1/3
Effective stacks of relevant players:
V1 (EP) 250
Hero (MP) 300
V2 (BB) 700+ (covers, ldo)

Preflop:
UTG limps, V1 makes his standard raise to 12, hero calls with AT, button calls, V2 calls in BB, UTG calls. Five to the flop.

Flop: QT2
Checked to preflop raiser, who makes his standard c-bet of around half the pot, which in this case is 30. Hero calls. Button folds. BB/V2 makes it 140. UTG folds. V1 calls. Hero?

Hero calls V1's initial flop bet because he has a good sense of how V1 plays. Basically, V1 will bet the turn with any hand that beats hero and check any hand that hero beats. The main exception is when the turn is a ten and V1 has a hand like JT.

Hero has played over 1000 hours with V2 and call very accurately range him as having 22/QT/Q2/T2. Maybe an outside chance that he has TT or AQ, but he usually three-bets those in the BB, given the pf action. V2 respects hero's call sufficiently that he only check-raises the flop with hands that are ahead of KQ. I consider it non-negotiable that hero is at least 95% accurate about V2's range. I am that confident about my hand-reading (pattern-matching, really) skills against some regs.

V1's range once he calls is basically KJ/J9 for OESD and flush draws. This includes combo draws. He's the sort to just flat with KJ once he gets raised. Hero's ranging of V1 is less certain, but still probably 90% that I am exactly right. If I am wrong, he probably has AA/KK/AQ/KQ. Once he puts in that call, he's never folding. His range is kind of annoying because KJ takes away potential ace outs for me and flush draws take away at least two outs, four if he has the open-ended straight flush draw.

Heads-up against V2, I would just jam knowing I am taking slightly the worst of it against his range because it's close and I have the meta reason of making sure that he calls with two pair when I jam with a set.

I actually have two lines to consider three-handed. One is to just jam the flop for a practically certain three-way all-in. The other is a bit fancier. I can call with the intention of calling any turn bet unless the board pairs. I am fairly certain that V2 will not put any money without a boat once the board pairs. If he boats (or quads) up, he will probably bet the turn to get money from draws that have seemingly irresistible pot odds, but there is a chance he checks. If he checks a turn Q then bets a river heart, my hand is no good and I can throw it away. There are also turn cards that will make V2 check the turn. I think he will check an ace or king unless he has a set. He might check a jack. Possibly a nine or eight. So by calling I don't always face a turn bet that I have to call.

I think that jamming and calling with the intention of folding if the board pairs are both +EV when compared to folding the flop (which I am never doing). One play is definitely easier. The other is really hard to evaluate at the table and requires making a lot of assumptions.

I trust your reads.

I guess the only two real questions here are how often does Vil2 call bad if the turn is an A, Spade or T. Also what's our read on Vil 1 calling vs jamming so shallow. A jam is whatever for a board run out. A likely flat should get us is there more often obv.

We have 90 to call to win the the 150 and then the other 145+95 back. We need to consider the 145+(95 which goes in easier) getting in, in our tricky scenario.

... I assume we also always jam a K/J turn correctly here because we're AsianNit. Idk which play is more +Ev but I like being creative for the meta game.

A call sounds fine overall. Could be good for the game also if we frustrate them by bluffing or sucking out.

"... His range is kind of annoying because KJ takes away potential ace outs for me and flush draws take away at least two outs, four if he has the open-ended straight flush draw...."

If it is non-negotiable about being 95% sure that our Villain has two pair or better already, why do we care about an alleged "out" in the form of one of the (probably) other three aces?

Stove says we have only 24% equity against top set and KsJs. And about 29%+ equity against top two. If our reads are 95% certain this is a fold.

But if the other Villain has KT without any spades we are 45% good to go.

Usually a sub-optimal decision to put any Villain on a specific hand, better to assign him a range.

Tried to crunch the reads, but I didn't get the same numbers.

V1:AA-KK, AQs+, KJs, J9s, AQo+, KJo, J9o (18.18%)

V2:QQ, TT, 22, AQs, KQs, KsJs, QTs, Q2s, T2s, AQo, KQo, QTo, Q2o, T2o (40.46%)

Hero:41.36%

With those numbers, why isn't a no brainer an All-in?

Based upon your reads, I am in favor of jamming. You don't put V2 on QQ/TT, so 22 is the only set he could have.

If he has QT/Q2/22 & V1 has KJ you have 31.9% equity.

