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Proposing to expand puzzles’ possible types of scenario

To @dboing’s #10:

Surely I’m not in a hurry and can wait for you to parse and comprehend my text. /sincere

But maybe I can present the same ideas in some other format, more convenient for you? Add some visual illustrations?
@Hott said in #11:
>
well sure. it would give me also an idea of how I could deal with my own later. how can i help? so you don't work double?
i could have a first pass. and try to make an attempt at rephrasing or where I lose certainty of understanding. (sometimes there is that too, the scope assumed across the internet "distances", I mean chess is something in common, but the rest... or even chess experience... why I like discussions is that they allow the acknowledgment that words and sentences rarely are enough of things not yet sure to be common experience (and there is plenty of that around the more of us try to communicate). going philosophical again.. another abstraction crutch.... or tool. ok let be practical. how could i help you help me.... :)

or give it a whirl! anyway you think. Maybe it even helps you with your idea to have a second iteration.... (disculping myself from not yet having done the parsing effort... lol). disculping is not english says the browser. dang.
I’ve recently noticed that there are puzzles categorized as “Defensive move”. (A thing which I had not realised/remembered being relevant to the original idea.)
They could’ve been the puzzles of the scenario of surviving (see the post #6). But checking eight puzzles showed that each of them is still about taking advantage of an opponent’s blunder, thus they are not what I want. And by the way, this category is crowd-sourced—which means anyone can vote[1] on whether a puzzle belongs to this category—therefore “Defensive move” is a subjective motif; a motif that cannot be detected automatically by some algorithm—would it be the scenario of surviving, it couldn’t be voted upon[2], as such puzzles would be placed in this category automatically.

[1] You can see the voting buttons next to each category in the list shown when you solve (or fail) a puzzle.
[2] Such categories (for example, “Advantage”, “Crushing” and “Middlegame”) have a lock icon next to them instead of voting buttons.

The “Defensive move” category: lichess.org/training/defensiveMove
An official explanation of it: lichess.org/study/viiWlKjv/mbI3OkEB
I have collected some data by hand and placed it there: desmos.com/calculator/ffg60j6pi8. It’s clear from it that all or almost all puzzles are about taking advantage of an opponent’s mistake worth at least 3.5 points, plus after it you must be not worse than +2.5 points.

Those exact statements may be wrong, but the general idea is that it seems to me that puzzles pass through some filters which can be removed to allow inherently new types of puzzles.
Update: previous dataset discarded; 200 new random puzzles of “Healthy mix” analysed and plotted: www.desmos.com/calculator/y21zn7xdkd. Again, the exact constraints can easily be some different, but still, they seem to be present. I expect them to spread wider in upper-right, lower-left and lower-right directions otherwise.

I guess that there are three aspects present:
— you must be not too well before the opponent’s last move
— you must be well after the opponent’s last move
— the opponent’s last move must be a mistake

I’m going to also plot how “Advantage”, “Crushing”, “Equality”, “Defensive move” and “Quiet move” spread. It takes a lot of effort doing the work manually though; is there a way to automatize it somehow?
@Hott said in #1:
> As far as I guess, currently all puzzles are generated somewhat this way . . .

There used to be a Lichess blog post explaining how puzzles are generated. I assume it was removed due to being out of date after updates to the system.

A more recent post doesn't go as deeply into the details but does address some of the issues you raise so you don't have to guess as much: lichess.org/@/lichess/blog/new-puzzles-are-here/X-S6gRUA
I appreciate those experience trajectory plots. I was too lazy to do so myself, but kept accumulating puzzles that gave me pause.
There is one "theme" of puzzle observation, that you mentioned about the depth of success/failure of the accepted unique solution, in the sense that one having the skill set level to "solve" the puzzle that far (or shallow) might not be enough to also at success depth tie the then current position human assessment as being as spectacular as a puzzle (or SF blunder score) would have us seeking. SF puzzler might be sure of the positoin value, but even with my low skills that solved it, i find my experience with such puzzle unsatisfying. I would have liked to associate the dynamics I just experienced with the static features I could see at end of puzzles. Sorry if I buried stuff here. I skipped to my interpretation of the many unsatisfying endinds, hypothesis of mine.

The tactical solving bottleneck skill level not on par with the last solving position complexity of feature or static pattern perception. So, I would like to add that concern to possible off shoots of your exploration about how to extend the teaching power of the puzzle offerings. It does touch the use of SF as analytical tools, and its actual full position (at least maximal) information based leaf evaluations at depth. If SF only sees the gain at depths beyond our human horizon, and if the stopping solving position, we see does not contain our solving skill level clues, we are missing a component of the puzzle teaching experience (potential). Usually we all can count material. But then when that is not visible, it would be nice to find ways for us to test or learn about "reading" those clues (not have to dig through the hidden SF partial but deep enough search trees).
@Hott said in #14:
> I’ve recently noticed that there are puzzles categorized as “Defensive move”. (A thing which I had not realised/remembered being relevant to the original idea.)
> They could’ve been the puzzles of the scenario of surviving (see the post #6). But checking eight puzzles showed that each of them is still about taking advantage of an opponent’s blunder, thus they are not what I want.

You're right, they are defensive moves still in a winning position, e. g. avoiding perpetual check when you have a checkmate in sight.

On the contrary, I sometimes try "strongest" puzzles and some of them seem to be aimed at preserving equality. I'll post some example if it turns out to be the case.