Hi Guys,
I always struggling in that spot (and might be result oriented).
Here is the hand in a 1-3 Game (Blinds 5). $ to 6 callers in every hand whaetever raise you have. Ranges don't really apply as vilains don't really have any.

Hero, is Big Blind.
UTG calls, UTG+1 (vilain) raise, Calls 2 time. Hero calls with AAT8s. UTG calls. (I know I should raise but I call from time to time out of position with AA to disguise my hand strength)
Flop: Ah7h2 pot 105$. Hero plays 450$ , vilain 500$.
Vilain is super agressif. I know he will try to represent AA and pot if I check. What line would you adopt to maximize your EV and profits ?

Here is what I have in mind:
1) Check raise pot to go broke on flop: he will probably call with all his flus draws. Cons: it's not a huge mistake from him as he has approx 27-30% and needs 33%. It also increase the variance while I'm trying to build a bankroll.

2) Donk pot and repot on safe turn. Pros: make sure we have a safe turn before piling everything in. If he calls on river, his mistake is bigger as his % falling. Cons: if board doubles up, we won't extract anymore value.

3)check call turn. Bet close to pot on turn to deny their equity. low variance. win/losses lower.

Any mathematical approach of why one line is better than the other ones.

Thank you so much

The whole problem in one sentence. Your job is to maximize EV and to play only in games that you can afford. I'd much rather risk going broke than choose lines that lose tons of EV. Of course I am assuming poker isn't your (main) source of income. If it is, you are ****ed.

In the actual hand, c/r flop every time.

You called AA to try and flop a set or flush draw + over pair and you have hit your set.

No reason to lead out since "we don't have anything" and just called out of position because of the size of the pot.

Let someone else bet, then check rip it in and whatever happens happens.

If it gets checked around and the turn is safe then lead away.

You set your trap, now spring it.

Agree - I'am asking the question as I want to maximise my EV.
I did c/R but I'm not sure this is the most EV+ move

Against someone you describe there is absolutely no doubt it is the most +EV. You want to get the money in against a flush draw! It doesn't matter he "has the odds to call", you are putting a lot of money in as a favorite, that is the thing that matters.

Leading is not great, because now he can correctly call. Check-calling flop intending to donk turn is bad, now he can correctly fold on many cards.

Neither getting it in on the flop nor him just calling your raise is giving him the proper odds, you are +EV in every scenario.

On a single street he has 20% (perhaps less) to hit a flush. Calling a pot sized reraise requires him to have 33%. This board is so dry that he cannot have more than 2-3% to improve via other cards (except if he has precisely 3456 or something like that)

If you think he rips it in on the flop after your reraise, he has around 30-35% to make a flush without you making a boat. And he needs a bit over 45% (105 pot and 450 x 2 total pot with him needing to put in 450).

if you're not comfortable c/r this flop on this board, PLO ain't the game for you.

OP didn't give a detailed read on villain other than "super aggressive" but in my experience, most people with that sort of profile in smaller live PLO games will be unable to make the correct fold after a turn donkbet from hero. If he actually has a flush draw that is.

In fact a good aspect to delaying on this particular texture against this player type is the turn often allows him to pick up some piece that he won't be able to fold, while he would've just folded his air/backdoors to a flop checkraise.

Check rip flop and it’s not close? You don’t need to get fancy with top set 4 ways at this stack depth, anything else is dumb vs player types you described.

I have no problem with slow playing AAxx Pre-Flop with a table dynamic as described .. unless you can isolate somehow there's just too many Players seeing 'every' Flop.

The issue with a Donk bet on this Board is that you pretty much imply that you have a set or NFD, so any Player behind can play perfectly (and even bluff should you check the Turn for some reason).

I do both x/r and x/c here .. then Donk safe Turns to deny any equity going to the River.

You seem to understand variance. Some Players use Run-It-Twice as variance 'control' while others use pot control by waiting for safe Turns before applying max pressure with only one card to come. PLO Players have a really difficult time folding on the Flop, but they do fold lots of Turns even though the Pot Odds are the same .. especially at the low limits. They are more than wiling to put in $600 with 2 cards to come, but not $400 with one card to come at the same Odds with somewhat similar equity.

I prefer getting folds and taking down those pots 100% of the time. But I also do make more than the average Folds in the same spots when the Turn is 'bad'. Am I getting bluffed? Sure, some of the time, but not as often as some may think. Would I have regained the pot on some Rivers? Sure, but not at the rate I'd like to see for the chips required.

Only you can choose you PLO 'attitude'. Are you a 'pot'/GII guy? That's fine, your variance data will show those swings.

I look at this hand in particular as an opportunity to make 'safer' profits by keeping more Players in the hand. If you x/r here you are only getting called by Players that can beat you with one card, mainly being flush draws but there are some wheel combos out there too perhaps. So even if a V bets pot you pretty much get to see what the other Players do before you have to act. If 'everyone' calls, then you may have to shove in order to get a couple folds, but if only 1 other Player calls then you can just flat and allow them to hopefully Turn 2-pr or a wrap, which will allow both Players to see the River in a much bigger pot. Otherwise if the Turn is a blank then you got the extra $105 into the pot as dead money and V is calling off anyway based on their image.

If they both fold Turn, then you only risked $105 to win $210 additional. You can do this 3 more times based on your current stack size .. how many times do you triple your money and how many times will you see 'bad' Turn cards where you fall behind? To me this is better than RIT variance as you actually get 4 theoretical chances instead of two. If you produce folds in 3 of the 4, then you net $630. If you x/r then you are risking $450 to win $450 additional and have to win 100% to show any profit.

So I'm suggesting that you can actually win more by risking less on this exact Board long term if you continue the passive PF approach here on the Flop .. then hit them hard when you have max equity denial. GL