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Puzzles: sometimes (rarelyBTW) the line in reply to solution's first move isn't the most challenging

Example: lichess.org/training/xw5bg . After 11. ...Bxe5 the site delivers the solution 12.Bxe5 Bxc4 . Indeed it is fine, but... the line I would subject my students to if I were an instructor is not "what after 12.Bxe5" (12. ...Bxc4), instead "what after 12.Bxe6" (12. ...Bxf4). I don't know if it's something related to puzzles' auto-generation process. Both are "bishop takes bishop, bishop takes bishop" but to me 12.Bxe6 is a little bit more challenging for the solver (even to see from the start).

Santé !!

S. P. A.
en.wikipedia.org/wiki/Pale_ale#Strong_pale_ale
Sometimes the real hard work was calculating a 4-move forced mate, so the engine just gives the Queen or something similar.
This has happened to me quite a few more times than once. I mainly do mates in 4...and I'll see a move that seems fairly straightforward, except for one line (let's call it Line X). But I don't see anything else, so I play my move (hoping that I'll be able to spot the right continuation against Line X, now that it's become a mate in 3)...but instead the machine just falls into one of the straightforward mates.

Presumably it's because to SF a loss is a loss...since it's a solved problem, all lines are equivalent to it.
yep the puzzler is not human. but was programmed by some to always do the same thing it was programmed for, that thing is what I would like for us to understand better, before relying on it so much. Not saying we should not use it, but knowing its conception limits without becoming developers ourselves, i.e., in some for that can be interpreted in chess land, might do that.

Also, no hiding its entrails behind a modesty veil, not to hurt our users delicate eyes, might help.

Another case of "AI" just doing the motions.? (always assume I am asking, in spite of the tone otherwise).
It is because the puzzle is generated and acted upon by an engine and not human. What we may think of as challenging may not be the case with engine. The replies computer make are best as per top engine.
Though, 12.Bxe6 Bxf4 is SF16's second best while 12.Bxe5 Bxc4 is fifth... (SF16 AVX2 16CPU depth 40 x 8 lines). If the process selects by "Only Reasonable Move" criteria, 12.Bxe6 Bxf4 ORM has even another one to follow (13.Qxf4 fe ORM).
I vote for a human transcription/mistyping oversight. Look how similar: "Bishop takes Bishop, Bishop takes Bishop..."
12.Bxe6 Bxf4
12.Bxe5 Bxc4
Or maybe the criteria is to select lines which best point out specific themes ("removing the defender" in this case).
no such themes are human subjective. Engine do not have any concept like that. Even if the source code might have words that would look like it did, the number crunching would make ground meat of such interpretation.
@MrPushwood said in #3:
> Presumably it's because to SF a loss is a loss...since it's a solved problem, all lines are equivalent to it.

Yes, that's the core issue in many of these lines. SF has no way to guess what would be the most challenging for a human.
Ok, "a loss is a loss" ...but why did the engine choose the fifth best line as the solution to deliver on the puzzle?
(-3.95 vs -3.48)
Was it a random choice?

rn3rk1/ppp2ppp/4b3/q3b3/2BP1B2/2P5/PP1Q1PPP/R4RK1 w - - 0 1

Analysis by Stockfish 16:

1. -+ (-3.48): 12.d5 Bxf4 13.Qxf4 Bc8
2. -+ (-3.81): 12.Bxe6 Bxf4 13.Qxf4 fxe6
3. -+ (-3.88): 12.b4 Qb6 13.Be2 Bxf4
4. -+ (-3.93): 12.Bd3 Bxf4 13.Qxf4 Nd7
5. -+ (-3.95): 12.Bxe5 Bxc4 13.Rfe1 f6
6. -+ (-3.98): 12.Bb3 Bxf4 13.Qxf4 c6
7. -+ (-4.13): 12.Be2 Bxf4 13.Qxf4 Nd7
8. -+ (-4.22): 12.dxe5 Bxc4 13.Rfe1 Nc6
#9 -- I have seen a five-move problem recently, where, on the third move, your opponent can play one of two winning lines with subtly different vibes, but that perfectly transpose, resulting in the exact same winning position. It is frustrating, but the automation of generating the puzzles isn't perfect, and in such cases they can pick the less challenging choice.

In your example case it would likely (if not transposing) be a different evaluation at whichever depth was used in puzzle generation and so the "best" defence was chosen there. But the underlying point stands.

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