The Bishop and Knight Mate

 

Note: I have a revised and upgraded edition of this article in pdf format. If you would like to receive it kindly write me at tenderdragon@optonline.net  

By Louis Lima

Special thanks to Brent Hefley mortadulo@hotmail.com for his insightful recommendations, and to my wife for helping me take care of our daughter while working on this piece during the evenings.

INTRODUCTION

The Bishop and Knight Mate is the most difficult of the so-called “elementary” mates and there is nothing elementary about them for a beginner player.  Some positions can take up to thirty five moves to realize, and some techniques laborious to learn for a beginner player. To top it all, this mate rarely surfaces in practical play.

So why learn it? It is my belief that mastering this mate can help increase our ability to coordinate pieces in general. Whether we are conducting an attack, maneuvering for defensive purposes, or simply developing our pieces in the opening -all these require the effective harmonization of our pieces. The Bishop and Knight Mate is one of the purest examples of piece harmony in chess. In order to succeed, the attacker’s King and minor pieces must work in perfect harmony or else the mate cannot be executed. According to official chess rules, the attacker has fifty moves to exact mate. This demands that the attacker be precise, understand the goal at hand, and be technically fluent. 

The Bishop and Knight Mate can be an effective tool in helping beginner students exercise and understand important chess concepts and techniques for other areas of the game. Some of these are:

• Coordination of the pieces

• Temporizing moves

• Zugzwang

• The opposition

• Centralization

• Stalemating

• Square and diagonal control 

• Natural abilities of the minor pieces

• Visualization

GOAL

Our goal is to mate in the same corner as the color of the bishop.

 

(The highlighted squares show alternative mating squares)

The above diagrams are examples of end positions we want to aim for, although it sometimes happens that the defender makes a gross error and gets caught while being driven to the right corner…

 

We must be alert all the way, especially in the last stages, as we do not want to stalemate our opponent…

 

CHALLENGES

The defending King can be quite unpredictable in his struggle. He may try to stay in the center until forced to move, or try heading to another edge once he has been confined to one.  Sometimes the defender is content to shuffle his King back and forth to any adjacent squares available, when the attacker must carefully reposition his pieces to take those squares away without letting him slip out to the center of the board. 

Sometimes the King runs to the corner that cannot be controlled by the attacker’s bishop, where we must learn the right technique for driving him over to the correct corner (the correct corner is one that matches the color of the attacker’s bishop. Light square for a light squared bishop, and dark for dark).

Sometimes the King seems to be heading for a corner, and in the way, changes his mind and heads somewhere else if allowed to. Anything to confuse the opponent will do. Even the actual playing position can be a challenge as some positions take longer to execute than others.

STRATEGY

• The attacker takes squares away from the defending King until it is driven to the edge of the board.

In the initial position the defender can choose to roam just about anywhere on the board. We can aim towards confining him to a group of squares. Once we achieve this, we proceed to confine him to an even smaller number of squares, until the King is incarcerated in the edge of the board, or in one of the corners.  

• We drive him to the appropriate corner.

Here we need to arm ourselves with some techniques to drive the King over to the correct corner, otherwise we run the risk of letting the King out of the wedge we’ve created, or worse, stalemate him.

• We checkmate.

This sounds obvious, but we can easily stalemate our opponent if careless. Sometimes the attacker needs to first reposition his pieces without letting the King out of the mating net, and then checkmate.

CONCEPTS AND TECHNIQUES

Introduction

This section outlines ten concepts and techniques related to this mate. Credit is given when possible, but it is difficult to accurately credit the original source because the ideas presented by one author are likely to have historical antecedents. For instance, David Hooper’s wonderful description of the cordon technique traces its roots to Daniel Deletang’s triangles. This triangle process was probably suggested in earlier analysis as well.  Thus, any new information by the reader will be appended to this article, and I will credit the contributor as well.

DELETANG’S TRIANGLES

This method was systematized by Daniel Deletang, a Frenchman living in Argentina in the 20’s. According to a blog in the “Kibitzer’s Corner”, Mr. Deletang was a chess amateur belonging to Club Argentino and in 1923 published his system of triangles. Guillermo Vassaux in his book “Iniciacion a la Estrategia”, suggests that although Mr.Deletang systematized this method, it was based on suggested past analysis.  

Well, he might have been a chess amateur, but as GM Andy Soltis once said “The best chess teachers are often just interested amateurs”. Deletang’s method is still one of the simplest to grasp.

