^ agreed but id still 3bet given how small the river raise is

3-bet river is probably not great. He never calls with a flush (likely doesn't raise it to begin with), He's at least as likely to have AK as KK, and there is only one combo each of A3s and 77. In all likelihood you will have less than 50% equity when called and there's a reasonable risk of facing a balanced 4-bet range which makes it even worse for you.

Oh and as for your question, yeah you can fold 100% of range in this situation. It never comes up and you can adjust to the outcome. He is basically gambling that you will fold near nutted hands the first time here, and he'll gain nothing from the knowledge that you did if you don't do it in a similar situation down the road. You can/should also flat AKo deep vs CO open a decent amount of the time.

What are you talking about? Add up how many AK combos vs KK, 77, A3s...

If you think he's folding KK, 77 to the 3bet then ofc just call. But I don't...

And fwiw I think with his small raise sizing he can absolutely have a flush (although the probably not calling the 3bet)

AK - 3 combos
KK - 3 combos
A3s - 1 combo
77 - 1 combo

So if it was a pure range of all boats we face, we would have 62.5% equity vs it. However, I think that AK is more likely to slowplay flop than KK for obvious reasons. When you hold 2 kings its an ideal spot to just hope he has an ace and get 3 streets of value. I'd consider AK to be somewhat discounted in his range, KK to be heavily discounted, and A3/77 to be fully included.

AK - 2 combos
KK - 1 combo
77 - 1 combo
A3s - 1 combo

So that would give us 60% equity. Which would be easily enough to shove if we had like 1k behind after the river bet. The problem is that the 40% of the time we lose, he can reshove those hands + some bluffs. So the fact that we can't apparently (he posted the HH here) play perfectly vs that results in a significant tax to the 60% equity we have. In other words our ex-showdown equity is likely negative for a 3-bet even though we're a favorite vs his raising range.

Yeah you lost me with that last part. If we have 60% seems like a clear 3bet.

In short, he 4-bets with the nuts enough of the time and we're forced to call it off or fold the best hand, which makes pushing a 3:2 edge far less clear-cut than you think. There are some specific conditions under which 3-bet river is good:

1) he calls with flushes some
2) he never 4-bet bluffs and we safely fold our 0% equity hand
3) he substantially overbluffs with 4-betting here and we make a large profit calling it off

Note that even if we can call the all in barely, it's still bad for us because at that point we count our 750 as dead money that prices us in to call. Same in the opposite direction if he does bluff sometimes but not enough for us to be able to call. Hence the italics.

Unless you're talking about the 500bb situation, calling the 4bet every time is playing perfectly. If you give him a ship range of AK, A7, and the case A3s, you have 33% equity.

Let us say his range for the initial raise is five combos of flushes, three combos of pocket pair fulls (KK x1, 77 x1, 33 x1), one combo of A3s, two combos of A7, and two combos of AK, for a total of 13 combos. I've adopted your weighting for AK and KK. I am trying to give the most charitable set up for your position.

You have 71% equity against that range, so flatting makes:

620*0.71-180*0.29=~$390

When you 3b, assume he folds the flushes and even folds threes full half of the time (5.5 combos), calls it the other half, along with the remaining pocket pair fulls (2.5 combos), and jams the Ace high fulls. Then raising to $750 makes:

620*(5.5/13)+1080*(2.5/13)+2220*(2/13)-1780*(3/13)=~$400

(I've treated Villain's two A7 combos as one additional combo of win all-in and one additional combo of lose all-in).

Like I said, I think this is pretty generous to your point of view, in that it assumes he never tilt calls a flush or value owns himself with an underfull, and it's still coming out in favor of raise/call.

He doesn't have 33, and he prob doesn't raise A7o from the CO. To expect A3 to 4-bet the river is ambitious, and just because we have to call the all in (if that's your assessment) doesn't make it a good thing. It's an equity disaster for us to reopen the betting against his better hands regardless of whether we must call it off or not.

You can remove A7os, it makes little difference (the numbers above become ~$405 and ~$415 resp).

It is far too absolutist to say he never has 33 here, simply because it would involve a questionable call of a 6bb turn bet. Downweight, sure, but I already took two out of three combos away which I think is fair.

Idk what you mean by equity disaster. Unless you dramatically disagree with the ranges I based largely on your assumptions above, the calculations show that the amount of money made by flatting and raise/calling will be similar.

Well your example shows a 10 dollar difference in profit for a massive difference in standard deviation. Unfortunately, for 95% of players, this isn't an edge worth chasing. If you're such a mental game and BR management boss that you would risk 1700 to win 10, then carry on.

By equity disaster I mean the general case of forcing yourself to call it off for a large amount of stack for a near 0ev edge, or fold the best hand some amount of the time in a very large pot.

Funny, I was thinking of the mental game boss you'd have to be in order to be able to keep playing tiltless after letting your opponent off the hook for only 30 bigs with an underfull. Would be replaying the hand in my head for the rest of the sesh. Taking my coolers with the second nuts heads up doesn't bother me.

Also the $10 difference is only because I tried to calculate under your assumptions, not mine. Personally, I would expect him to call the 3b with flushes sometimes and spew jam KK sometimes also.

The more I think about this, the more I want to stick to my original point and even claim that it's GTO against villain's raise given his/her range not to 3-bet A7s on the river at least 50 % of the time.

Lots of discussion about the exact hand in here (which is fine- I fold btw vs. almost anyone) but on the theory part it's clear that it's often correct to fold the top of your range, and it becomes more and more correct to do so the worse your opponents are. For a more extreme example, I'm sure anyone who has played a decent amount of lowstakes live in the same area have encountered guys that only 3-bet AA/KK so you can fold AK/KK, etc.