Also, as you said, there's the meta reason of making sure that he calls with two pair when you jam with a set.

If a comes ott, you're not getting any more $$ from V2, correct? If you are, then calling is a viable option.

Not tracking the pot size is a significant leak.

Pot otf is $60 - rake. $55.

Pot to Hero after stated action is $365.

V1 has $98 left.

V2 has $148 left.

You're getting 365:110, 3.3:1 to see the turn, so folding is absurd.

Once you see the turn, you'll be getting at least 475:98 to see the river, so folding ott is absurd unless the board pairs.

Since you're only folding ott if the board pairs, which will happen at most 15% of the time, and sometimes you're folding badly if no one actually boats...

and since its possible that you don't get paid if you flush hits...

and since its possible that you could get someone to fold their significant equity...

I move in.

Folding the turn is too fancy for me. Losing v1 if the flush comes on the turn is a much bigger consideration than saving a few bucks on the occasion a non ten pairing card comes. Plus there's a villains be crazy factor. Even the best read isn't 100%.

Moving in when nothing worse can really call doesn't sound like a good plan, neither does folding when we have this much equity with 2 players in the pot, so I am leaning towards a call.

What happens to your equity if you miss OTT?

I am not sure I understand your reasoning for the initial flop decision. You claim you are calling because you can read V1 perfectly on the turn? I don't see how that is sufficient to imply that calling the flop is the best play.

EDIT: I also don't think I understand the logic behind why you would jam heads-up with V2. Why does this hand specifically have to be in some kind of meta-game back-raising range? Should you even have a back-raising range at all?

Sorry for the double post--every decision point in this hand is interesting. (Yes, including preflop, but I'm not that interested in making that an argument here.)

As played on the flop: let's assume your reads are right and that we get all-in 3 ways if we jam. We have then built a $750 main pot (let's round it down for rake) and a $100 side pot.

Let's also assume you're exactly right and that V2's range is all 2 pair and 22, and V1's range is KJ/J9 including some flush draws with it as well. The sentence in the OP is poorly constructed so I couldn't evaluate V1's range exactly, but let's say you have about 40% equity in the main pot and V1 has 18% equity in the main pot.

You will beat V2 about 47% of the time, so you will win $100 47% of the time. You also will win the main pot about 40% of the time, so you'll win $750 40% of the time. The total expected win is 347. That's bigger than your starting stack, let alone your starting stack minus your preflop and flop calls. You have a +EV shove. Since your stack would be $258 if you folded, but the average size of your stack will be $347 after a shove, shoving is about $89 better than folding on average.

It is very tough to say whether calling the flop is better. I suspect it is not. The reason why is that if V2 has two pair and a spade comes, he might shut down. And there are more spades in the deck than there are board-pairing cards, even if you count the possibility of V1 having spades and even if you count board-pairing cards that counterfeit V2 instead of giving him a boat.

I think it's probably better to shove here, since we know a shove is significantly +EV and we don't want to accidentally do something wrong on the turn or river.

EDIT: I think calling in order to fold to a board pair can be a useful play sometimes but here, when we are so close to being all-in already, and V2 might have only 2 pair instead of a set, it's not really the time for it.

I like shoving best because it helps prevent me overthinking it.

I also buy the argument that third spade risks shutting down v2 and that board pairing with a 2 potentially counterfeits v2's hand and we inadvertently fold while way ahead.

I don't buy the argument that gii only gets called by better hands and is therefore bad. The initial raise is only with hands that are ahead of us anyway and v1 is only calling the raise with hands that are ahead of us too or have a strong draw. Point is we have a lot of equity - we don't ever expect to be able to either call or gii and be way ahead here but we do expect to still have lots of equity.

The only further quibble I have here is that we're giving V2 all combos of Q2 and T2. There's very little chance he shows up with Q2o or T2o unless he's a special kind of sticky -- which OP does not claim.

I'm not even sure I like giving V2 all the remaining 5 combos of Q2s and T2s, since at the least, he's like to 1) fold some of these pre and 2) possibly not be so eager to get his $$$ in on this flop.

I dont think this actually changes much though, since we have more equity against the other hands in V2's range (which are not sets).

IOW, I'm taking some Q2 and T2 hands out of V2's range, so then his range is now more weighted towards KX, especially KJ, which we're happy to do battle with.

Given how OP has described V2, I'm guessing that V2 has 22 exactly. I am not sanguine on OP's insistence that V2 can have much Q2 and T2 hands in this spot without having a ton of other speculative hands.

