You are on the button. You flopped the nut (top set), SPR over 40, HU against an absolute maniac who bets whenever he connects with the flop.
Here is the hand:
Hero’s hand on the button is JJ33 dbl suited, your stack is 1000 BB. All fold to you, you raise to 3.5 BB, small blind folds, villain the maniac raises to 11 BB, you call.
Flop J86 two tones (not yours), Villain bet 20 BB. His range is so large that your set remains the nut for only 5 of the 45 unknown turns (one jack, one 3 and three two). Obviously you can’t fold the nut, even if it crossed my mind.
Will you just call to conceal your set? And then what will you do when the turn completes a possible straight or flush and he fires again?
Or, will you put your risk averse aside, and raise the maximum on the flop and be ready to raise again his automatic bet on almost 90% of turns?
I raised, and guess what? he raised me again and we went all in. His hand QQ97 with flush draw). Not so crazy play.
Thank you

I would raise the flop. Gotta give villain a chance to wig out. Better not to share results with your post btw, as they can unduly influence the commentary.

Both options look great and you should mix. If we are calling flop it’s not to fold any turns

Raise his bet and GII on the turn

Tough luck if the turn brings a flush but you got so much money in the pot that way already, that you can't afford to fold then.

Don't just call.

You want to fold top set because villain is a maniac?

I would just call down all streets on any runout and raise if you boat or quad up. Raising versus a maniac is suboptimal I think if he keeps firing away indiscriminately. If you GII on the flop he is only likely to continue with high-equity range.

there is no world where you should fold the nuts, not all non-nut turns are bad, i.e. a 6 or an 8 have you pretty comfortably ahead of a maniacs range where only 1 combo beats you, on A and K he won't have KK enough to be a huge fear etc. yes there are straight filling cards and he can't have every hand that makes a straight draw at the same time.

I don't mind flatting with this though and seeing turns with position, but ultimately you can get it in versus like bare 88 versus a maniac, or just like bare J8, or like a combo draw you are 2:1 versus.

Why even play?

You are on the button with top set against a maniac. I would take this scenario all day long.

The stack-to-pot (SPR) is about 40, but since this hand is heads up on the flop, your entire stack is NOT at risk unless you decide to bet or raise at some point against this maniac. If post-flop you never bet or raise, then the SPR is 13, not 40.

An SPR of 1 means that there is one pot-sized bet left; an SPR of 4 means there is enough left for two pot-sized bets heads up or a pot-sized bet and a pot-sized raise; an SPR of 13 is the equivalent of three pot-sized bets heads up. If post-flop you never bet or raise, then all the maniac can do is make pot-sized bets on the flop, turn and river for a total of three pot-sized bets (an SPR of 13).

Note that if the effective SPR is over 13, and only two players contest the pot after the flop, the only way for all the money to go in is if somebody puts in a raise at some point in the hand.

You also have the positional advantage. All the maniac can do is make this an SPR 13 sized hand, but you get to cherry pick when it becomes an SPR 40 sized hand. Choose wisely.

What would I do? Calling down all the way unless I make a full house+. On this particular hand, for me the flop is always a call. The turn or river are where you get the chance to cherry pick playing for stacks which on this particular hand are my full house+. And since I know I'm calling down every hand (raising full house), I am not taking my eyes off the maniac, I want to see how he reacts to an ace, king or queen hitting the board, because I might not raise my Jack's full if I get a tell that he made a higher full house.

Some people in this thread have recommended loosely raising on the flop. Be careful turning an SPR 13 situation into an SPR 40 situation. Also the maximum buy-in structure at the table is important. You said you started this hand with 1,000bb. If there is a cap on the buy-in and you needlessly donk off 1,000bb on this hand and can only rebuy for 200-300bb, then you are going to be hating life staring at the maniac/whale's deep stack compared to your rebuy stack.

Too long didn't read...heads up on the flop, the worse the maniac can do if you never bet or raise is get you for about 300bb of your 1,000bb stack. You can cherry pick when to get him for his whole 1,000bb.

That is a good point, in a capped game you are somewhat incentivized to pass up marginal opportunities. On the other hand, the maniac might pick up the next hand. If we have an average equity advantage of 15-20% when stacking off with top set that is a pretty huge opportunity, earning 150-200 bbs in a single hand, plus our share of any dead money. And many mid to large plo games are uncapped. This is also a bankroll question, since if you had less than 100 buyins in your bankroll you should have already quit the game since risking 10% of your bankroll on a single hand is not advised.

To be more precise. the minimum buy in is 100 BB, and there is no cap on the buy In. BTW I started with 400 BB and was ahead by 600 BB. Loosing my entire stack would be awkward but definitely not dramatic.
To be honest, I decided to raise on the flop, knowing very well that he will re raise and we will go all in, loosing my positional advantage. The only reason to call on the flop is if there is a possibility for me to fold on the turn or on the river. I discarded this possibility against this specific opponent. Also, if I flat on the flop and raise his automatic bet on the turn, there is a slight chance that he folds.
A lot of modern poker literature boil around solvers (which i don't use and think they are useless for PLO live games). I am curious to know how a PLO solver will analyse this situation.

OP, in the title of thread and in your multiple posts you keep mentioning folding. You have received different suggestions from several posters, but every single posters is in agreement that folding is crazy.

So folding is a bad idea. If the idea of you or him folding at some point in the hand was nagging at you, then I'm not mad at you for getting it in on the flop and realizing your equity.

But I will say that how you play certain hands shifts dramatically as the SPR increases from 1, 4, 13 to 40. Certain plays that were an easy get it in at lower SPRs quickly become questionable at SPR 13 and bankroll suicide at SPR 40.

Here is an SPR example, all cards are dealt out on the river and you have the king high flush on a non-paired board. There is action in front of you from multiple players, are you calling SPR 1? Yes. Are you calling SPR 4? Questionable. Are you callling SPR 13? Questionable. Are you calling SPR 40? CRAP NO. This example is why I suggested in your particular hand not betting on raising and only allowing the maniac to get the hand up to SPR 13 instead of SPR 40.

I just wanted to add that my king high flush example was overly simple, but you get the point.

Crap gets real at SPR 13. Furthermore if you play SPR 40 hands poorly, then your yearly results are screwed.