wider cold calling ranges

By far the biggest reason to differ CC ranges is because of aggressive squeezes/3b's behind. Getting squeezed is really, really bad. If you're not getting squeezed can CC a tonne, if you are, then need to be tight.

I mainly adapt my defending ranges based on open raise range. I will call and 3bet wider if UTG is opening 20% instead of 14-15%, etc. And also based on open raise size. But I think that's obvious.

Other than that, I don't like to use stats for that purpose very much. I think that's too optimistic, but I suppose that the biggest leaks that someone can have is to give up way too much on the flop or bet/folding too much. Those would be good reasons to call wider (be careful with squeezes,etc.).

Opponent gives up too much on the flop. His check/fold % is way over his cbet%. For example: cbet 60%, check-fold 80%. But even in that case, we aren't autoprofiting, becasue when we float bet and opponent check-calls or check-raises we lose our bet. You can calculate EV like this (check that it makes sense):
EV=%opponent checks*(%check-fold*pot + %check-defend*(-floatbet)). In the example that I gave you (60% cbet, 80% check fold) our EV would be around 2bb but we had invested 3bb preflop (utg opens to 3bb, we call on the BU for example). So our total EV would still be EV-, but we will also hit strong hands with our bottom range as well, so it is difficult to know exactly how much is too much.

Opponent bet-folds too much: cbet-fold over 50%. Everyone knows that

But as I said, I don't like to make this kind of adjustments based on postflop stats. I would mainly concentrate on openraise range and also on fold to 3bet (in case we can 3bet wider).

EV=%opponent checks*(%check-fold*pot + %check-defend*(-floatbet)). In the example that I gave you (60% cbet, 80% check fold) our EV would be around 2bb but we had invested 3bb preflop (utg opens to 3bb, we call on the BU for example). So our total EV would still be EV-, but we will also hit strong hands with our bottom range as well, so it is difficult to know exactly how much is too much.

If you are calculating what is EV of a hand that calls preflop having preflop 0% equity, then you miss one part in your equition, it is the time when a player cbets and you lose your preflop call (3bb). But in reality, our hands have equity, and it is almost impossible to turn such equity into EV. Still, I guess it can be approximated, how much vs average villian we can realize our equity.

I calculated Ev of worse hands on the flop. I assumed that when opponent cbets our flop EV is 0 since we fold. If you take into account that you lose 3bb in those scenarios then you have to substract 3bb from the benefit we gain when opponent check folds as well. I calculated flop EV and then compare it with our preflop investment. I think both ways are ok. And then of course we will have equity, etc.

I calculated Ev of worse hands on the flop. I assumed that when opponent cbets our flop EV is 0 since we fold.

It cant be zero. The hand starts preflop, not on the flop. We cold call and invest 3bb, where we have 0% chance to win the hand preflop, so we have postflop to win at least 3bb. So if you fold vs cbet then you lost 3bb.
very similar logic is for calculating EV for a flop float, where you pay flop bet, to win the pot on the turn, and if villian cbets turn, you lose what you invested on the flop and not EV = 0. So similar is with preflop cold call, you are basically floating preflop, to steal the pot on the flop. Sure you can hit a good hand, but for most of hands, it will be mostly a bluff catcher once villian starts barreling. And similar is with flop float, still you can improve a hand on the turn, you have only one card, and preflop 3 cards, which makes actually preflop float much more profitable than flop float.

I calculated flop EV and then compare it with our preflop investment. I think both ways are ok. And then of course we will have equity, etc.

yes, equity part is the toughest to calculate. If we calculate EV with a GS for floating flop, it is much easier because we almost exactly know our chances to improve and can approximately calculate EV when we hit, and EV when we dont. In pokerstrategy article about floating, they gave nice example with EV calculation for floating flop, where hero holds low GS (something like 78s), so on that board, it is obvious that hero wins a hand only if he hits a GS and then he has the best hand almonst allways (pure nuts).
But what if board is Js 9s 3c, and we float KQo? then we can improve to top pair, but also to GS, and it is not clear what is our EV for what card on turn and river, and how often do we win vs villian range. So similar is preflop, it is even more complicated since we see 3 cards.

I think you didn't understand what I meant. My english is not native, maybe it is because of that.

