Bishop, Knight & King versus King.

One move quicker is:

I bought Keres' book once, though it opted not to get off the train at the same stop as me a few days later.

I was put off Keres' explanation by the fact that he blundered with Black on move 2 and then failed to take advantage on move 3 with White.

Curiously I had occasion to get Batsford Chess endings recently and noticed they do exactly the same, and as far as I can remember (it was about 45 years ago I bought Keres) from the same starting position. (Not accusing anyone of copying you understand.)

This is not a small blunder. I tried playing the Nalimov EGTB  from the position after move 2 in BCE and finished in half the time the text takes. I think Keres might even have taken one move longer than BCE.

My Keres book has long gone too, but someone on this site explained it much better than Keres and now having looked at this forum I wouldn't be scared of encountering the ending!

@playerafar: In response to your post #118:

There is nothing wrong with your memory, but there is something wrong with my text editing. It was actually a post by Squod that stated the 10x10 idea and I copied too much of the post.

You ask if the mate is possible on a 10x10 board if the king is in the centre. I think the answer is not necessarily, (This is why I said the position I gave would be drawn if the king positions were interchanged. In that case I think the black king could reach a position in the centre where White could not avoid a draw by repetition - or 50/75 move rule if taken into account). But to allow a mate by White, the Black king need be neither at the edge nor close to the "right" corner. E.g.

White wins if the Black king is in the coloured area (White to play)

or red area (either side to play).

 (The area shown for the Black king above is by no means  exhaustive.)

When I said I would guess that mate would be possible within the 50 move rule on a 10x10 board I was, of course, referring only to positions where mate would be possible in the first place. Even so after looking at it a bit closer I would now say I guessed wrong and the longest mate would probably be nearer 60 moves than 50.

I will answer the remainder of you post shortly. This ties in with xman720's query on how to avoid ceding moves at the start of the endgame so I will make it a joint answer.  But the answer will necessarily be a little more comprehensive, so it will have to wait till I've moved house. 

Lol! - had to delete this comment - as it was WRONG -
unfortunately - this forum doesn't accommodate a complete delete.
Which much of V3 does.

Interesting post on a 10x10 board by MARattigan on post #147.

Hard enough to force the mate on an 8x8 board never mind 10x10😀

I guess the idea might be -
that how this works on a 10x10 might help with understanding the 8x8.
That doesn't mean it works out that way though.

The N+ B versus lone King endgame is one of the irksome little gremlins of chess.
And there are so many of them.
Its almost like - its about how much time one has to deal with it all.
And even if ALL of one's time is spare time - its not going to be enough time ... 

ok

Yes I see the point if it is illustrating an idea. I suppose they might change the 50 move rule for a 10x10 board and apart from 4 extra pawns you would have to have an extra piece to sit outside the rooks. A whole new game!

In Chinese chess - there's a "river" in the middle.
And if I remember correctly - once you've crossed it - you can't go back.
An interesting game.  
Maybe a thread could be started on it.

Interesting point.
Threads can be started - without being part of a Club.
In a way - each one of same - is a kind of Club.
And the original poster - is the admin.

I never was aware of any of this before - because I didn't use forums and threads and topics.
I was only in chatrooms ...

There are two main parts: pushing to the side then pushing to the corner. Both are easily mastered with practice.

But you have to let the King off the side.
I believe that that idea of forcing the King to the side of the board - misleads players.
And creates needless difficulty.

Much much better is Deletang's Triangles.
You confine the King to a triangular zone.
Fits very well with how a bishop moves.
Pushing to the side would make more sense with a rook.   But you haven't got a rook.
As for getting the target King out of the center - that's super-easy.

You just bring your King to the center.  You've got two extra pieces to move.
You can get him out of there - using zugzwang - and controlling squares next to him.
So he retreats from the center.  Its not necessary to force him to the edge.
He's coming off the edge anyway.

Its tricky, but of course possible.

I studied this combination for a week

The most difficult endgame is queen/king versus rook/king

There are two approaches for Part 1 (getting to the side) which may be the source of confusion, but general ideas are the same: use the bishop to gain/lose tempo, and the knight to cover the squares the bishop cannot. I don't use the triangles approach which requires more memory.

Forcing the King to the side is part of the confusion - even though that part is easy.
You have to let him off the side anyway.
That's where it gets tough if you're not using the Triangles approach.

As for "more memory" - its my experience that the other approach is harder to remember.
Maybe there's a middle ground between the two.  Haven't looked into that yet.

Interesting Grischuck didn't use the Deletang method.

I solved the endgame myself in a weekend. It's not difficult to solve and that way you remember it.

I don't use the solution any more though because it wasn't optimal. These days I try for mate in the least moves.

I haven't seen any books or videos on this endgame that are optimal. Neither Philidor's method nor Delétang's triangles are optimal as normally explained, and even if they're taken together they amount to a only a very partial solution.

I think you might be a long way off on that one, though I'd agree it's more difficult than KBNvK.

Have you tried this one, for instance? (It should finish with queen v rook.)

or this one, still with 4 pieces?

But they get harder with more pieces. You could try this.

But this is probably the most difficult.