting. Not sure if I'm bet/folding, or bet/calling, but definitely betting. Something like 80k. If he double checkraises you, well it's villain dependent obv., but 90% of the time live that's the near nuts lol.