How do we decide what flops to have a raising range on, and what flops to only call on?

I have an understanding of this topic when it comes to extreme examples. For example, if we call the BB facing an UTG open, we probably won't have a raising range on a AcQsTd flop.

But let's say we call a CO open from the BTN, and the flop comes JsTc5s. Do we want to have a raising range on this board? We can't have JJ or TT because we didn't 3bet pre, and the BTN can still have both of those hands. Our only very strong hands here are JTs (2 combos) or 55 (3 combos). On this kind of board, should we have a very small raising range, with our few very strong hands and a few very strong bluffs (9s8s)? Or should we not have a raising range on this board, so that we can protect our flop calling range on a board that favors our opponent?

Basically, my question is how do we decide whether to have a raising range or not? And on boards where we can't have very many strong hands, is it better to have a very small raising range, or to just flat all our of our continuing hands?

depends on sizing and range used by opponent.

When slowplaying is more profitable than fastplaying. Thus if we have no value raising range, then our bluff range is also (empty).

You don't need to 3bet your TT and JJ from the button against C/O.

Exploitative players just work out which play will make the most money with the particular hand they hold against the villains range. We don't worry about the other hands we could hold in this situation. So we wouldn't bother working out our raising range.

As you didn't mention what hand we actually hold, and have told me nothing of the villain or history, I can't tell you whether or not we should raise.

.... There should be a section on this site for GTO questions like this one. To save confusion. Or, better still, someone should make another site where exploitation dominates.

It depends on sizings and frequencies like Broken said, but I think the general rule is that you want/need to have some nutted combos in your range and be able to balance with some bluffs that either reduce/block villain's continuance range, or have robust equity against it. If raising often would mean that your flatting range ends up too weak/capped, then that will limit your scope for raising.
You could have a raising range in that spot, because you've got KJ, TT, AQ, QT in your range, and you can balance with some Jx. You also don't want to do too much calling down when OOP, as it doesn't maximise value of your strongest hands, and obviously you can't bluff by pressing CALL.
I have some combos of JJ/TT in that spot, but I don't have 55, so I can raise some of the sets and JTs, and balance with combo draws like AQss. If your range is different, then you might not want to raise anything. I'll re-iterate that it depends how often villain is c-betting and the size he chooses (and the size you choose if you raise).
Tbh, I think you can build a raising range on almost every flop if your pre-flop range is "good". Just be less likely to raise on the boards where villain has a huge range/nut advantage and a high continuance frequency, because then you'll typically be bloating the pot with the worst of it.

FWIW, the kind of flops I'd be least likely to check-raise OOP (e.g. BBvUTG) would be things like AK2r, and IP (e.g. BTN v UTG) I'd be unlikely to raise stuff like A63r, K66, 833 etc, because I just don't have any very strong hands or strong draws in those spots. Raising would make even less sense if the c-bet is large.

You are literally posting in the section of this website dedicated to discussion of theory?

GTO = Game THEORY Optimal

Edit: sorry to answer the OP I agree with Arty, Broken, and Bob. You need to understand how ranges involved in the hand interact with the board and where the concentration of nut or future nut combos lie. Your opponent's sizing should help you read his hand better (depending on your opponent's skill and understanding of the same range interactions) and your sizing will be determined by the nut combos in your range and how often you can bluff.

There are two sections to theory. GTO and exploitative. This player made his post sound like a general theory question but it was purely a GTO question.. It's not complicated mate.

Here's how I think about range advantage and how to construct my ranges;

It's not enough to just say "we have a range advantage" or "villain has a range advantage". We should try to identify range advantageS (I think there are TWO distinct range advantages and they mean different things to our strategy)
We can have the nut advantage; we have the nuts in our range or more nutted hands that we will be happy to get stacks in with
We can have frequent strength advantage/less air; sometimes we just have less air and more "somethings" than villain, this is a different type of range advantage.

Simply having a range advantage does not in and of itself mean that we have the most incentive to aggress. If we have a lot of somethings and maybe even the least capped range because we happen to have the only 3 combos of the nuts that either player (in a heads up pot) could have, we still may not want to have an agro range because we might have a very high concentration of medium strength hands and very few extremely strong hands and bluffs. If we have the more merged range and a low concentration of nutted value hands then our opponent may still have more incentive to aggress if he has a more polarized range with less bluff catchers and more air/draws (bluffs) and very strong hands that can bet for value and be called by worse hands.

So its not clear to me that we can just use a cookie cutter "I have range advantage so I am going to be aggressive in this spot" approach.

But here are some rules of thumb I find useful;

1) The more often villain c-bets or bets against our non-procedural checks the more we should just check to him regardless of range distributions.
2) The more aggressively the villain barrles turns the less incentive we have to do anything but call flop
3) the more often villain triples the more we ought to be thinking "call flop, call turn, check river"

Vs good players and/or vs unknowns in tough fields;

the more nutted value advantage we have the more we should consider being aggressive on the flop if we are DEEPER

Frequent strength advantage and lack of air in range is the dominant force in assigning aggressive incentive if the SPR is low and we are playing more shallow

The more polarized our range is the more we should consider having some agro ranges and the bigger our bets/raises should be

The more mid strength/merged our range is compared to villain's the less incentive we have to bet and raise.

Again, just basic rules of thumb. I didn't read all the other responses but I don't hear many people talk about these specific ideas so I thought it would be the best contribution I could personaly bring to the table.

I hope it's helpful;

L8rs,

Navonod