To understand the nature of Deletang’s triangles, let’s first start with the following chess problem. You can try to solve it on your own before continue reading this article. There is no substitute for learning by doing.

Problem no.1

For each one of the diagrams below, place the White King, Bishop and Knight in such a way that the King cannot escape if it was giving an unlimited number of consecutive moves:

  

Black’s King on f3

The easiest piece to place here is the Bishop which takes the most squares when placed on the b1-h7 diagonal. Next, we need to place the King and Knight in such a way that they protect all the escaping darks squares in the a1-h8 diagonal the Black King could get to. One solution is placing the White King on g2, the Knight on c4, and the Bishop on c2:

In order to create an inescapable net all three pieces must be used to their maximum potential. The Bishop controls all seven squares in the b1-h7 diagonal. The Knight is so effectively placed here that it controls four escape squares! (The Knight indirectly controls c1). The King controls the three squares in front of him.

Another effective formation would be placing the Bishop on d3. The King cannot attack the Bishop because the Knight protects the dark squares around it. However, it is more effective to place the Bishop on either c2 or g6 so that it’s ready to set a smaller triangle by moving to d1 or h5 at the right moment.  

Black’s King on g2

Here the job is a lot of easier, and kudos if you discovered that the White’s King is not even necessary.

 

Black’s King on h1

Here it is White’s Knight which can be relieved of its duties, as the King and Bishop are enough to seal the King’s escape. Trapping the King with the Bishop and Knight is not so effective here as we would be stalemating Black’s King.

Based on the above example we can summarize Deletang’s technique here:

1. Pieces are aligned to confine the defending King inside the larger triangle (in this case the b1-h7-h1 triangle)

2. White’s King takes the role of driving Black’s King back, with the occasional help of his teammates.

3. The Bishop takes the lead and moves to the second diagonal (in this case, the d1-h5 diagonal.)

4. The King and Bishop help drive the defending King further back.

5. At some point the Knight repositions to a better square and complete the second triangle. 

6. With the Bishop and Knight in its proper positions, we can now begin to use our King to push the defending King to the last triangle.

7. As with the previous transition, the Bishop will move in to the last triangle (f1 or h3 in this case) 

8. Once the last triangle has been secured, the pieces are carefully repositioned to deliver mate.

We will be looking at some concrete examples in a moment. For now, let us continue exploring other concepts and techniques, as they can come in handy when using Deleteng’s method. 

CORDONS

David Hooper’s (A Pocket Guide to Chess Endgames) talks about setting up “cordons” around the defending the King. His description and examples are identical to Deletang’s triangles, so he simply substituted the word triangles for cordons.

However, I think the idea of cordons can be rather useful here. Although a cordon does not completely seal the defending King, they take a large number of squares away. Effective cordons can be set up with the defending King just about anywhere on the chess board.

Let’s take a look at the following position:

Here White does not have a perfect triangle that seals the Black King. Theoretically speaking the Black King can travel to the Queenside via e8, but that is an awful lot of moves to make. Thus, from a practical perspective White really controls the entire Queenside and a portion of the Kingside as well.  Cordons are the second best thing after a Deletang triangle, and often times just as good from a practical perspective. Let’s see an example here.

1…Kf4

White’s Knight and Bishop cannot be touched by Black’s King, so they are most effective if they left there for the moment. Therefore, Black strives to limit White’s King, which is the only piece free to move without disturbing the triangle.

2.Ke6 Kg5 3.Kf7 Kh6 4.Bc2

There are several right moves here, but 4.Kc2 positions the Bishop to move to d1 at the right moment to set up Deleteng’s second triangle. Notice that we have yet to reach the first of Deleteng’s triangles, so 4.Bc2 is the beginning of the upgrade from the “cordon” to the “triangle”

4…Kg5 5.Nd2 Kh6 (or any legal King move) 6.Nc4 Kg5 7.Kg7

And we have reached the first of Deletang’s triangles.

Problem no. 2  - Exercise for Beginner Players

Place the King anywhere on the sixteen squares inside the center box. Then, place the White’s King, Bishop and Knight in such a way that they take the most possible squares away from Black’s  King. You can do this exercise several times to help you get a feel for how the three pieces work together to limit the mobility of the defending King.

 

ZUGZWANG AND TEMPORIZING MOVES

Problem no.3 - White to Move

 

To illustrate these concepts let’s return to the previous position after 7.Kg7 and imagine it is White to move instead.

