PLO100 AKQ9ss 3bet pot versus maniac, turn and river line with practical nuts?

That deep he could have AA. But on the turn you are either way ahead (he has 2 outs for pair) or way behind (he has AA). Therefore checkback is the play. It would be hard to get 3 streets of value from Axxx, and his flop raise should have more bluffs than Axxx. On the river the situation is nasty. If you raise, his calling range should be maximum Axxx/9xxx. That line doesn't look like Axxx at all, so you are left with 9xxx. But to raise flop with naked 9? There are A9/A2/92 too in his range though.

To raise we need to beat over 50% of his calling range. To me his line looks a lot like air/AA or rare boat, so I am not sure if we can even raise the river. It sounds weird, but anyway it's close. A2/92/22 makes some sense with that line, but how often even those call if you raise river? A2 probably calls as it's blocking AA. But your line looks super strong. In the end raise is probably +EV, but close.

In the game, I would probably have played it exactly like that with the raise on the river.
But after thinking about it calmly, nothing worse will call us, only better hands than ours.

For profit with raise-move - we need 33 % calls with worse hands than ours. FALSE I had a mistake in thinking

Example: pot is 10, opponent bets 5, we raise to 20.

Let's assume that we have a value raise and we think between calling and raising. With raise, we are risking 15 more to win 15 more.

First things first, let's look at valuebets. It's kinda universal for any sizing. Pot is 10, we bet N for value. Opponent never folds a better hand (assumption). If we don't bet, we win the pot X% of times. If we raise and opponent folds, we won the same amount we would have won if we just checked (opponent had a worse hand). So we focus on the times when opponent calls us. What ever amount we bet (N), if we win exactly 50% of times when opponent calls, we are breakeven for the bet. That same logic applies to pure value raises (when we assume that opponent never folds a better hand and we are never folding).

Let's assume that when opponent calls, he has 66% of times a better hand when he calls. Pot is 10, opponent bets 5 and we can call or raise to 20.

When opponent has a weak hand (or a bluff) that wouldn't call a raise, we make profit of 15 whether we call or raise.
When we raise and opponent calls, we are risking 15 more to win 15 more from the call. We lose 66% of times when called, not profitable.

More numbers, let's assume that opponent folds 50% to our raise, and has better hand 66% of times when he calls. That means that in his overall range he has 33% better hands.

If we call, we win the pot 66% of times. 15*66% = EV 9,9
If we raise, we win 15 50% of times, 30 17% of times and lose 15 more 33% of times. Total EV 7,65 (7,5+5,1-4,95). Worse than just calli.

Let's change the number to that we win 50% when he calls, giving him a better hand 25% for whole range.

If we call, we win the pot 75% of times. 15*75% = EV 11,25
If we raise, we win 15 50% of times, 30 25% of times and lose 15 more 25% of times. Total EV 11,26 (7,5+7,5-3,75). The exact same as with a call.

I am not a math geek, so I might be wrong with this. But I have made these pure value bet/raise calcs and sims with pokerjuice a lot back in the days. And it always fells to that same 50%. Now it's imoprtant to understand the difference between normal river raise and pure value raise, when our only options are to call or raise, and opponent never folds a better hand. AND we compare raise to a call, not as just isolated raise.

You are right - I had a mistake in thinking.

Checking back on the turn with blockers makes sense, and your half-pot raise on the river seems reasonable for value. Balancing between extracting value and not over-sizing your bet is key here.

It is bit tricky spot with these over active villains. Versus solid looking player we would probably want to just call on river. Though this preflop 3bet is not my default line and exploitation starts from there.

Usually these guys are not ones to make big folds so there is decent chance to get value if he has weaker boat at least. That said 92 and 22 should still be quite rare. Another question is if villain would actually check turn with AA and not aim to build pot bigger. But then again with maniacs it can sometimes be that when they slow down you should be more worried.

Anyway villain did snap call river with A22x which is ok bluff catcher blocking A I suppose. It is sort of irrelevant whatever he has 22 though at least if he has like AK2x. I would not bluff river probably ever versus this type of player. But if I did it would probably be with some sort of AJT8ds type hand blocking boats but having somewhat low showdown value.

So I think versus maniac we probably have to look for more value on river. If we face river shove my plan was to fold as it should be AA extremely often.

Very good analysis