Too difficult for computers

If you put it into the analysis tool on this site (indeed either of the two Stockfish options in the tool) at 20 ply it fails to see the mate, believing Nf5 to be the best move (this move may lead to a much slower mate). I have verified this more than once.

I believe the reason is that unassisted by a tablebase it is incorrectly believing the loss of a piece (leaving knight versus 2 pawns) has to leave no chance of a win and thus it fails to look at the moves after Bf6 gxf6. This is surprising, but the facts require explanation.

I wish I had screen-grabbed yesterday. Today it is solving it without difficulty when exactly the same thing is done. I can only assume there has been a change of configuration, hopefully inspired by this thread.

[I can be sure the right position was entered yesterday as after Bf6 was played on the board it was able to see the right mate in 2]

I still find this very surprising and I am kicking myself that I did not do a screen grab.

I'm wondering if the pruning algorithm may miss the mate in 3 because it finds a way to ultimately capture the 2 black pawns and win with the knight and bishop? It still should always find a mate in 3 first no matter what. Stockfish usually instantly finds a forced mate from between 12 and 15 moves depending on the day, sometimes after a minute or two.

It finds longer mates with two other moves. This is how I thought that it managed to convince itself not to devote any time to Bf6 gxf6 (which would be very poor reasoning, as Bf6 forces a single move and then there is another forcing move to give mate in 2 - very cheap analysis, especially to a computer!)

https://www.chess.com/forum/view/endgames/best-underpromotion-endgame-compilation

Interestingly, stockfish has no trouble with most of these even though they are more moves, I'm specifically curious about the one where the winning solution is 5 consecutive underpromotions to bishops.

Also about the previous puzzle, even if white misses it and plays Nf7+ first for example, stockfish gives a mate in 13 anyway: (Stockfish on my phone saw the mate in 3 instantly btw)

[48] m13 Ng5 h5 Ne6 h4 Bxg7 h3 Be5 Kh7 Kf6 Kh6 Ng7 h2 Bxh2 Kh7 Kf7 Kh6 Bf4+ Kh7 Ne6 Kh8 Bd2 Kh7 Nf8+ Kh8 Bc3#

d:49/26 6:Nd6 t:38.59 n:52524k nps:1361k h:54

Yes, there are many longer mates. You could also play around after the sacrifice with Kf7-f8-f7-f8, taunting the imaginary opponent.

Thanks for your input, I appreciate it. I have no idea why this particular chess problem stuck with me all these years! Again thanks for going over it, it opened a reason why I was so fascinated with it!? Now I can rest in peace could have been 56 years ago I came across it?

It is very odd that the analysis failed on Saturday - if someone else told me this, I would have difficulty believing them! And I recall that it found the longer mate with Nf5.

It is also surprising that it would behave differently - and less oddly - the very next day. Really kicking myself for not screengrabbing on Saturday,

Engines can't find the underpromotion.

This is beyond engine calculation horizon as well!

It supposedly takes the most recent version of stockfish several minutes at 500 kns to solve this one, and Leila couldn't solve it at all interestingly.

LeelaChess is not great at tactics. But it is great at practical chess despite this.

Stockfish can't seem to find the drawing idea here..forcing the 2nd black pawn onto the wrong color promotion square so it will be a drawn king and pawn endgame. And it's only 3 moves!

If it had a tablebase it would help. Otherwise the poor thing needs to analyse the KBP v K ending.

Are you sure about that? .

Actually Stockfish finds the drawing idea instantly, but it does not evaluate the position after 3...gxh6 as 0.00 as it should. But we know that Black cannot win, as all possible Black moves are equally evaluated.

My stockfish didn't even suggest bh6 at any point.

Without a tablebase or a very specific heuristic, this takes a lot of analysis to evaluate to a definite draw. Engines cannot abstract at all - they need to analyse attempts to advance the pawns with the pieces everywhere they could be, to be sure.

I knew that almost all versions of Stockfish that I have could solve this one, so just for fun I tried out Stockfish 1.6.3 from 2010 and in 2 seconds it shows the correct score: