Background:
Pretty simple hand, just wondering if the math checks out.

Table has been fairly passive. Has been quite easy to limp and not get blown off hands.

UTG (~$500): Young AF, splashy, new to table
Hero UTG + 2 ($230): Young AM, tight
HJ ($600): Middle aged guy, tight
BU ($420): Young WM, splashy competent reg
SB ($98): Young WF, passive Level 1 player
BB ($350): Old WM, nit

Preflop:
UTG opens to $12
Hero calls with A4
HJ calls $12
BU calls $12
SB calls $12
BB calls $12

Flop ($72): JT7
UTG (original raiser) bets $20
Hero calls
HJ raises to $220
BU all-in $408
SB all-in $86
UTG folds

Hero action?

Thoughts:
1. Effective pot (what Hero can win) is now at $594 (if I did the math right)
2. Therefore, Hero has to call $198 to win $594 (3:1)
3. The assumption here is that there are definitely some made hands (flopped set, straight, etc.)
4. How many clean outs does Hero need to have to make this a call vs. fold (i.e. I am assuming 7 is 99% not a clean out here)?

Thanks.

I think it’s a pretty easy call, not a fist pump but just have to call it. 75bb deep, calling. Plus you get your $198 back when you bink so more favorable than you presented.

I think the biggest problem in this hand is that there might be multiple FD's out there, which means we have less outs.
3:1 = 25% needed, which means we need ~7 outs to be able to call here. In game i mostly shrug and call, but it's probably really close and it might be a fold.

Hmm i just realized HJ still has 180 behind and is likely never folding, so we are actually getting almost 4:1, in which case it's not that close at all. Call.

Preflop is really bad at this stacksize, btw.

HJ and BU are already in for >$198 (which is my effective all-in), so from a pot odds perspective, it doesn't matter what HJ does after my decision (I assumed he would call for the side pot).

So, still 3:1 I believe.

Worst case scenario is running into set vs. straight vs. flush draw, in which case I'm down to 5-6 outs (and that's not even including dirty straight flush outs, the flopped straight having a club or both clubs, etc.).

For less than 100bb with the chance to triple up, I gii with the nut flush draw here. Rebuy if the poker gods deny you a non-7 club.

I would have folded pre, but as played, I would have raised UTG's $20 bet.

Agreed it is usually a fold pre, but as mentioned in OP, there was not much 3! squeezing going on pre at the time.

What are the reasons for raising UTG's $20 bet?

It's a tiny little c-bet so we should have some FE, and I'm willing to gii with less than 100bb with the nut flush draw.

Grunching:

Your math is a bit off because against a # of V's, you aren't putting in your full $198. Better to think of it as getting better than 3:1 odds (AI vs. 3 V's + $90 of dead money.) This is enough for a call but not a hugely profitable spot.

Given the action, someone is going to have a set the majority of the time. You will win 24% of time vs. a set. That's more than enough to call.

The problem is that, given the action, one of the other V's very likely may have two of your 's. If so, your odds drop to 21% or so. About even money.

There will also be the off chance that there is no set and the call is hugely +EV.

Your dollar values look right. If you give the tighty a 10% range and the splashy competent a 25% range, your nut flush draw has about a 38% equity(Equilab), much more than you need for a +EV call.

Snap

Results:

Hero calls $198 all-in
HJ calls all-in

Turn/River:

JT796

SB shows 99
Hero shows A4
HJ shows JJ
BU shows 98

Hero wins main pot
BU wins side pot

As played, I had 24.39% equity on the flop, almost exactly even money.

In a worst case scenario, if SB had a flush draw I would not have had the correct odds to call.