Third hand into the start of the session. I have extensive history with V1 and his ATC style.
V1 ($450) - 80+ years old and in poor health. He is a gambler to the max. He has announced at the table today and in the past that if he lives another 3 months he will consider himself lucky. He is wealthy and couldn't care less about money. Dumping $2k in a session doesn't phase him in the slightest.
V2 ($40) - Older female. Always plays short stack like it's 100bb+. Loves to call nearly any bet preflop and then call off rest of stack on flop. She becomes irrelevant after the flop.
V3 ($40) Older male. Plays identical to V2. Also becomes irrelevant after the flop.
Hero ($285, has won the first two hands) - Male, 40s, loves to talk at the table. Reputation of being a nit. Generally, plays first hour very tight and then loosens up and steps up the aggression as the session progresses.

Hero is SB with JJ

V1 (UTG) - Opens to $8
fold
V2 (UTG + 2) - Flats $8
fold
V3 (MP) - Flats $8
fold
fold
Hero (SB) - Raises to $27, I know V1 will call 100% of the time.
fold
V1, V2, V3 all flat $27. V2 and V3 each have $13 left and are no longer relevant to the hand.

Flop ($84):
JQ8
Hero fires $55, at this point I know I will get a call from all three villains
V1, V2, V3 all call (V2, V3 for remaining $13)
Turn ($136 main, $84 side):
10

At this point V1 could be holding anything since he will not fold any pair, two pair, draw, or over cards. Since V1 called the flop there is a 99% that he will call a bet or shove, with bottom pair or better, on the turn. The only hands I can think of eliminating from his range are AK, AA, KK, QQ, 1010 because he didn't 4-bet preflop.
Is there a way to put V1 on a range? Is this a value shove given his wide open range or is this a curse the poker gods c/f? Given his range I'm leaning toward a shove knowing that even if he has the straight I have 20% chance to pair board.

Hero??

You've already answered your own question really, the range of V2 and V3 is pretty much ATC, and V1 is calling any pair and any draw. As such, even on a 4-liner I'm shoving a set into the dry side-pot for straight-up value against V1, and expecting to be ahead for the main pot as well a decent amount of the time.

Edit:

Just for the heck of it, I ran our equities against their described ranges:


Board: JcQd8sTc
Equity Win Tie
UTG 48.20% 46.90% 1.30% { JdJh }
UTG+1 20.00% 16.38% 3.63% { Q2s+, J2s+, T2s+, 92s+, 82s+, KcAc, QcAc, JcAc, TcAc, 9cAc, 8cAc, 7cAc, 6cAc, 5cAc, 4cAc, 3cAc, 2cAc, QcKc, JcKc, TcKc, 9cKc, 8cKc, 7cKc, 6cKc, 5cKc, 4cKc, 3cKc, 2cKc, 6c7c, 5c7c, 4c7c, 3c7c, 2c7c, 5c6c, 4c6c, 3c6c, 2c6c, 4c5c, 3c5c, 2c5c, 3c4c, 2c4c, 2c3c, Q2o+, J2o+, T2o+, 92o+, 82o+ }
UTG+2 15.90% 12.62% 3.29% { random }
MP1 15.90% 12.61% 3.29% { random }

Sounds like you already put him on a range pre-flop, any two cards.

The turn is horrible for you only if he has a 9. Might give him a flush draw but not worth worrying about IMO.

Sounds like you've already kind of ranged him for calling you. any JQ8... A10+ 22+ Basically ATC, and you're way ahead of most of this range.

So what beats you? 9x QQ (unlikely) 88 (unlikely). Again, you're way ahead of everything else.

If your read is good and you're convinced he will either 1) ship it on the turn; or 2) be willing to call his stack off on the river, then I figure get it in now.

You could make another bet, 1/2 to pot-size. He's calling everything. 1/2 doesn't totally commit you (you'll have 150 behind) but a pot-size bet does. But it doesn't sound like any card that comes is going to make you fold because his range is so wide so betting half loses value and betting pot commits you. Plus, if you bet and he calls you give him a way out on the river.

OTOH, If you shove he's probably calling and can't change his mind later (which he won't anyway).

If you check and he has draw and or bottom pair and is willing to check, you lost an opportunity to get value and gave him a free card. You're not folding and you want your money in the pot so this is bad.

I like your shove. Sometimes you lose, but mostly you win, and you win a lot when he calls. GII, go to the bathroom and puke if he shows up with a 9, then brush your teeth come back, reload, and get it back from him.

I would check/call here. He's never calling unless he has a 9. I like giving him a chance to bet it himself.

According to OP this isn't true. Sounds like he'll call with any J, Q, or 8 or overcards.

If what you said were the case then I think this is an OK move.. maybe even c/r.

where does it say that this guy goes broke with bottom pair or any pair for that matter, on a 4 straight card board? I was also under the assumption that vil 2 and 3 did not matter so idk

Where is this game at? I want a seat.

If this guy is going to spew money like a maniac, then we have to bet bigger. Our 3-bet is too small. It needs to be at least $35. On the flop, bet the pot. $55 into $84 is too small. We need bigger bets in order to extract fat value. The turn card is bad, but once we have bloated the pot, we should just open shove the turn, as this V will call with hands that we beat (plus, we have a re-draw if we are behind).

Here:

Math is off. On the flop it's 27*4~108.

I like a 3b to 40 rather than 27. If he's going to call 3b w/ atc let's charge him for it. That would also get the 2 short stacks outta the way. I might just overbet shove the flop, bc given description I believe he would probably call with any piece of the flop. He's not there to fold hands.

oic, missed that boredoo. crazy good game i guess. What the hells the question? If he's calling everything he would have called the flop with and he will call the flop with anything, including bottom pair, then obviously go all in.

Bet and never fold. If he hit the 3-outer then whatever....I would have gone $85 on the flop though. There should be $108 in the pot, not $84. Apparently there are two people on this forum with the SN Axel Foley. That's kind of weird....you guys must love you some Beverly Hills Cop.

Yeah, at least the first two. The third one at the amusement park wasn't so hot.

And yeah, with about $200 behind and a gambooly old man (pretty cool variant that you don't see every day), I like the value shove with the set. We can get called by two pairs/pair + straight draw a lot, and when he a redraw in the event that we're behind.