White would like to make a move with the King which forces Black’s King further back, but at the moment this is not possible. Therefore we need to make a temporizing move that does not disturb the triangle. One possibility is 1.Bd3, but after 1…Kh5 2.Kf6 Kh6 we reach a position where technique is required to drive the King to the appropriate corner. Nothing wrong with that if you know how to coordinate the pieces to do so.

A more optional solution, and keeping in the spirit of the triangles, would be the temporizing move 1.Bg6. This forces our opponent into zugzwang, a term referring to when our opponent runs out of good moves. Later on we will be looking at other examples of temporizing moves.

ROLES OF PIECES

It is useful to understand the nature of the role each piece plays in the Bishop and Knight Mate. In Deletang’s technique the King and Bishop take on the main task of driving the defending King to the corner, while the Knight covers key squares and moves to a better square only when there is time to do so.

Other techniques, such as driving the opponent’s King from the wrong corner to the right one requires the more active involvement of the three pieces, and we will see this through a concrete example later on.  For now, let’s see what could happen after 1.Bg6.

1.Bg6 Kg4 2.Kh6 Kh4 3.Bh5 Kg3 4.Kg5 (or the longer 1…Kg4 2.Kf6 Kh4 3. Kf5 Kg3 4.Bh5 Kh4 5.Kg6 Kg3 6.Kg4) and we have succeeded in closing the second triangle. Noticed how the Knight did not make a single move in this sequence!

If Black tries to make a move like 4…Kh3, then White has time to reposition his Knight to d3. If 4…Kf2 White’s King can move forward with 5.Kf4 Ke1 6.Ke3 Kf1.

There are various winning routes for White here. After 4…Kh3, White could play 5.Kf4 instead of repositioning the Knight on c3. Now if Black attempts to dislodge the Bishop with 5…Kh4 White plays 6.Bd1 and the triangle is preserved. After the forced 6…Kh3 White can reposition his Knight to d3. For example: 7.Ne5 Kg2 8.Nd3 Kh2 9.Be2 Kh3 and we reach the following position in the next diagram:

Problem no.4 -White to Move

 

White now brings his knight closer to take on further squares away from Black’s King. 10.Ne1 Kh4 (if 10…Kh2 11.Kg4 forcing the King back, 11…Kg1 12.Kg3 Kh1 13.Bf1 closing the last triangle 13…Kg1 14.Bh3 Kh1 15.Bg2+ Kg1 16.Nf3 mate) 11.Ng2+ Kh3 12.Bf3 Kh2 13.Kg4 Kg1 14.Kg3 Kf1 and we have pushed the defending King back to one available square. 14.Bg4 a temporizing move. 14…Kg1 15.Be2 robbing more squares 15…Kh1 16.Nf4 Kg1 17.Nh3+ Kh1 18.Bf3 mate.

IM DANNY KOPEC’S CONCEPT OF GOOD FORMATIONS

In his excellent DVD “Basic Chess Endings” (Which has some  terrific concepts for handling King + Rook + Pawn endgames) IM Danny Kopec discusses the concept of healthy piece formations in the Bishop and Knight Mate. According to Mr.Kopec, these formations are effective because they take most number of squares away from the King. Notice how, in both of the above diagrams, the Knight and Bishop alone manage to take a huge number of squares on the board. As our initial role is usually to drive the King away from the center, we can aim at setting up one of these formations and simply utilize our King to encircle Black’s King.

Mr. Kopec’s concept of good formations has been suggested earlier. The cordon technique works well because both the Bishop and Knight take on one of the “healthy” formations. Emanuel Lasker states in his book Chess: The Complete Self-Tutor that “In driving him where you want him to go, the most efficient position of your pieces will always be one in which your Knight is on a square of the same color as your Bishop, because then he controls squares of the opposite color.” (p.33)

Nevertheless, what Mr.Kopec has done is present the subject in a way that is better visualized and understood by the learner, focusing on understanding rather than rote-memorization of best moves.

CONCEPT OF CENTRALIZATION

 

This is an easy concept to understand. The pieces have greater influence over the board when placed in the center. We therefore seek to centralize our pieces. A line here might go like 1.Kc3 Kd5 2.Nf2 Ke5 3.Ne4 Kd5 4.Bc2 Ke5 5.Kc4 Kf5 6.Kd4 and the King has been driven off the center.

