I think I might have made an incorrect fold, but not sure. Could use some help with the numbers here and clarifying some math

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I think I might have made an incorrect fold, but not sure. Could use some help with the numbers here and clarifying some math

Live 1-3

4 Limps

Hero on BB w AcKs and raise to $28(some pretty sticky guys in game, will make it 25+ here, just made it $28 because they already pulled my $3 in and it doesn't make a huge difference, and also dont mind making it tad bigger with AK trying to get it heads up/folded thru.

get a short stack caller who can be very wide

Bttn calls as well and is probably pretty wide, he is like $550 Eff

Flop QcTc7h
Pot = $84
Hero Checks
Short stack jams for $72

Bttn deliberates quite a bit and makes the call, he has another $500ish back. between $450-550

Action on Hero...

Basically I need around 1:3.1 here, which I don't exactly have given the Bttn will certainly have some turn bets and I will underrealize my equity.

However, I think if we say 2 of my A outs are clean, and none of my K outs are clean, and 3 of my J outs are clean, we effectively are looking at around 20-24%, but say we only realize 70% of that equity. 14%-17%; 1:5.5 - 1:3.1 = 2.4. So we need to make around $173 back to find a break even point. I suspect we don't get bluffed off the best hand when we hit an A or K, and can likely make at least a 2/3 bet back on a J(not always). However, this is accounting for times when we only have a clean A 2/3 times, no clean K, and 3 clean Jx. There will certainly be scenarios where the guy jamming will have something like Q9 or Tx, or 98s, and the guy calling will have something like KJ, J9, or a FD. So our hand can actually have showdown value however small..

I folded in the hand, and afterwards I realized I think I made a mistake.. If the Bttn only had like $200 behind or something, I can get behind a fold, but I think as he gets deeper, we can actually make a call here. The only thing however, is there is also the scenario where the player jamming will have a made hand, and the bttn caller will be on a draw, in which case we dont make money, but I guess our equity will realize fully and we will see a river, so that is okay.

I'm also not sure how the math works out since we basically get to showdown our hand/make small value bet on an A/K, or fold if we face heat, but may make a decent sized bet on a J, if he has something. So half our outs carry implied odds, while half of them mostly are looking to see a showdown. So wonder if there is some sort of weighting affect that needs to be accounted for. I think it doesn't quite matter, as if we have 16% equity, we have 16% equity and really just need to make up the difference for needing 24% equity.

I think my process is making more sense now and I made an incorrect fold. Is there a simple way of looking at this and I'm making it way to complicated?

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