Live 1-3

LJ Limps $150 eff
Hero CO raise K8dd to $15
Bttn Cold calls playing $450 some sort of loose aggro rec, not crazy tho

BB calls, sticky weak lady $300
Limper Calls(Weak Recreational guy in 50's)

Flop AdQd9h
Pot = $57
Check Check, Hero C-Bet $25

Bttn Fold, BB fold, Limper calls

Turn Tx
Pot = $107
Limper checks with about $110 Behind

Hero?

I range this guy to have maybe all combos of Axo, maybe raising AK, but totally capable of just limp calling AQ, potentially even AK, but prob lower frequency. Imagine Raising range is something like 99+, AQs, AK, and then limping the rest.

On turn, I think his range looks alot like Ax, some two pair, some pair+draws, including alot of offsuit combos like JTo, 98o, as well as Q7s, Q6s, maybe Q8o.

I broke this down into flopzilla and gave him a range of about 244 combos on the turn, and expected him to fold something like 90ish combos to a turn jam, which with our equity would lead to about a 0 ev jam. Give or take a little, as maybe he folds more Ax than I am giving him credit for, but think it balances out a bit because population of players that fit his description might still just call off with any Ax at this stack depth.)

244 Total combos. need 122 folds, but have 25% equity. So 122x .75 = 92.

Basically, I think jamming is good for sure, but I also think checking is good. I just don't know how to quantify the two options. A jam I estimate is around 0EV, BUT, it does get villain to fold a large portion of his range that checking would not be able to capitalize on, say the 98o or KT or K9o of his world. They would all get to realize their full equity, as I am likely not reopening the action if I check back the river, plus some of them may get to bluff me(less of a concern here)

While I think the jam is 0EV, the capitalization of dead money has to be worth something, right? I mean checking back I realize my 25% equity for free, and then can get stacks on a diamond vs like 80 combos. I don't lose the $110 vs his snap calls, but I also don't gain the $110 vs his folds.

On the surface, if a play is 0EV, then if an alternate option(checking) realizes our 25% (free), and then can get clean value when we hit, and fold when we miss, that seems like a win as well. I suppose, there is a slight margin of error here however, where if he folds slightly more than we predict(say any weak Ax), then jamming quickly becomes superior.

If I am not bluffing this combo, I am basically not bluffing here against this player, which I don't think is an issue as he will not be aware of this as I don't play with him often. So I am just looking for the highest EV line and not concerned about having bluffs to incentivize him to make loose calls. He will do this on his own.

So, my main question is, is even if a bluff is around the threshold of breakeven/0EV, is there a gain I am missing that would be greater than the gain of checking back?

My guess is no. If we lose equal parts vs his calls, and win equal parts vs his folds, then if an alternate option would net a 25% gain vs 33% of his range, than it will still be marginally better to just check behind, realize our equity, not have turn bluffs, and get stacks in when we get there.

FWIW, I estimate around 81 combos that would stack off on a 2d river for example. so thats worth $110x81 = $8100x .25 = 2025.

It's pretty close for sure, as my estimation has him folding say A2-A5, and calling A6-A8. It's possible he just folds A2-A7, which would be an additional 24 combos or 2640 in EV.

Suppose it just is a really close spot between the two options and I don't hate either or. Suppose the most important thing is to have a solid understanding if he actually has things like A2o in range, and will he be willing to fold them for a 33bb pot size jam or not, and that will be the most important determinate in if it is better to jam or check.

In the moment i went with the check, but in hindsight I think just going ahead with the jam is totally fine. Because something else that is relevant is the future EV of jamming. If the two options are really that close, then the EV of just taking the aggressive action for sake of image is pretty nice. If you get called you are now perceived as possibly being overly aggro which can help getting paid in the future. so there are some non-tangibles in play here I think.