Mates that are difficult for engines

Here's another "lose the move" mate that engines struggle with.

White to move and mate in 31:

White to move and mate in 26:

Strictly speaking a queen will win 86.7% of ply count 0 positions against a bishop (and strictly speaking the bishop will never be lone because he'll always have his king for company).

Unless the queen is already pinned or skewered, the Queen will always win.

The tablebase stats are even crazyer that you imagined! Most of the 13% failures consist of direct captures in the diagram. "Just grab them by the p...y" in the words of an elderly statesman (hahahahahahah).

Or if the pawn is too far advanced for the weaker side.

I meant vs a sole bishop.

But nevertheless completely accurate so long as it's restricted to positions with ply count 0 under the 50 move rule at the point a move is made under FIDE art. 4. Otherwise under competition rules the vast majority of positions are drawn.

It's the normal parlance of chess players that is really crazy.

Absolutely untrue, especially with regard to chess players! Mathematics is always the halfway point for providing useful information. You know all the things they say about statistics - which are very true! The point is that players looking for sensible endgame stats are completely uninterested in the mathematical stats but in the game positions. Games have a logical flow and - unless you play losing chess - are not about giving away your queens to opponents. Players always want to know the outcomes from a stable starting position as those are the ones they meet in their games and need answers to.

Btw, weather stats make the same error. It's always weather men talking to weather men and not to us. I will spare you the details but I guarantee that we are lied to every day on that front. They speak of the weather that is, but most of us are interested in the weather we experience. See the analogy with the endgame stats?

Have a mate in 20 that engines struggle with:

White to move and mate in 20.

objection: the bishop isnt royal so you cant mate it

Sort of my point. If it's a lone bishop against K+Q it's a dead position.

#167 so like this

Yes - neither side can checkmate by any series of legal moves.

yes

because its an illegal position 

so the moves cant even be legal

also, 32 bishops all of the same color, with their own king, generally lose to a single bishop of the opposite color with its own king; on a 8x8 board

thats probably the most grotesque general win in all of chess (no matter its way illegal)

The fact that it's an illegal position doesn't stop the moves being legal under the definition of legal move in FIDE art. 3. But it does make them illegitimate, because the game has terminated at some point before they're made.

Possibly more grotesque? (Also illegal of course, because you can't have 10 queens.)

Edit: Just noticed the word "general" in your post. (I usually respond to posts first and read them second.) I don't think there are any endgame classifications that are 100% winning, but I think K+32 light squared bishops+28 rooks v king+bishop is a win for the latter so long as it's not already stalemate or forced stalemate on the move and the latter's bishop is not en prise.

King+31 bishops on the same colour+0 to 31 knights mostly draw against a lone king, but maybe not often enough for you to regard it as a "general draw".

Edit of edit: Don't know what I was thinking about when I wrote, "I don't think there are any endgame classifications that are 100% winning". Obviously fatuous in this context. K+62 anything but pawns v lone king is obviously 100% winning.

@Marattigan: It's not about the lax interpretation of statistics but about the relevance of the statistics presented. Chess players will assume there is a significant danger to land in a draw with an 87% win percentage - which is completely untrue. It's mathematicians talking to mathematicians not to players. Much more useful would be to report a 99% win (don't know the exact number) for all realistic Q vs B endgames. Useful, not very hard to define and totally acceptable to chess players!

All non-zero move counters are absolutely irrelevant as the question is always asked - by the chess player not the mathematician - at the very first occurrence of the endgame. Obviously - when there is an intrinsic 50M draw risk involved - the whole scenario changes as 50-move lines are relevant for chess players as well. Not for Q vs B though.

A better variation of that puzzle would be to start the king on b7 so white has to make a waiting move before mate!

That's true! In fact, that waiting move is already uniquely available - no work to be done:

....Bf5xe6-f5xd7xc6#