Hey there,
I definitely think there should be much more to raising or 3betting postflop than just equity, however the general guidelines should help you decide what to do. However, one thing I see many people do is using equity as excuse for bad plays (like I don't have XY% equity, therefore..., or I have XY% equity, therefore).
Equity for preflop and flop is a very misleading thing. In theory, by equity you can call any2 against most openraises from the BB, and certainly anytwo 3ways against any range. However we're talking about hot-cold equity, which assumes we're gonna go to showdown a 100% of the times, and that's definitely not true. Your real equity (aka how many times you actually win the pot) will be massively different from the value Equilab and other equity tools are showing.
On later streets HCEq is much more relevant, since you're gonna rarely fold on these streets, and people often have a more polarized range on these streets. However, our equity in general (against the whole range, or a calling range) will still mean little to us. We can set guidelines, like I'm always raising with 66%+ equity against a calling range, and that's fine. However valuebetting (or more like blockbetting) can be the best move even if you only have 10-15% equity against your opponent's calling range.
I'm not saying HCEq should be ignored or anything, I just say, that even in LHE there are much more factors you have to take into account than just pure equty.
For 3betting preflop I draw the line at around 46-7% equity, depending on the nature of the hand, but for balance reasons and because of their future implied odds, even worse hands can be good 3betting hands. From the SB I 3bet with ~43% equity. From the BB I think nowadays the standard play is not to 3bet anything against a single raiser and no limpers/coldcallers, and I definitely think that's the best play, unless your opponent is a checkback-monkey on the flop.
Of course the chance of getting capped lowers our expected value, it happens so infrequently that it's not big of an issue at all. If it happens more frequently, your opponent has a wider range you're doing better against, so I don't think that's much of an issue. Also nowadays it's pretty standard not to cap HU also.
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On the second post: I think raising the flop represents a wider range of hands on our part, and we should do that usually. By not raising flops, you opponent can exploit you by checking turns (especially if he's IP), therefore I believe fastplaying OOP is certainly the way to go, IP it's more dependent on the board texture and your opponent.
Now what I found also, is that on most board textures if you raise your stronger made hands (usually Middle Pair+), and your draws, you're gonna raise a so-so balanced range, which is kind of really cool, since your natural way of playing is balanced there. However if you delay your action to the turn, in theory you should have more bluffs in your range, which means you should turn pure air hands into a bluff on the turn, if you never raise the flop - and that's gonna bring less EV for your overall range there.
I hope I could help, if you have any questions, or you didn't get something, let me know!
Cheers,
Madi