I first calculate Ev based on flop foldequity only and then you have to take into account that you will hit strong hands with your bottom cold calling range as well (and you can also float bet and improve on the turn and river as you said)

Method 1: you calculate flop EV and then substract preflop investment. Let's say UTG opens to 3bb, flop pot is 7,5bb and float bet 3,5bb. He cbets 60% and check folds 80%.
EV=0,4*(0,8*7,5 - 0,2*3,5= 2,12
Flop Ev is 2,12 and if we substract preflop investment total result is = -0,88

Method 2: you calculate total EV from preflop. Same situation as before.
Ev= 0,6*-3 + 0,4(0,8*4,5-0,2*6,5)= -0,88

The results are the same. 2 ways of doing the numbers, but results are the same. That's what I tried to say. And then you have to consider/estimate if that EV is very high or very low taking into account that not only we will be able to win the pot when opponent gives up on the flop but also when we hit strong hands with our bottom preflop range (or when we improve and beat him on turn and river).

I like the first method beacause it helps you visualize that opponent is giving you back 2,12 out of your 3bb investment by folding a lot on the flop. So if you are able to win 0,88bb the times he doesn't give up and we hit a strong hand then we have a Ev+ spot. I think it is a useful method to spot big frequency leaks that can encourage you to expand your coldcalling range.

Conclusion: when opponent has a high check fold% in relation to his cbet%, we could argue that he is giving up too much and we could expand our cc range. But we will never be sure if he follows the same strategy against us, on which flop textures does he check fodls, etc., etc. And that's why I wouldn't do huge adaptations based on that. But you said you wanted math calculations and here I am ♦

Method 1: you calculate flop EV and then substract preflop investment. Let's say UTG opens to 3bb, flop pot is 7,5bb and float bet 3,5bb. He cbets 60% and check folds 80%.
EV=0,4*(0,8*7,5 - 0,2*3,5= 2,12
Flop Ev is 2,12 and if we substract preflop investment total result is = -0,88

yeah, this looks like something what I meant. We lost -0.88 BB, but thats only when we consider that our hand never hits. If we add equity to our hand, then it should be (I guess) +EV. If e.g. our hand has preflop 30% equity, can we use some kind of equity realisation, so that we can approximate EV of a hand for postflop?

Method 2: you calculate total EV from preflop. Same situation as before.
Ev= 0,6*-3 + 0,4(0,8*4,5-0,2*6,5)= -0,88

OK, now it is more clear what you mean, since you wrote it in math format
Now, there is also a possibility that somebody sqeezes preflop. Lets say the possibility that at least one from 2 players behind sqeeze is 15%, then our EV is:

Ev = 0.15 * (-3) + 0.85* (your_calculated_ev)

off course it assumes that we fold 100% vs sqeeze, which is likely truth for most hands, since we analyse here when we should widen our cold call range. But anyway, the possibility of agro sqeeze lowers EV a lot. Lets say your calculated EV is 1bb, then considering preflop sqeeze, total EV of a hand is:

EV = 0.15 * (-3) + 0.85 * 1 = 0.4

So, sqeeze really sucks especially if it is very frequent like in BB vs SB situation.

Conclusion: when opponent has a high check fold% in relation to his cbet%, we could argue that he is giving up too much and we could expand our cc range. But we will never be sure if he follows the same strategy against us, on which flop textures does he check fodls, etc., etc. And that's why I wouldn't do huge adaptations based on that. But you said you wanted math calculations and here I am ♦ ♦

This is imo interesting topic as well, how much do we beleive in our stats. On one hand it is truth that if villian cbets 50% in average vs all opponents and 80% folds after check, then it doesnt mean that he will play that way vs hero (he can play totally different), or that he will play that way on each board (e.g on Axx he might cbet 80%, on 579 he might cbet 30%).

But on the other hand, if villian is cbetting 50% in average vs all opponents, than it is very likely that he is doing it as well vs you. The probability that he does something far away from this, is very low. So if somebody has a leak, that he gives up too much on flop, then very likely he has a leak vs you as well. And if you start exploiting that leak, it is more likely that you will win more money by doing so, than that you will loose money. And after all, if he really does it vs hero specifically very different, then we have vs hero stats and should notice something is wrong.
Similar is for different board, if he cbets 50% and gives up too much on flop, then it doesnt matter if he cbets 80% on Axx, if he is still in average giving up too much, and in average we are exploiting him.

So, I am not blindly trusting my stats and I am aware that stats are not even close to100% correct, but imo using stats is better than not using stats (it will increase EV if used properly). E.g if villian folded 5/6 times preflop vs 3bet, I am already going to 3bet him wider, because 5/6 sample makes it very likely that he folds too much, and i will do so until the stats show something else (e.g. after somet time 8/21 fold, then I start being a on value heavy side)

Thanks for the answers, nice discussion.