5-5 live 4-way

CO Fold
BTN (1200) AQT5 raise to 20
SB (1200) 3-Bet to 65
BB (350) Call 65
BTN Call 65

Flop (195) AT9
SB bet 125
BB raise all-in 285
BTN ???

BB is playing pretty loose, probably getting it in here with any 2-pair or FD/SD + pair.
SB is playing very tight, rarely 3-betting preflop (mostly with AA or premium rundowns, so hands like TTJQds, 99TJds are well in his range). Postflop he's playing very aggressively, but is overly-cautious of going all-in. So he is probably c-betting plain FD, A+OESD etc type of hands here, but only stacking off with very good hands (AA, TT). I've seen him do some big laydowns before on flops.

BTN is seen as solid tight player.
Given how tight SB is playing, is this just a fold since he has AA there alot?
Or since he is c-betting alot but over-folding vs all-in and we are blocking both A and T here, should we just shove? For 240bb stacks, I believe he is willing to fold 99 and NFD+gutshot there.

Id just call the jam and see what SB does - repotting just folds out worse hands and gets call by better hands.

We have 36% equity against {AA, TT, AKcQJc} and 44% against {AA, TT, 99} so I would jam and try and get him to fold his equity

I slightly prefer shove given what we know about villain.

I've tried to do some math here, please correct me if you find anything wrong.

SB C-betting range
5%: (AA, TT, 99, AT, A9, T9, AJQ, cc) = Total of 2073 hands after AhQcTc5h and AcTd9c are dead
SB AI calling range
5%: (AA, TT, Kc:QJ:*cc) = Total of 960 hands after AhQcTc5h and AcTd9c are dead

Meaning that SB will call 960/2073 = 0.46 = 46% of the time

Equities
A) BTN vs BB (SB Folds)

B) BTN vs SB vs BB (SB Calls)

C) BTN vs SB - Used for side pot EV calculation

I do not know how to determine the equities for the side pot, so I will use a simplified version of just simulating BTN vs SB. In reality it should be little bit in favour of BTN? Since BB winning means that he is likelier to have AA and therefore SB does not? Not sure if it makes much of a difference.

EV Calculations
SB Folds
A) BTN vs BB
EV_A = 0.57*615 - 0.43*295 = 224

SB Calls
B) BTN > SB, BB
EV_B = 0.15*(195+295+1135) = 244
C) BB > BTN > SB
EV_C = 0.24*(-295) + 0.32*840 = 198
D) BB > SB > BTN
EV_D = 0.24*(-295) + 0.32*(-840) = -642
E) SB > BTN, SB
EV_E = 0.61*(-1135) = -692

Final EV
EV = 0.46*EV_A + 0.54*(EV_B + EV_C + EV_D + EV_E) = 0.54*224 + 0.46*(244+196-642-692) = -290

Based on this, shoving is losing a lot of money here.
Also "cc" in both ranges should be narrowed down a bit, I don't think they are betting 8-high flushdraws here.
How does BB range affect SB fold equity?
Are there any other variables that could make shoving here profitable?

SB will be betting the flop significantly wider than that range imo

What would you consider his c-betting range to be in this case?

Looks good .. smells bad?

The c-bet is interesting .. is he willing to GII with short stack but wants to see what's going to happen behind first?

Will he pay us off with weaker holdings if the Board gets worse? Probably not based on description.

Are we folding to his re-pot if we flat?

I'm probably bad, but I'd like to min-raise to send a subtle message to SB and also open the side pot so if I lose the main I can still get a return. We are still in a pickle if SB shoves blank Turn .. we also have to shove a blank Turn.

I tend to believe that Players are more willing to fold Turn with only one card to come. So I don't mind flatting either, in position, which means I don't always have to sigh-call-off for 200BB.

I've done it all here, been 'correct' and been way wrong. It comes down to taking 2.5 to 1 to try and see a Turn or denying a cautious tight Player their equity in a potentially marginal spot 'for them'. GL

It's going to be hard to get away from top two pair plus the NFD and backdoor straight draws.

That being said, what is the purpose of raising here? You're never folding out AAxx if you happen to be getting coolered. And it's doubtful this villain is going to show up with 99xx given he raised OOP and how you've described him.

If you're worried he has Axxx where he has some sort of broadway draw and could conceivably make a better two pair on the turn if a K or J fall, that's still not really a reason to jam. You have the NFD so a number of his outs in that instance would be dead. And you also have a broadway blocker and would still have outs to the nut straight or the flush should your opponent hit a miracle K or J to make a better two pair on the turn.

So raising as others have stated just pushes out hands you want to call, and gets you putting in stacks when he does show up with AAxx here.

If you just call the raise and the SB jams it in, well now you have a decision to make. But what could he possibly be jamming with outside of AAxx here? I guess if he had Axxx with a weaker flush draw and a broadway draw that would make sense, but you block some of those combinations (although you also block him having AA as well)

Still, I think a call is fine and don't see a ton of value or protection gained by shoving.

I'm not sure I could really define a range, but given the board texture and that small bet size, I'd agree with the above that SB's c-bet range is a lot wider than in your analysis.

2nd nut fd. NFD is very much in SB range.