Why is the analysis board sometimes an authoritarian cheapskate?

This is from 2014 but is a good starting point : lichess.org/blog/U4sjakQAAEAAhH9d/how-training-puzzles-are-generated

I don't see why single blunders wouldn't make for good puzzles. Ridiculous hangings are trivial puzzles (puzzle rank 1100 elo) because everyone will solve them, but nothing is wrong about this. And more complicated blunders make for more difficult puzzles.

Alright alright since I was beaten to provide the first link, here is another complementary one : lichess.org/qa/773/all-about-puzzles-questions-and-answers

I read about it once, and without reading to check, here is my take on things.

(1) Suppose in a position analysis at depth 1,2,3,..,n (where n is quite small) shows the best move to be xxxx and roughly equal to "no improvement in position", but at depth n+1 shows another move yyyy has significant value, then that move is presumably not obvious (or it would have been seen at lower depth).

(2) Now let's also suppose that if you do not play the key move yyyy immediately, then there is also "no improvement in position", i.e. the opponent can defend the threat if given a chance. (At depth n+2 any move but yyyy also shows no significant improvement.)

Positions which satisfy these conditions are candidates for puzzles.
Find the not-so-obvious move which requires depth n+1 to be seen,
and also you cannot simply delay things with a intermediate move.

@Sidonia-ChessEngine

@farmersrice

Thanks. So it uses centipawn changes and radical advantage graph shifts, which are usually the same as blunders. Often the puzzles feel as if their stopping points are arbitrary, or as if the material gain was strategically not the best move sequence; now I see why.

@lecw

Your links lead back to the same thread as farmersrice's linked thread.

"Ridiculous hangings are trivial puzzles (puzzle rank 1100 elo) because everyone will solve them, but nothing is wrong about this."

Well that is the point, isn't it? If "everyone will solve them" then, in technical terms, they suck as puzzles. I think a program could use double blunders, one by each player in immediate succession. In games, the best natural puzzles are those where a substantial material gain was available but missed by a good player; that filters out the sucky puzzle variety. There would be two blunders, the initial allowing of the material gain opportunity, then the missing of the opportunity. I'm trying to think of a way to filter out successive blunders that are unrelated.