I think its very rare that we want to fold a set on the flop. I would say never, but if you’re >150bb deep with bottom set there might be some situations where you want to fold to a shove (maybe). Aside from very rare set over sets, you’re always going to have decent equity against the very top of villain’s range. Many players fall in love with two pair on the flop, and you generally don’t want to fold when you’re crushing a good portion of villain’s value range.

Turns are a lot different, and there are spots where sets can find a fold. Still pretty rare but, at least in multi-way pots, when someone shows a lot of strength and there’s an obvious nutty hand on board, you often won’t be getting the right price vs. too much of their range to justify a call. I once folded KK on KQ5 T rainbow (on a short-handed final table) where 4 people saw the turn, and I’m pretty confident that it was the right play. Still, the fact that I remember that hand 2 years later should illustrate that we don’t want to be doing that often.

That hand is one of the few times that I felt rushed to make a decision as my 100+ second timebank was running out. It’s very possible that I made a bad fold, but I think I would do it again in the same spot against that type of player.

One thing I didn’t think to mention. On flops with three broadway cards, I’m not always looking to play a big pot with sets. Not looking to fold, but I’ll occasionally pot control the turn if 2 bets go in on the flop. Two pair is often going to consider folding once the fourth bet goes in (ie. either flop or turn gets raised and a bet on every street). There aren’t a ton of combos that, for example, JJ on AKJxx is beating if two pair isn’t always paying off.