Mate with 2 Bishops (not same colour) vs Knight

[mistermac]

I got a freebie program recently which one can enter positions.

In general, it succeeds in accomplishing mate in about 40 moves. I have tried to work out the theory. I cannot.

The program seems to do it by analysis only. Its plan is not at all obvious.

Any ideas on the theory of such endings?

[mistermac]

A sample of the above.

Numbers represent empty squares.
Each line represents a row.
Capitals are white pieces
Non capitals are black pieces

8
8
8
3n1BBK
3k
8
8
8

which conventionally is

White: Bishops on f5 and g5, King on h5
Black: Knight on d5, King on d4

1 Bf5g6 Nd5b6
2 Bg5f6+ Kd4c4
3 Kh5g4 Kb6d7
4 Bf6g7 Nd7b8
5 Bg6f7+ Kc4d3
6 Kg4f3 Nb8a6
7 Bf7g6+ Kd3c4
8 Kf3e3 Kc4d5
9 Bg6f7+ Kd5d6
10 Ke3d4 Na6b8
11 Bg7f8+ Kd6d7
12 Kd4d5 Nb8a6
13 Bf7e6+ Kd7c7
14 Bf8e7 Na6b8
15 Be6f5 Nb8d7
16 Be7d6+ Kc7d8
17 Bd6b4 Kd7b6+
18 Kd5c5 Nb6d7+
19 Kc5d6 Nd7f8
20 Bf5g4 Kd8e8
21 Bg4h5+ Ke8d8
22 Bb4d2 Kd8c8
23 Bh5g4+ Kc8b7
24 Bg4f5 Kb7b6
25 Bd2h6 Kb6b7
26 Bf5e4+ Kb7b6
27 Bh6xf8
Black goes home<br><br>Post edited by: mistermac, at: 2007/07/14 09:35

[mistermac]

Further to this.

It is evident that White cannot afford to lose a Bishop.

White (the stronger) wins, if at all, by taking the Knight and then mating with the two Bishops.

Black draws (if not by the 50 move rule) by forking King and a Bishop with the Kt. White, if he is in a forkable position, must watch that the Kt cannot land on a forking square. The tricky fellow can do this sometimes by attacking the other bishop, which has to move away, and then(!) forking the other Bishop and King. Even worse, there was a position in my latest efforts at the theory where the King was checked from a non forking square, and then the knight was able to perform the maneouvre mentioned in the previous sentence.

The danger for Black lies in pins and skewers of Kt and King.

White must force the Black king from the centre to the side of the board to trap the knight, who eventually may be forced away from the king's defensive arms and caught at the edge of the board by one Bishop blocking escape squares and the Bishop or king coming in for the coup de grace.

All this is very tricky, but I am determined to learn this quite useless mate (because how it could arise is hardly feasible, all pawns and other pieces having to be off) as an exercise.<br><br>Post edited by: mistermac, at: 2007/07/27 11:42

[mistermac]

I am surprised that not anybody has a word to say about this subject. Is it too hard? Or is the theory useless?

I must say it is difficult, and I have not developed a method, but I think the analysis is the problem.

With King, Bishop and Knight versus lone King, the theory is not easy, but the method is describable, and once the King has been driven to the side of the board, a few short variations can describe the final mating process.

So, is K,B,B vs K,N too hard for you all, even the top experts?

[thechesscorner]

well I have to admit that I rarely came accross that type of position whether OTB or on the net...


I guess top players assume that eventually they or their opponent would have resigned by now...

And there is also the small matter of the 50 moves rules....

I have to admit I never spent time tryiong to over analyse this type of scenario ( my bad )

:sick:

[mistermac]

I have never seen it in real play.

All majors and pawns off and only minors on is not a very realistic scenario.

The constant threat of knight forks keeps the weaker side in the game.

But my chess program wins usually by a series of zugswangs incorporating two or three waiting moves which give the stronger side a chance of forcing the opponent to take his king away from the centre, and then to have the king unable to stave off the bishops from hemming in the knight.

But, I still do not have the theory off.

[ChessTeacher]

The program probably uses Nalimov Endgame Tablebases.

You can also enter this kind of positions using the applet at http://www.k4it.de/index.php?topic=egtb&lang=en

With the help of this applet all of the currently published Nalimov Tablebases can be queried online (incl. 6-men databases).

[mistermac]

Thank you very much indeed. I am very grateful.

Do you know if this applet is reliable to give best play for both sides?

Some of the positions I feed in have over 70 moves as the answer to how long to mate.

I feel that if I learnt the technique needed to win in such an improbable situation, I would learn a lot about Bishops and Knights, and how the King cooperates on each side.

You see, the general rule that I was taught for assessing a position was that all other things being equal, that to win, a minor piece advantage without pawns on the board is a draw. Not so in my scenario.<br><br>Post edited by: mistermac, at: 2007/09/03 03:58

[ChessTeacher]

mistermac wrote:

Thank you very much indeed. I am very grateful.

Do you know if this applet is reliable to give best play for both sides?

Some of the positions I feed in have over 70 moves as the answer to how long to mate.

......

Yes,

Tablebases are generated backwards, starting from the checkmated position. In addition to the outcome they contain the number of moves it takes (if it is not a draw).

A nice article describing the longest shortest mate known (262 moves) is Play Chess with God (written by Tim Krabbe) and can be found at http://http://www.xs4all.nl/~timkr/chess2/diary_3.htm

[subasis]

I don't think it makes it by analysis. It should have some algorythms behind. The endgame was considered a draw, before computers became strong (there is even a study by Troitsky on the theme). About 19 years ago I received a chess computing bulletin in England. The article about your theme was replete with new concepts and formulae, a whole theory. It seems that the win requires a perfect play (most moves, if not all, are unique). I wanted to decipher it, but I couldn't (please note that I have a math degree and worked as system analyst). Given time, one can of course learn the procedure, but I don't think it's worth that time. It's a lot more difficult than 2N against (blocked) enemy pawn, which occures once in a lifetime.