YEAH YOU ARE RIGHT
Mate with Bishop and Knight?

It's still 18 moves to go at the end of the sequence you show.
Firstly its not my sequence or analysis but that of Fine, Muller and Lamprecht. Secondly you need to look at both game examples (post 13 above) to understand what's going on. Both games start at the same material position except in the first game example it is Black to move, therefore a couple of intermediate Bishop moves are required to arrive back at the position with white to move! These intermediate moves are shown in the first example, I thought that was made clear in the game analysis "Black to move 1...Ke8 2.Be6 Kf8 3.Bd7 Kg8 4.Bf5 Kf8 White to move".
The second game example then demonstrates the mate in 18!
It's still 18 moves to go at the end of the sequence you show.
Firstly its not my sequence or analysis but that of Fine, Muller and Lamprecht. Secondly you need to look at both game examples (posts 13 & 14 above) to understand what's going on. Both games start at the same material position except in the first game example it is Black to move, therefore a couple of intermediate Bishop moves are required to arrive back at the position with white to move! These intermediate moves are shown in the first example, I thought that was made clear in the game analysis "Black to move 1...Ke8 2.Be6 Kf8 3.Bd7 Kg8 4.Bf5 Kf8 White to move".
The second game example (see post 14 above) then demonstrates the mate in 18!
I realise it's M&L. I'm not blaming you for it.
What I'm saying is, if it's Black to move and he plays Ke8 (he should play Kg8) you don't want to arrive back at the same position with White to move because then you've gone in the wrong direction. You want to carry on to to the mating corner instead. It could make the difference between a win and a draw under the 50 move rule.

That is very different to your first comment of "being well inaccurate" and "still needing 18 moves to checkmate". Clearly you haven't fully grasped what was being presented by M&L. The salient part of the analysis being a lead in to the second part which starts off by demonstrating how White prevents Black from playing Kg8 and reaching the 'safe corner' which is a key part of the KBN vs K checkmate.

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King + Bishop + Knight versus lone King forced checkmate endgame, its the subject of this thread!!

Here's a link to a class presented by GM Varuzhan Akobian at the St. Louis Chess Club which shows an easy to learn method of accomplishing this mate. You could almost call it "child's play" as a lot of the audience was very young! I very recently had a chance to employ it in a game against Chess.com's Beth Harmon bot at its highest level. I was so glad I knew it as I had no problem completing the checkmate within 50 moves and can now say I've got a win against "her" at her best!
https://www.youtube.com/watch?v=7OGAiz5p_L4&t=1122s
Gordon
nice video, thanks
That is very different to your first comment of "being well inaccurate" and "still needing 18 moves to checkmate". Clearly you haven't fully grasped what was being presented by M&L. The salient part of the analysis being a lead in to the second part which starts off by demonstrating how White prevents Black from playing Kg8 and reaching the 'safe corner' which is a key part of the KBN vs K checkmate.
I'd say dropping six moves right at the start of pushing the king from a wrong corner to a right corner is well inaccurate and yes, after you've pushed the king in the wrong direction it needs another 18 moves to mate (so the whole procedure was a waste of moves). I don't see that I'm saying anything at all different. The point is the Black to move part of the analysis shouldn't lead into the White to play part if Black plays his king to e8. I've got the book and been through that section. I don't think I misunderstood anything.
Note that in their phase 1 in the variation I've marked "Var B" the black king is also driven to the wrong corner. The variation I've inserted played against SF would mate 8 moves faster.
Edit: I've changed the number of moves dropped in the first sequence from three to six. Three was a combination of my inaccurate play and my inaccurate arithmetic. (See edit to #20.)

I see your point. On the one hand M&L advise the lone Black King to "...head for the corner opposite to the Bishops colour" (Kg8) and then in the Black to move analysis they do the opposite with the move Ke8. The reason for this is M&L are teaching a method and to keep things simple are using a well documented and easy to remember start position where they need to get back to the initial move of white to move Bf5-h7.

There is no point in comparing tablebase output with M&L's analysis because M&L are teaching a method.
I see your point. On the one hand M&L advise the lone Black King to "...head for the corner opposite to the Bishops colour" (Kg8) and then in the Black to move analysis they do the opposite with the move Ke8. The reason for this is M&L are teaching a method and to keep things simple are using a well documented and easy to remember start position where they need to get back to the initial move of white to move Bf5-h7.
Exactly, but it would have been easier to show the position as a Black to play position with the king in the corner and say if it's White to play he just wastes a move (as Fine does). I see that they want to repeat the procedure on the second half of the rank, but that itself loses one move (see edit at move 9 below) and there's not much point in learning these things by rote anyway, because Black can mostly refuse to go in the wrong corner in the first place so that leaves you on your own.

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King + Bishop + Knight versus lone King forced checkmate endgame, its the subject of this thread!!
YEAH I SAW IT IN THAT VIDEO

I think if M&L used the same starting position as Fine there may be a copyright issue.
Fair point, and the downside of playing these endgames out against a chess engines and/or tablebases is that they will always take the path of most resistance which a human opponent may not. Although whether a lone King heads for the right or wrong corner I'd expect a well co-ordinated KBN to be able to checkmate without issue once the method has been digested.

I think if M&L used the same starting position as Fine there may be a copyright issue.
Fair point, and the downside of playing these endgames out against a chess engines and/or tablebases is that they will always take the path of most resistance which a human opponent may not. Although whether a lone King heads for the right or wrong corner I'd expect a well co-ordinated KBN to be able to checkmate without issue once the method has been digested.
WHAT??
I think if M&L used the same starting position as Fine there may be a copyright issue.
Fair point, and the downside of playing these endgames out against a chess engines and/or tablebases is that they will always take the path of most resistance which a human opponent may not. Although whether a lone King heads for the right or wrong corner I'd expect a well co-ordinated KBN to be able to checkmate without issue once the method has been digested.
Well Philidor used it first and I can't see him objecting.
About 85% of the time from I think over 90% of positions a tablebase with the lone king will finish up in the wrong corner. That's why many people think if they've learned the "W manoeuvre" they've learned how to play the endgame. The answer for a human player with the lone king is to stay out of it if possible.
If you can trap the king behind a seven square diagonal of the bishop's colour it's usually quickest to do that. E.g. on your move 4 instead of moving the knight:
Similarly after his blunder on move 11 you have him trapped behind the other seven square diagonal, but you let him out again on move 16. You should have continued towards the h1 corner.