Sat a 3 hour 1/2 session for the first time in a while and ran into this spot where I wasn't sure how to maximize.

Around $250 effective stacks, I cover by a lot.

4 limpers and Hero looks down at J2 in the BB. Check.

Flop: ($9 after rake) JJ2
I'm first and check, action checks around.

Turn: ($9) JJ2A
Hero checks, checks to V who is MAWG relatively new to the table (45 mins?) but has been playing tighter than most pre (not 2+2 tight, but tighter than the table average), a little sticky post when he hits and not very aggressive. I wouldn't say he's a station, he has been aggressive in some spots but not enough sample to know if he's really aggressive or just made a couple big hands. So, semi-Tight, semi-Aggressive, semi-sticky with a piece but small sample post. Anyway V makes it $10, and it folds back around to Hero who is hoping V has the Ace or the flush and puts in a raise to $25. Folds back to V who confidently tosses in three green chips to 3 bet to $75. I now have him on only a flush or a medium / strong Jack (JT, QJ, KJ...).

After the 3! to $75 I feel like whatever I do seems super strong and he only has about $175 left. If I flat, I'm OOP and feel checking OTR is missing value because his flush or Jx is VERY frequently checking behind. MAYBE the nut flush or a KJ might stab but even that could be optimistic as he would be betting into a large stack with tons of showdown value and risks getting x/r (again). If I flat and lead river it's pretty much the same as 4! turn except we give him a free-ish card that could kill action or let hero win / chop. If I 4! it seems uber strong and I honestly dont think V calls with anything we can beat unless V can somehow convince himself we are bluffing. In your experience what's the best line here against said Villain?
1 - Make a super small 4! to $125 / $150 so he still has $100 behind before I rip it in OTR?
2 - Rip it in and hope he stations it off?
3 - Flat and pray he finds a super thin value bet OTR?

In previous hands like this I've tended to go for the small value raise but after reading similar posts I've seen a lot of "if they were calling that amount, they would call more so you missed value" arguments.

FWIW I'm not at all concerned about AA or AJ. If he played it this way, good for him.

I don't know villain, but if he's okay with a casual 3! OTT, I don't see him folding to a jam. He probably feels committed. So I'd jam.

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Once villain makes the turn 3 bet I don't think it matters much. OOP you need to lead river anyways and villain isn't likely to raise unless they are terrible or have you beat. There is an optimal line here but it depends on villain and you don't have that kind of detailed read yet. My order of preference is this.

1. Raise to $150 now and shove river. Looks super strong but villain has a strong hand and it will be hard to fold at any point no matter what card hits river.
2. Flat now and shove river. Not quite a strong as option 1 but there are cards that might scare villain off on river.
3. Shove now. 4 bet over shove on turn is nutted strong. Your hoping villain has a hand he can't lay down but that is likely after the turn 3 bet.

In a situation where two players are likely holding a boat and you feel confident that you're holding the better one, then large bets/jams are going to print money in the long run.

In a situation like this, even medicore V's may fold a flush to a 4b, and a flush is by far his most likely holding here. I think I just tank-call and then check the river and hope he bets/jams behind. Maybe just open jam the river if it's a club or a low card. If a K/Q/T hits the river and you just jam into him, I doubt he's calling with even a K-high flush.

Villain could totally have aj, but I would rip it as played. He could get spooked on scary rivers with weaker hands.

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I realize it's not impossible for V to have AA or AJ and I didn't give his relative position but he was Mid / Late position maybe LJ? And there was almost no 3 betting pre. He should be raising AJ pre but he could limp, then check and chose to bet after he makes the second nuts OTT. I was just pointing out if he's taking this type of line with one of the two hands that beat me he wins the double up from me every time.

Thanks all for the feedback. Not much of a consensus though.
2 - 4! jams
1 - small 4!
1 - flat, then check (which I follow your logic but wasn't expecting anyone to suggest). If I tank call and a blank hits I agree he may value bet, but everything has to go right. We really don't want to see a K, Q, J, T, or club, or the board to pair... seems like a long shot. If I call he's got to put me on a J a flush or a boat.

I'll wait for a few more. So far I like the small 4! line suggestion the best but that is my standard and again I'm not sure what hands call $150 that fold $250...

#1 … he'll call with a JX hand but may fold a bad river.

Not saying there's a great answer here regardless, but if you guys are getting turn 4bs called by flushes then I'd love to find out where your games are. If my turn 4b was called I'd be pretty convinced I'm losing to AJ here. I can't even remember the last time I saw a turn 4b in a 1/2 game that wasn't all-in, either. I definitely don't remember it happening where someone called and both players weren't super nutted.

grunch

I think you're freezing too much here just because you have the boat. I think you should be leading the flop for $4 or $5 here to start building a pot and getting value from pocket pairs, a J, and flush draws. If this board was rainbow I'd like the check more.

On the turn we should DEFINITELY be betting to get value from aces and club draws. Just because we have a boat doesn't mean we have to slowplay when there are draws that are drawing dead and will call you.

As played, the raise to $25 is ok. When it goes to $75 here, probably flat and check/jam river. I think you're overestimating the likelihood that he bet/three bets the turn planning to check behind the river. He either is trying an elaborate bluff or he has a value hand worth betting again on the river. Let him either try to bluff more or value bet his worse (or better) hand.

By the way, it hasn’t been said yet: I don’t think you should necessarily word your post and title thread in the manner you did because it implies the result of the hand was that you were ahead and didn’t get max value. It might change some of the replies here a bit. Try to keep things a bit less steered to get the best answers possible. You may have done it unintentionally but that’s the way it reads to me.

maybe he's balancing his post title range by saying "how to get max value" when he actually ran into AJ.

Haha, that was good.

Make it 150 and lead out on the river.

Shove turn.

I would not bet flop, we want PPs to stick around and turn/river sets plus out hand is locking the board/needs zero protection (whereas say 22 can get oversetted)

I just don't see 33-TT folding to a $5 bet on this flop pretty much ever. At least in most $1/$2 games.

I think you should lead the flop, and if you don't, definitely the T. If the V has a big flush, on the T, he'll be more inclined to think you have a smaller one as well. C/Rs look strong, regardless of V's holdings.

Noted, but I really wanted to focus the discussion on what to do OTT if you're trying to get max value AP. I appreciate the other feedback about flop and turn but as another poster said, a 4! on the turn in 1/2 is rare enough that I wanted to focus the discussion around that decision point.

This was my thinking, which is why I was hesitant to 4!, but then how do I go for max? Let's tally up the responses:
4! jam turn = 3
4! small turn = 3
flat and check/jam = 2

Almost an even distribution.

And to the other comments, all the action had recently left the table or busted. I did not describe Vs other than main V, again to steer the discussion. At a normal table I usually bet 5 OTF (unless there is a guaranteed raise behind me who will barrel it off) and another 5-10 OTT but the players left were folding 33-99 there for fear of a J and only calling a flush draw, a J, or if they hit an over card. The turn was perfect and I could have led there but since the flush came in the naked J is only flatting. I figured the x/r was optimal but didn't plan for the 3!