i think i do, but i feel like the concept is being taken too far. for example, a pretty straightforward/generic strategy would be:
876x2 (22% of our range) call/break
876x3 (11% of our range) fold
this alone gives villain incentive to make plays at us with.
if we're also breaking 875x2, that's another 11% of our range, leaving us breaking/folding 44%.
i disagree we should have any 9's, but if so, then our break/fold% is even more. this has to be way too much.

mostly i feel like if we were to have 9's in our range, breaking 874 shouldn't even be a consideration imo.
like, even if we were to have a theoretical folding range on river after call/patting, 874 wouldn't even be close to a fold.

I think you have to analyze your range. And see how much you are breaking and how vulnerable you are.

You listed two hands the 8763 (I fold pre) and 8762(I play as an 762) that I do not have in my range.

I make my range stronger as I think it should be. I do not have many nines, not breaking often, and thus I feel I may be able to break.

But it’s close and I will look deeper later.

not sure about 8763, but i'd have no prob 3betting vs a d3 and isoraise. i could be wrong tho.. and 8762 draw only accounts for very small % of total 876x2 pats.

I actually want to spend some more time studying Td, as there are so many spots where striking the right balance is difficult. 96 and 95 are clear pats for me and 97 is more situational. I agree that patting 98 is almost always incorrect.

2 points
Having more 9s in our pat range (as well as some rare snows) should create value for other parts of our range, as well as make it difficult for opponent to play weak 8s and all 9s.
I think the tough decision for patting hands like a 97632, is not so much whether to pat (we can reasonably estimate equity) but optimal play for the rest of the hand.

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In the hand the limper ended up D2 but yeah usually it's a D3. Yes, I guess you could label it an isoraise but it's probably not part of what we would consider part of the steal portion of the CO range. It's usually at least a solid D2. Then there is a big blind left to act.

I'm not playing 8763 nor am I playing the deuce dependent gutshots such as 3457 and 3467. Then instead of 8762,8752,8742, and 8732 as 1cd I'm probably playing them as D2. I will however play 8543 and 8643 as a 1cd. I have a feeling we probably don't see eye to eye on this.

Assuming we don't, given this action we both have radically different pat hand distributions. Not taking any of the 87XX combos as a 1cd dramatically reduces the amount of combos of them because we only have them when we get the 8 on the first draw (and sometimes we have already seen an 8). Then with 8543 and 8643 I am keeping the 87543 and 87643 and not breaking on a raise turn.

So in general I haven't summed up combos but my range is strong and not a lot of breaking. Therefore it doesn't seem like I'm going to be exploited by over-raising the turn even if I do break a hand as good as 87432. But it's not a linear breaking decision as I'm patting 87543.

But I'm not sure, haven't crunched it all down

When we have a 97 and don’t know the result of two opponents drawing two I think we actually have more equity drawing as opposed to staying pat after 1st draw. So I don’t think that’s close especially when we can exchange reverse implied for implied odds

It’s my opinion but I don’t think we need to do anything suboptimal to create advantageous situations. Players balance their play a lot on general population and from the looks of responses it seems like we are getting plenty of action on our big hands regardless.

I went through the EV of each in an approximate manner. I don't have the capacity to do a detailed range versus range breakdown with all the combinations properly weighted, but I don't think that will change the results that much from my back of the envelope math.

I put CO on hands 1-13, and because of how slim UTG is drawing most likely it's not actually worth much if anything to force him out. He's going to fold his worst draws even if we don't 3! because he's stuck between two patters. How often he'll fold is also related to his tendencies, but in the end the values are so close when he calls and folds I don't think a slight variation in his frequency will affect us. Even though he spikes 15% of the time, the extra big bet subsidy for the times it's you against CO more or less makes up for it.

