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I think it depends on the makeup of the ranges and how they interact.
See, I don't think it depends on this at all. If we somehow happen to arrive at the river with perfectly symmetrical ranges the solution might look one way and if we have a massive range vs range advantage the solution might look another way, but the method for determining which hands we can bet for value remains the same as far as I can tell.
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In the pure (bluffcatchers) vs (nuts + bluffs) scenario, yes you're right. However, having a range that is only (bluffcatchers) is clearly not part of a gto solution.
I'm not sure what you're getting at here. In such a situation determining our value range becomes trivial and not worth discussing since those hands win at showdown 100% of the time. But I think that it's pretty clear that if we have hands in our range that will win at showdown 90% of the time we should be betting those for value also. Same with hands that will win 80% of the time, and so on. There is a threshold at which point betting the hand in question moves from a value bet into spew. Our task is to determine which hands can be bet for value. Including hands that are spew is incorrect. I hate to keep harping on this concept but I feel that it's extremely important and I am honestly shocked that we can't all agree on this small point.
As for our opponent having a range that is only (bluffcatchers), I never said that that has to be the case. However, when we are in position on the river and our opponent checks to us, that opponent should have MOSTLY folds and bluffcatchers -- some slightly stronger than others. The best bluff catchers might be able to beat some of our worst value bets, but mostly they will lose when we value bet. They will also have some checkraises -- some for value, and some as bluffs. These checkraises and the bluffcatchers together make up our opponent's "continuing range". When determining whether or not our hand should be included in our betting range as a value bet, we compare how it is doing against our opponent's continuing range (which, by definition, takes our opponent's checkraises into account). If it's strong enough we bet for value.
All of the excerpt that you cut-and-pasted regarding river play basically makes the same point as thesilverbail makes here:
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You might have some candidates for a value bet, and you try to figure out an appropriate number of bluffs, but then you realize you don’t have enough bluffs (i.e. some hands you are looking to bluff with actually have >EV by checking), this means villain can fold a wider range than you were thinking which means you might have to pare back your value bets, rinse and repeat.
This is an interesting point and it's something that I have not thought about very much, but I don't see any flaws with this in theory.
I would say that if we are in a situation where we don't have enough bluffs on the river that might mean that we have played a previous street suboptimally. For example, we might semi-bluff certain types of hands on a previous street -- say, flush draws. In that example, if the flush card comes in on the river then we have no river bluffs. This is probably an indication that how we constructed our bluffing range on that previous street was unbalanced.
The other possibility where I could legitimately see this happening is on extremely narrow range situations -- in those spots there are just only so many total combos to go around. So then if the board runs out a certain way (somewhat rare) we just might not have any bluffs on the river.
In these cases, assuming both players actually played well up until the river, it's an interesting concept that we might actually have to value bet less often so that our opponent cannot just auto-fold his whole range. However, notice that we have still not yet come up with any legitimate situation where it is correct to ADD MORE value bets to our betting range. That's because the very next hand that we try to value bet is spew. It just is.
Determine our value bets by comparing how the hand is doing against our opponent's range. THEN add bluffs. Come on guys, work with me here . . .