1/2 at local casino. Sunday night 8:00PM or so.

V1 (UTG+1, $200): MAWG nit regular, plays mostly TAG and rarely bluffs. Is capable of making big folds both pre and post flop and rarely gets it in without the absolute nuts.

V2 (UTG+2, $95): Young middle-eastern guy, playing short-stacked strategy. Seen him 3bet/push hands as wide as AJo and 99. Started with $50 and recently doubled up with AK vs AJ on an ace flop.

V3 (MP, $600): Young Indian or Persian guy, regular at another card room. Very loud and aggro, has been berating some of the fish at the table for bad plays. Stuck for a good chunk (he's in for $1000) and has been playing for 20+ hours because some of the dealers have asked him if he went home and came back (which he says he didn't). Definitely capable of 3-betting light and reacting to light 3-bets and has been pushing people around pre-flop.

V4 (HJ, $320): Young black guy, sunglasses. The fish at the table playing ATC. Calling station when facing aggression, but will become aggro when he picks up a real hand. Recently sucked out runner-runner one-card straight on a flop where he had bottom pair against a set.

Hero (BB, $500): Middle-aged Asian guy, but looks early-20s. Been card dead for a good 3 hours with the rest of the table noticing. Value-owned himself on the river in 3-bet pot 2 hours ago (to a V not in this hand) with an overpair vs turned trips when V checked backed the turn in position. Reloaded and recently got into a big pot with V2 where V2 open raised from MP, got 2 callers. Hero squeezed from SB with A4 suited and V2 called. Flop came A54 monotone. V2 donked, Hero put in a large raise, and V2 folded after tanking. V2 didn't show but tells the table he had AQ with the Q flush draw.

On to the hand.

UTG folds.
V1 in UTG+1 to $10.
V2 in UTG+2 immediately 3bets to $30.
V3 in MP calls.
Folds to V4 in HJ who calls.
CO, BU, and SB all fold.
Hero looks down at JJ.

Hero's options:

FOLD: We have a top 5 hand, even if not ultra premium and have been mostly card dead. Given the significant action before the flop, we could be well behind (esp. against V2), but we are probably ahead of V3 and V4. Folding here is probably way too nitty, but we only have a $2 BB invested and we don't know what V1 will do after we act.

CALL: We would be playing purely to set-mine and we definitely have the odds if V1 also calls. However, we would be first to act on all subsequent streets and that's assuming V1 doesn't 4bet to iso, which would totally suck for us.

RAISE: We can 4bet ourselves, maybe iso against V2's short stack since he will likely be committed. We have been card-dead and are cold-4betting from the SB so it will look like we have a real hand. We wouldn't mind everyone folding and we pick up over $100 in dead money uncontested. We probably don't want to shove and isolate ourselves against AA/KK. Given that several stacks are deep, maybe there is an amount we can 4bet and fold to a shove from another deep stack representing AA/KK.

Hero?

What range do you put v1 when he opens UTG+1? What is his 4bet range, is it exactly KK+?

This really just depends on your assigned range for V1. If he is only opening AA-QQ UTG+1 and he's likely to raise/jam then fold. If he is wider than that and MUBsy and more likely to call then feel free to set mine.

I don't have that much history with V1 even though I do know he is a regular.

V1 is probably wider than only premium pocket pairs, but not by a ridiculous margin. From UTG+1 probably TT+, AJs+, AQo+. His 4bet range is most likely AA/KK and maybe AK (perhaps AK only when effective stacks are short).

I think you have to call, if you 3! enough to be a real 3!, you end up committed to calling off a shove anyway. Not sure I can fold JJ when we can play it 6 ways instead which is great if we're set mining and can sometimes win outright anyway.

I'm concerned by V3's cold-call. Without V3 in the hand, this is a clear raise for value against V2 and V4. I think a call is best. You have the IO to stack 3/4 villains. You can safely fold if V1 repops it because it's only KK+. I'm checking almost every flop.

CORRECTION: Hero's had with A4 on the A54 monotone flop was against V3, not V2 as written in the OP.

Hero 4bets to $120, planning on folding if a deep-stacked shoves.

V1 folds.

V2 calls and is all-in.

V3 folds.

V4 calls.

3 to the flop ($325 main pot, $50 side pot).

Flop is 2 3 J

Hero is first to act, holding JJ with J.

V4 has $200 behind, Hero covers.

Does Hero check, bet small, or shove?

The calling station who plays ATC? I just stick it in. He'll call with all his draws and probably mid pockets as well when he puts you on AK.

This depends on what kind of station V4 is, and whether he folds more often to large dollar amount bets.
I might bet something around $80 if he tends to fold when facing "lots of money", and stick it in on all turns.
If he is totally inflexible to bet sizing then I agree with WereBeer above to just shove it in.

Checking is pretty bad since he only sticks money in with a solid hand, which is really difficult for him to have here.

What about a raise to $60 pre, so that the short stack shove re-opens the door for us, and we get some cheaper intel on V1s holding. Depending on what happens, we can either call when it gets back to us, fold if V1 shoves, or re-shove to isolate against V2.

+1

I dont get the PAHWM anymore when it hits the flop.

I like just calling preflop and i would be comfortable calling the shove from V1. And maybe even call/shove if V1 were to shove.

Flop plays itself. Never check.

Hero shoves since V4 has less than 2/3 pot behind. V4 folds.

V1 shows AK

Turn A, river Q

Hero's set of Jacks hold.