Hardest mate in 2!!!

It mate in 2!

Not so long ago the chess.com engines (Komodo and StockFish) had trouble with the first move but the current versions quickly give the right answer: Mate-in-2.

I am very suspicious of the engine software which often appears hesitant on finding the correct first move while having no trouble with the remainder after feeding it move 1. That does not depend on the duration of the solution. The same thing happens to a #2, #4, #6 or #12. Perhaps it does not apply to the latest installments of the engine software - I haven't seen any hickups with it yet!

Stockfish says it's mate in 3.

Martin (me) says it's mate in 2.

It's a vey pretty puzzle.

@SubMinhPiChannelPls gives a partial solution above.

After White moves Qa8 Black can move only his queen or rook. White has a choice of Nc5# or Nd6#. Whichever black piece is moved the only piece that attacks the knight on one of these squares is pinned, ergo mate in 2. White chooses the mate according to which piece Black moves.

The analysis button is just wrong.

No, that was a few months ago. Now both chess.com versions of StockFish 16 and Komodo find the #2 immediately. It may however depend on your Internet client - according to Rocky if I recall well. I use Chrome.

So do I.

When I clicked the magnifying glass icon today it told me mate in 3.

(But if I give it to SF15.1 on my own machine it does find #2 immediately.)

If your Analysis board can't solve a M2 problem, it's most likely because you're using Chess.com's default depth setting for Stockfish, which is too low. Go to "Browser Analysis" settings and change the Maximum Depth to "99 unlimited" and SF will find the M2 instantly.

Not convinced.

I've often been struck by exactly the opposite.

As an example, consider the sequence of games I posted here.

These were played by SF14 against itself from the same same position (below) at different fixed think times ranging from 1 second to 37 minutes.

Apart from the 1 second per move example SF14 always responds to 1...Ka4 with 2.Ne4.

I thought it should be playing 2.Nd5, so when it was still doing it at 16 seconds per move I looked it up on Syzygy. 2.Ne4 is in fact the only move to win with the 50 move rule in effect. SF14 nevertheless cocked up every single game in subsequent play. (I also beat it comfortably within the 50 move rule as White with my duff first move at 40 moves in 2 hours repeating.)

I've seen SF do similar things from a fair number of other positions.

Interesting to speculate how its algorithm can come up with the unique (and unintuitive) winning move when it does't actually know where it's going.

Mieeeeeee

Since I have no local SF versions I can only verify results with the current SF16 versions. It's weird that it would produce different results on your machinery from mine since I have no particularly powerful computer and it's 9 years old. The irreproducibility of results in itself makes one suspicious of the consistency and quality of the SF software (on chess.com)

Now we are talking about problems that ought to be easily within SF's short term horizon. Obviously things get more complicated for the harder and longer challenges (like your last diagram). For instance I wouldn't know whether or not SF would include some randomization in ranking the candidates when the solution obviously runs circles around the planet. That could account for different results at different times or in different machines. But not in a twomover!

Btw I know a great solution to your last diagram if you move Nf6 to d2 - and SF will never find it

Is the mate in 3 error by stockfish because of a certain number of lines it checks? (Not so much a depth issue but a number of paths problem?)

I can imagine stockfish first looks for moves that give a check, and since there are quite a couple M3s that start with a check I can imagine it not looking for regular moves altogether and therefore never finding the M2

StockFish evaluation are not final. What you see is always an 'underway'state. So when SF says it's +M3, it will continue chewing and come up with +M2 in the end though it may take a long while. Much longer than one would expect for such a simple problem.

It's a good lesson to learn about engines. When you wait long enough the moves and the scores may change and there is no way to know if they do.

Btw, it's quite possible that SF stops when it has evaluated all relevant moves though it will not tell you. The pitfall is in the word relevant. Like when you let the analysis display 5 lines you are not just demanding 1 solution line but also the next 4 best moves. Possibly the number 4 move will checkmate in 568 moves so SF may continue to plow for a long, long time. Reducing the number of lines to 1 will likely speed up finding the primary checkmate variation but of course then you won't see the successful alternatives - if they exist!

Interesting! Thanks for the insight!

Possibly @Rocky64's comment here. I only get #3 with the default setting.

Why use the default setting? I am never at ease with any piece of apparatus until I changed all the defaults. Based on the observation that setting factory defaults is classified as unskilled labour

Another thing I've seen happening is that when chess.com upgrades its engines the user setting continues to point to the old engine version, though it's probably no longer available. You need to reselect a current version to be sure what your analysis is running on.

I don't actually use the chess.com analysis much. I use versions of the programs on my own PC. Much more scope for changing defaults and they don't change when you're not looking.

Beaten by good ol' Charlie Brown - for once

Intriguing. Can you post it?

According to Nalimov it's mate in 87 so I think you're certainly right about SF never finding it. I think it will be some time before you see SF announcing any mate in 87. Neither can SF15.1 win it against a tablebase (I don't have SF16). This is it against Nalimov (attached to Rybka) up to the point it blunders into a basic rules draw.

It's illegal! Though one can have a legal debate about whether or not that counts as a solution

Ahh! Very clever.

Totally missed it - suspected you'd meant to say d4 or d6.

I think it counts as a solution.

As an irrelevant aside, the SF15.1 v Nalimov game I posted in #37 may be a nice illustration on the minimax pathology I was talking about in the link from which I got the position. This is an unexpected phenomenon whereby an engine using a minimax (or alpha-beta pruning) search can play worse if you give it more time to think.

I set my time controls down from their usual 40 moves in two hours repeating in that game to 40 moves in 15 minutes repeating to save time.

I subsequently tried reverting back to the longer controls to see if SF15.1 did any better.

This was the result.

after which Black can just push the pawn.

It not only didn't play better, I did the opposite of saving time.