NF vs 2NF? What's the default line?

Pre and flop are standard. Most AKxx want to open from BU as default and on flop we have no business cbetting this combo without A♣: In general we should be careful on this flop in general. SB range is supposed to be very broadway heavy and most people dont lead nearly as much as they should. E.g. trainer cbets only 32% with assumption that SB leads almost 40% of time. If SB has no leading range cbet% might be like 15-20 for BU. Assuming solid pre range.

Checked in trainer BUvsBB which is quite a bit different but there are no turn/river sims in BUvsSB single raised pots:

In here we can see that 2nd nut flush is always calling if you have 3 or 4 spades. But does fold more if we also have two pair or set. I think logic in that could be that we block hands that can check in hope of getting to showdown but then turns into bluff when facing river bet. E.g. hand BB could x-r bluff could be something like AQT5 with A♠:.

Now if we compare this BUvsBB spot into BUvsSB huge difference should be in preflop ranges. Its way way easier for BB to show up with As!ss combos in this spot with way wider pre range. So I think in practice we want to ask how wide SB is in first place. E.g. if I check SB pre range in plo50 sim:

There is basically no non nut suit Ax hand that should call. So hands like AQT9ss or AQQ5ss are supposed to just 3bet. Now I dont think this spot is quite as grim as this. Most likely even reggy player calls too much from SB and some of those hands that are supposed to be 3bets could be just called. But its still hard to show up with hands that he could bluff with and he also needs to go for it which is kinda ballsy play especially versus pot river bet. So imo good approach might be to mainly fold if we dont have flush with three or four diamond. That way we give lot of respect for villain line but still have some calls. For river versus most its actually kind of irrelevant if we have 2nnd nut flush or weaker one as most only raise nuts for value. So I would prefer to call weaker flush with three flush blocker over 2nd nuts with only two.

Thank you for detailed response. There is a lot of info to take in. Calling with 3-4 is a nice simplification. Unlike solver though, I don't think most players are turning sets into bluffs. I agree players are overcalling and under 3betting from SB. There are no sims for turn BUvsBB but what do you think of the delayed turn bet? I was planning to continue vs a x/r OTT.

Turn bet is bit mergy in its nature I would say. E.g. does villain have straights, sets or better two pair in his check, check range? I would say usually straights and most sets will bet big on turn. Some of weaker two pairs might want to check though. I think we face turn x-r extremely rarely so I dont hate bet but its good to recognice that its imo thin bet.

Calling versus raise is probably still ok. We should be able to rep rivered boats in case board pairs. Versus some players though danger is that they will have some hands like set+nfd and we can be in really bad shape. Another issue is if plain nut straight will go for x-r. Again danger being our fd is dominated.

Without good reads that raise to pot bet isn't often enough a blocker bluff. But then again, to check turn and river with nutflush seems odd too. It might be a trap, or he has a hand that has some equity vs your turn bet and has Ad in it. And on the river he knows that just a lead is not enough to make you fold a flush, but big c-raise is.

If you were oop and he calls turn, raises river I would fold easily. But here, it seems a bit weird. If you have a habit of barreling a lot of rivers, then he could easily trap you.

As a simplified rule of thumb, I wouldn't usually worry about losing to NF with 2ndNF, as it's like AAvsKK in holdem. It evens out in the long run, and if we start to make a lot of hero folds there is a chance that we end making more bad folds than good ones. But still, every saved $ is also a won $. To call a pot sized raise, he needs to be bluffing (or valuebetting worse) 33% of times.

I knew that theory was I should be calling. But I was not sure if this is one of those spots where we should deviate a lot by overfolding because players aren't bluffing enough. As you said on one hand we can over fold but on the other we might be exploiting ourselves.
He had A788$ss (NF), he missed a 3bet pre. I think on flop he could lead having NST blocker, a pair and low GD + BDFD. He could barrel a lot of turns. Proably wants to have a though.

I agree I think most players bet big OTT with most strong hands. Yeah he could have hands that absolutely dominate but ranges are so wide at this point. Also those hands are not combinatorically frequent (did I use that term right?♦)