I would define pure bluffing as 2betting and 3betting a bottom 20% hand pre-flop, and betting a hand on the flop or turn where you have no pair and no backdoor draws. Essentially anything that people wouldn't regard as semi-bluffing.

I understand that there can be some occasional post-flop spots where we can bet 100% of our hands profitably on boards where our range does well, but if we average out over all boards, is pure bluffing a thing that solvers do before the river?

In solverland you can see BB 3betting a hand like J8o and you see airball type bluffs on all kinds of postflop spots.
In real life there are definitely spots where bluffing random air is profitable, more than in GTO

in addition some boards are cbet 100% of the time, so of course some of that must contain pure air

Yeah, I mentioned that in the OP.

Yes you did! I missed it

Do you think it is bad poker if we have a policy of never pure bluffing except on the river? I guess it can't cost us much EV right, and it simplifies our strategy.

Generally it is -ev. But there are some exceptions, such as barreling flush completing turns with 0 equity hands or turns that allow IP to polarize very effectively (such as K72T). But if you play with the rule of "don't bluff if you don't have any outs" you're not making a huge mistake.

You can't really call any preflop hand a pure bluff as even the worst preflop bluffs have about as much equity as a gutshot on the flop.

Quite terrible tbh, whenever someone is overfolding MDF, pure bluffing is profitable and probably the best line, unless there's some more severe overfold down the line by checking.
Most ABC players play like what you're proposing, they only bluff draws on earlier streets, and therefor their ranges are crystal clear to anyone using their brain.

Isn't bluffing just a concept we have created after all? We could just as easily say that bluffing doesn't really exist and every bet on the river for example is an attempt at a value bet, but sometimes we mess up and value bet Ten high and get called by a better hand whenever we are called. Therefore betting Ten high was a mistake by us and we overvalued our hand.

You can say that the propensity to make this 'mistake' means that we are more likely to be called by our opponent when we have a great hand so it is good for the metagame, but betting the Ten high could be viewed as a mistake in isolation as it is an incorrect value bet and we could have decreased our losses with this combo by not betting it on the end.

phew...
man i was getting irritated by u but now that it's clear ur a 10/10 troll i kinda like u

That is not fair dude, you obviously don't understand that it is a reframing of what is going on, but it doesn't make it inaccurate.

It is the same when people say someone 'doesn't bluff', but I think what they really mean is that they value bet the river depolarised, but even with that information, you still have to call and pay them off when you hold good hands yourself because when you call you are still hoping that you are calling for 'value'.

Perhaps we just think about poker in different ways, but that is totally cool and it is interesting to get other people's perspective on things.

Value betting10 high is an interesting concept.

To me, there's a very clear difference between betting thin value via a linear range, and bluffing.

I think a lot of this confusion can be resolved if you start thinking in terms of ranges rather than individual hands. If their range is top-down linear value that's different than if their range is nuts/air. They call for completely different defenses. "Depolarized" means they don't have air or super nutted hands, but rather mostly middling hands, AKA condensed.

I think trying to classify hands as bluffs or value (on any streets, even the river, but especially the streets before the river) is very limiting and can lead you to miss the bigger picture.

For the most part sure, but I think its fair to call a flop/turn pure bluff as hand with <1% equity vs. top pair (or a super low equity hand-class)

And to answer OP question, there are almost never absolute rules in poker, and a lot of times it makes sense to triple a low equity hand on runouts to make sure you have bluffs on runouts where draws come in

You can label anything with anything it doesn't mean it's going to be a useful classification. In this case I think it's strictly harmful thinking. If I was teaching someone who's never heard of poker how to play GTO as efficiently
as possible I'd never mention the words bluff or value.

How would you classify 65 on AKQ flop?

A hand that performs well by betting due to a preflop range asymmetry

But what if we defended the BB vs a BTN open?

I can't really agree with that statement. I think on the river, we can classify most hands as bluffs or value bets. Bluffs being hands we bet because they should fold out plenty of better hands, and value bets because they should get called by plenty of worse hands. I think it is a little more helpful to me to think of bluffs and value bets as being on a spectrum, and at one end of the spectrum, hands get all their value by the portion of villain's range which gets folded, and at the other extreme, the hands that get most value by getting raised. Then there are the in-between situations such as hands that get their value mainly through the part of villain's range which calls, and those hands, particularly on earlier streets, will also get part of their value from the equity that other parts of villain's range gives up by folding. Then there are the hands that mainly get value through the equity villain folds out, but will also get part of their value through the equity they have against the parts of villain's range which calls.

Whether or not you think bluff and value are valid concepts, as humans we tend to need simplifications to understand complex situations. I'd be pretty surprised if you were able to simplify things in an easier to understand and apply manner than bluffs and value bets, but maybe I'm wrong.

We bet if our hand performs well as a bet, we check if it performs well as a check, and we raise if it performs well as a raise in the context of our range vs opponents range.

Hands that want to bet in order to get folds, or bluffs, are a product of this and not because we need bluffs. There are many spots where we bet our entire range on the river, many spots where we don't bluff anything (ie we bet/raise but never bet/raise a hand with no equity when called), and many spots where we bet a hand that gets called by worse and also gets better to fold, what do you call that?

And I'm talking about rivers only, before the river it makes even less sense.

merge

So what are the reasons we would want to merge a hand?

make better fold and worse call