Very interesting hand, I know I am late to the party on this.
Villain is loose-aggressive with a high raise frequency but typical (low) 3-bet frequency for these stakes.
Villain rarely has true bluffs but he bets made hands aggressively… sometimes he has it at showdown, but he’s also frequently getting better hands to fold due to aggressive betting and check-raising.
UTG / Hero =


and open raises to $10 (standard for the table)
UTG+1 / Villain = 3-bets small to $25
Folds around to Hero who __________ (folds / calls / 4-bets)
I actually think preflop this is a very interesting decision. This action is read dependent, but I think I like a call in this spot out of position against an infrequent 3-better
The 3-bet to $25 is basically a min-click. Most 1/3 players don't 3-bet small for value or to trap; a min-click at this level is almost always weakness. He wants to see how serious you are, i.e. "where he's at."
AKs is too good to fold, too vulnerable to flat. I think you're 4-betting here to at least $85, maybe a little more since you'll be OOP.
At these stakes, crazy to just call a tiny 3 bet from an unknown, eh? A loose aggressive raises us to a small amount. Even if he doesn't 3bet too often I have to think this range has lots more than just KK/AA. If we call, we're playing OOP with a premium hand. Much rather raise. We can fold if we get 5 bet but for now we build a pot and play back with a hand that dominates some of his range.*
* = I suck at poker, so all of this isn't good advice.
I would probably follow this logic against a normal or a frequent 3-better, but I just think an infrequent 3-better is going to have a range unbalanced toward mid to high pairs and very few unpaired hands. I am probably going to maybe range such a player on 88+ (maybe 77) and AJ+, and maybe KQs as the one possible K-high holding. Either way AK dominates a few of these holdings, but I expect to be against pairs more often here, which is not great news for AK.
Furthermore, given where I would put villain's range, I don't think he's folding to a 4-bet very often so that reduces some of the upside for raising to me. And if we don't improve, we are going to have to make a careful decision on whether or not we can bluff later in the hand.
Also I think at this sizing, as hero, I am actually going to call this pretty widely, so I don't think it hurts to have a couple stronger-than-expected hands in our calling range here. AKs strikes me as a good candidate for this.
Even if not raising, this is more than a good enough hand to call $15 more with $39 already out there.
FLOP


Hero has a gut shot straight draw, backdoor flush draw, and 2 overs
Ranges are fairly close and I’m not sure if I’m ahead or behind, but I’ve got a world of possibilities.
HERO checks… I’m checking my entire range here in flow to see how the VILLAIN plays it.
VILLAIN bets $40
75% pot bet shows strength but the absolute dollar amount seems fair, especially given my hand and implied odds. Plus, VILLAIN loves to stab/overstab flops to apply pressure, even with A high and moderate made hands.
I’m never folding here and I see no reason to raise (better hands don’t fold and worse hands don’t call).
HERO calls to realize equity
100% agree with this. Checking in flow with everything makes sense. Calling to realize equity makes sense. At this point, I am assuming this board hit villain (AQ, maybe AT, maybe KQ, maybe a set) so I am probably not going to plan to have a bluff opportunity unless villain checks the turn. We are just trying to improve, play it straight.
Short of making a pair or a straight, this is a really good turn, we are definitely going to the river now. I don't think a lead helps us though given I think villain can call with anything that beats us. And I would not want to check-raise for stacks here either, though I can't imagine folding even if villain shoves.
Check and lead the river if checked behind. Might check/shove the turn if villain bets.
I agree with this line 100%. I think villain just doesn't have air on turn too often, and probably never has air if he bets the turn again. If he checks, then maybe he has a second pair or a pocket pair under the 9 he might fold on the end if his flop bet was just a c-bet. This would be a coup if we as hero don't improve.
HERO calls $100 and hopes to realize equity on the river.
RIVER is an interesting one
Full board is




Board doesn’t pair (Villain has no full houses) and HERO makes the A-high flush — but it’s only the 3rd nuts, losing to the Q-high straight flush and T-high straight flush).
Do I ever put the Villain on QJd or 76d?
HERO thinks for 30 seconds and ________ (shoves all in, leads for $100, checks)
Of these options I like the $100 lead. Yes, I don't think villain ever has air here, but I think a lot of his value is now checking behind with a 4-straight on board unless villain happens to have a straight. The only way I see that is if he has AJ or JJ. In short, to get value from the effective nuts here (I am never putting an infrequent 3-bettor on

or

btw, barely worth mentioning) you need to bet your own hand and hope for a crying call, or maybe that villain will overplay a straight and shove.
If I check, would he:
-Check behind? I lose value.
-Shove? I snap call. Max value.
-Bet small? Maybe. I check raise for value… does he call? Maybe.
I finally decided to put out a relatively small bet to rep non-nut hands to avoid a check-check situation and hope for either a call, or even better, induce a shove.
Pot = $334
HERO bets $100
VILLAIN tanks for 1 minute and shoves for $235.
HERO snap calls and turns over the A-high flush.

VILLAIN looks disgusted and shows


for top set.
Wow he decided to shove top set here? Would not have expected that ever. I would have expected a call for sure. And yes, I think it's an obvious call for hero at this point.
I think you thought this hand through really well on every street.
Villain made a huge error on the river.
He later said that if I shoved, he would have folded, but thought I was making a play for the pot and that his set was either good or could get me off a straight by repping a flush. He didn’t put me on AKd.
As long as players level themselves in this "logic" there are exploits to be had on the river.
He very perfectly makes a case to call to bluff catch, which I would argue is the correct play here 10 times out of 10. He is foolish to assume anyone is laying a straight down because a backdoor flush hit. Very rarely is someone in villain's position going to have a backdoor flush here. I don't even want to give him credit to consider that holding

is somehow a partial blocker (It really isn't given the

and

are conspicuously missing and frankly the

accounts for a decent hunk of hero's calling range on the turn) that makes it possible to rep a flush here, and less possible for hero to have a flush.
Bottom line, hero played this brilliantly, villain played fine until blowing up on the river.
There's not much villain could have done to prevent the draw-out here. Hero just isn't going to fold even if we judge villain's bet-sizes as too small. The river was inevitable once the turn hit. And there were other turns besides diamonds that would have worked in villain's favor as well.
But villain's river shove is a punt, no other way to think of it.
Bottom line, his shove ensures he loses the maximum every time he's beat and never gains himself any value when he's ahead.