Just wanted to say that this conversation is very interesting. I opened this hand when it was first posted and didn't respond because my first response was "I don't know WTF I would do in real time and I dn't have time to do ranges and math right now.

I particularly commend dgi for confidently explaining his real-time reaction, and then saying "maybe not," when he looked at OP's math and ran his own ranges as well. It's really nice to see a lack of justification and willingness to learn, even among one of our biggest crushers ITF.

I think the answer is as simple as the fact that our max EV comes when we don't see the river vs. both Villains. We don't want both of them to call wide because in combination we are drawing relatively thin. Our dream scenario is that they both fold, but if V1 calls and if it gets back to V2 getting >3:1 on a call we've just made his decision for him by raising smaller than AI.

Assuming V1 has to go AI to call, she needs 175/655 = 27% equity (less if V2 is calling behind). So V1 is calling with any pair+gutter and better. For V2 to call AI after V1 called, he needs 400/1055 = 38%. So we pretty much have to go AI to fold out V2's OESDs and FDs. So it looks like there isn't much point raising less than AI.

What did you use to run those EV calculations? What calling ranges did you assume for villains in the two scenarios? The AI calling ranges for villains in the two scenarios can't be the same, or calling flop shoving turn would definitely be better.

Just want to point out call > fold always here because we have immediate odds to draw to our 13 blanks.

"Jam>>call=fold if V2 folds >0% of the time."
Don't really understand this. If V2 folds 0% of the time are you assuming he calls with no pair no draw? Obviously shoving is best then.

It looks like you are just estimating equities for the flop and turn instead of calculating equities against ranges. I think your equity estimates are too low for flop and turn, but more inaccurate for the turn. I'm pretty confident we have more then 51% when we jam flop and only V1 calls, since she is calling with as bad as pair+gutter, and there are a lot of those kind of hands where she has 33% equity and she is calling. On the turn we have about 80% equity against a 9 out draw, and both villains have way more draws than sets/straights, so I think we have significantly more than 60% against one V.

I don't have access to any sort of equity calculator right now, but will crunch some numbers tomorrow. My intuition tells me our call flop, jam turn EV is closer to our jam flop EV.

Would the 5 or 6 pairing on the turn be considered good or bad cards for us? I'll assume that the 7 pairing (no heart) could be bad.

I counted the 5 and 6 as good cards and the 7 as bad when trying to calculate the chances of getting to the river after calling the flop.

It look like your deck has more than one 5d, 6h, 7h.

Not if we don't have enough equity to make up for the times we fold, and here it is close

I am assuming that neither Villain ever has complete air.

well, this one makes my head asplode but I actually think monkey jam is the best play because V2 probably has a huge folding range and V1's stack isolated probably gives us correct odds

breaking it down

shove

pro's: can fold out V2 a lot and decent equity vs V1
con's: allows V1 to fold all worse call all better and he covers

call
pros: keeps position and allows you to control the odds by continuing on good cards and fold to bad ones and you get more information out of the hand than shoving
cons: too many bad turns that may force us to fold the best hand sometimes and it gives v1 perfect draw odds

fold
pros: we are usually behind normal players on this flop 3way
cons: these aren't normal players

conclusion

shove because you will usually get the money back anyway and they pay off light

Since thread is petering out, here are the results:

After a long think I decided to call and wait for a blank turn, which came the glorious 2c.

V1 shoved, V2 sighed and folded what he later said was 44 and I called. River is Kc, V1 shows AhJh and MHIG.

After the fact I thought that maybe folding flop was better in light of the fact that V1's range is going to be big card heavy and thus have a ton of flush draws in it that would be jamming every turn. Interesting that until the numbers ran I thought the choices were something like fold>call>>jam and in reality it was pretty much the opposite.