Hero has ranged V2 as only having 2 pair and 22, with no combo draws. If V2 doesn't have Q2 and T2 in his range, that's really bad for our EV, not good.

EDIT: Everyone realizes that if we were heads-up, we'd be almost flipping with Q2 and we'd be ahead of T2 on the flop, right?

Well... OP did say, "Maybe an outside chance that he has TT or AQ"

I'm just saying that if we are giving V2 T2, then he is bad enough to have other stuff in his range as played OTF too.

yep.

ETA: even against 22 exactly, Hero still has 31% equity, and must call OTF. If V2 showed me 22, I would obviously not shove, but I would be happy to call and watch him squirm!

This doesn't follow at all because there was a decision point in there. V2 can call super-wide preflop but then can only check/raise the flop with 2 pair or better. That is not a contradiction--it just means V2 will call or fold the flop the vast majority of the time, but this happens to be a time when he didn't.

V2 is a LAG who can make big laydowns against me. When I am in the pot, he slows down. This is why his check-raise signifies that he can beat KQ. He'd have a wider range on his raise if I had folded to the initial bet.

If I never have a back-raising range, I open myself up to getting squeezed. I abuse opponents who are addicted to squeezing and can't dial it down a notch against me.

It's sort of implied by the range I gave. He is the sort who will call with any two in the BB facing a small raise in a pot that looks to be multi-way.

FWIW, I jammed after taking 10-15 seconds to think through V1's range. V2 turned a deuce to give him a boat with Q2. I failed to hit my two-outer on the river. V1 showed 98 and lamented his ability to his big draw. I did not reveal my hand. V2 doesn't know if he was ahead the whole way or sucked out against QT.

OP, awesome OP. Thanks.

You've basically built the framework, now you just need pen and paper to derive the right answer. I do think shoving is likely best for a lot of reasons - the turn rarely pairs as V2's range blocks pairing cards, turn flush cards are scare cards against worse (though with such a huge % of stacks in the middle, you have to wonder how much that matters), and with V1 largely on dominated draws and draws with dirty outs, you can almost look at his chips as overlay (like 8s7s has 2% equity; of course combo draws have more; overall, he's not in great shape), making a shove quite +EV. You hate to get folds from KJ no spade on spade turns.

Losing to an ace doesn't really matter as an ace doesn't improve you vs V1 anyway except for the fractional outs from runner runner two pair+ (edit: oops, not so, forgot the paired T). And there is no straight flush draw possible. I think you also get totally leveled sometimes when planning to fold on paired turns - like when V has Q2 and the T pairs or QT and the 2 pairs, etc. Action and the manner of folding matter, but after putting in more than half of stacks on the flop, I think folding on like ~12%-18% of turns when at any given time only like ~8%-10% actually spell your doom (really rough math, I'm on my phone) seems to suggest you might be making a "mistake" ~33%-50% of the time.

Again, pen and paper will help here, but my instinct and all indications I can think of say to shove. Again, great OP.

These two paragraphs are contradictory.

1. You're first claiming that V2 slows down when he is in a pot against you. In other words, you know his range here is big hands only. You seem to imply in the OP that you already know you have no fold equity on a back-raise.

2. You imply in the second paragraph that you need a back-raising range in order to "abuse opponents who are addicted to squeezing". Let's suppose you are right and such opponents exist in general. You've already stated in the first paragraph that V2 is not such an opponent, because he's adjusting to you already by never squeezing light. Therefore, by your own logic, you do not need a back-raising range when V2 is the one raising.

There are some other problems besides the self-contradiction:

3. Are you actually claiming that you would slowplay a set the first time it gets to you on the flop so that you can back-raise them over someone else's raise in a cooler spot? You implied that in the OP, but that sounds like FPS. And if you wouldn't, your back-raising range is pretty badly capped.

4. You're trying to apply balance in a spot where you know you don't need it. You have such good reads on these guys! When you are claiming you need to balance your ranges in a big pot for metagame reasons, you're basically throwing those reads away.

Now, all of that said, I do still think shoving the flop is the right play given your reads, but the reason I think so is because it exploits an equity edge against V1 and V2 in a multiway pot. I do not think metagame should be any consideration.

EDIT: Basically I'm questioning the logic that you would jam heads-up against V2 but would consider not jamming against both. Jamming is clearly better when you are collecting more dead money than it would be heads-up, purely for equity reasons with no metagame consideration at all.