Even if we let CO play masterfully and bet exactly all hands that beat us and check back the three worse 875s he pats the value looks something like this:
3/13 * 10 - 9/13 * 2 + 0.75/13 * 5 = 1.21 BB

When UTG calls I'll assume he checks to the patter and we have to pay off the same:
3/13 * 11 * 0.85 - 9/13 * 2 + 0.75/13 * 5.5 * 0.85 = 1.04 BB

Getting a very accurate value for breaking is hard too because the rare #1 vs #2 coolers can come up, and sometimes we get our 8 back but here is a generous take:
8/46 * 11 - 35/46 * 1 + (a mess similar to above when we hit an 8) * 3/46 = 1.27 BB

And if even one of our outs is dead this drops to 1.03 BB.

Now to compare it with 3! yes UTG syphons a little off the pot, but not nearly as much as we fire off into CO's range. To guess at the EV of 3! I had to make some more guesses about what CO will do. (I figure UTG folds 100% in this scenario.) What is his 4-betting range? Is it only #1? #1 and #2? Bigger? Hero can't even call the 4b if his range is that tight, and even when he just calls we're still behind more than half the time. Not only that but a 3! should alert CO that it's time to break hands that he can break which hurts our equity (since those hands have zero equity as pats). My first set of assumptions came to a value of 0.02 BB. If he folds the worst 86 for some reason that coup is worth a whole BB and it's still only barely as good as if UTG calls with a good 7 100%.

The more semi bluffs or worse 8s you put into CO's range the better 3! on the turn becomes. Breaking is also worse against the widened range. Because Hero is out of position and can't be sure if CO would try a semibluff or snow here I think the conservative line is safer. I stand by my gut instinct to call and pat, and that line is better than drawing or 3betting the turn.

Ok I’ll try and take a look at some of your math but a few quick points

1. If we just call can’t see the guy in the middle folding any draw to an 86 or better given this price
2. I wouldn’t consider the CO to be playing masterfully by betting only better and checking down worse. Our hand is right on the border so when we just call and pat our hand strength is such that it allows the other two in the pot to more or less play perfectly.
3. CO may break some hands anyway even when we just call and pat.

At any rate I think break or pat is close and useful to look and analyze your own range. My strategy is geared around arriving at this juncture with a stronger range than the average player. Therefore I may be able to break the 87432 without being exploited overall which I think is a good thing.

But if I’m patting I still think I like a 3bet but willing to look at more

The non-linear breaking stuff is worth noting. What hero's D1 range pre consists of should determine how hero approaches the spot once he gets here and I think it's the most interesting aspect of the hand. I don't see limpers very often (unless BvB), so it's a spot where I'm a little unsure of how weak of a D1 I'm playing.

I don't like 3!/pat as only hands that break are worse than ours and the pros of possibly k.o UTG don't seem to outweigh the cons of bloating the pot against CO, who has strong range, can re-open the action, and is prob playing the spot honestly (unless our image is that of a quick patter, prone to break or fold too often, which makes a lot of difference).

I don't break this hand. I just call/pat/payoff in a decent sized pot. To keep our range from being too narrow, hero can call/pat and then x/r river w nutty hands. Usually I lose and occasionally it gets checked around and we beat something like 98752 or we snap off 23456.

We don’t see a limper often but as a whole I don’t see me opening up my D1 range or changing my strategy of drawing 2 to a hand like 8742. I play it similar to if it was a raise and a reraise. At the end of the day we have two opponents OOP. Limper often D3 but they have two premium cards including a deuce so I’m not playing deuce dependent gutshots such as 3457.

The arguments against the three bet indicate that he’s mostly playing honestly which on the whole makes the call pat and call down line seem more dubious.

If I called and patted I would call down as well but let’s be honest that we are probably at least 30 to 1 to get the chips. CO needs to be running some snow against a power range or be overplaying his hand and we still need to dodge the UTG draw.

So we are paying quite a premium on that last call in order to sleep at night.

Would prefer to play a strategy that allows me to break and failing that still like 3bet if we are calling down. I discount sevens from CO range slightly as he may have raised with a D1 seven draw on flop to push what should be an equity edge