 PAUL KERES’ POSITION FOR DRIVNG THE KING TO THE CORNER

Problem no.5 - White to Move

 

In his book “Practical Chess Endings”, Paul Keres outlines an effective method of driving the King away from the center once centralization has been achieved. Here White to move plays 1.Nb3 and Black’s King can no longer stay along the a5-h5 rank. 1…Kc6 2.Kc4 Kb6 3.Nc5 Kc6 4.Na4 the same driving method as 1.Nb3. 4…Kb7 5.Kb5 Kc8 and we have succeeded in driving off the King to the edge of the board.

THE MAGIC POSITION

Problem no.6 - White to Move

One of the most challenging situations happens when the defending King manages to grab one of the corners that is not controlled by the attacker’s bishop. We will illustrate the driving process so that the learner not only memorizes the technique, but understands why it works.

1.Nf7+

Taking away the h8 square

1…Kg8 2. Bb1 (or c2, d3, f5, g6)

This temporizing move allows White to take away the g8 square on the next move.

2…Kf8 3.Bh7 Ke8 4.Ne5!

A key move to remember! It seems the King can now escape via d8 and c7, but White manages to set up a healthy minor piece formation with the Knight on d7 taking away the dark squares, and the Bishop on the f1-a6 diagonal taking away the light squares. Let’s see how that happens:

4…Kd8 5.Ke6

The King must protect the d7 square for the Knight. For 4… Kf8 see problem no. 7

5…Kc7

For 5…Ke8 see Problem no.8

6.Nd7

Another key move not to forget. The Knight takes away the dark squares. The defending King may want to escape to the a1 corner via c6-b5-a4, but White will be able to control the f1-a6 diagonal in time.

6…Kc6 7.Bd3! Kc7

The path to a1 is blocked, as well as the path to h8. Thus, the Black tries to limit the King’s mobility and stay as far away from the mating square (in this case a

8.Be4

Takes the c6 square away from the Black King.

8…Kc8

For 8…Kd8 see Problem no.9

9.Kd6

Taking away the c7 square

9…Kd8 10.Bg6

There are several ways to win here, so almost any sequence of moves that drives the King to a8 without letting him escape would do. There is a mate in eleven moves after 10.Bg6, 10.Bf5, 10.Bd3, 10.Bc2, 10.Bf3, 10.Bh1. 10.Bg6 is in the spirit of immediately taking the e8 square from the King. 10.Nf6 also takes e8 away and the mate takes place in twelve moves. You can try experimenting with these moves against a computer.

10…Kc8 11.Nc5

The Knight repositions to take control of b7 square and check the King if it attempts to go to d8.

11…Kd8 12.Nb7+ Kc8 13.Kc6 Kb8 14.Kb6

Takes away the a7 square

14…Kb8 15.Bf5 Ka7 16.Kc2 Ka8 17.Bc8 Ka7

The King is finally confined to the a8 and b8 squares. Only the king and bishop are necessary to confine the Black king to these two squares. Therefore, the Knight just needs to reposition itself to assist in the mate. For example:

18.Nd7 Ka8 19.Ne5 Ka7 20.Nc6+Ka8 21.Bb7++

 

Problem no.7 - White to Move

(Magic position after 1.Nf7+ Kg8 2.Bb1 Kf8 3.Bh7 Ke8 4.Ne5! Kf

Rather than trying to escape via 4…Kd8 and 5…Kc7 the defending king can play 4…Kf8, trying to stay as far away from the mating a8 square as possible. 

5. Nd7+

Taking the f8 square away.

5…Ke8 6.Ke6 Kd8 7.Kd6

Taking the c7 square away.

7…Ke8

If 7…Kc8 a sample line would be 8.Nc5 Kd8 9.Bg6 Kc8 10.Bf5+ Kb8 11.Be6 Ka7 12.Kc7 Ka8 etc.

8.Bg6+

Taking the e8 square and further driving the King to the mating corner.

8…Kd8 9.Nc5 Kc8 10.Bf5+ Kd8 11.Ne6+!

A neat driving maneuver. The King can’t go to e8 because of 11…Bg6 mate.

11…Kc8 12.Kc6 Kb8 13.Nc5 Ka7 (if 13…Ka8 14.Kc7 Ka7 15.Be6 Ka8 16.Kb6 Kb8 17.Na6+ Ka8 18.Bd5 ++)  14. Kc7 Ka8 15.Kb6 Kb8 16.Na6+ Ka8 17.Be4++.

Problem no.8 - White to Move

(Magic position after 1.Nf7+ Kg8 2.Bb1 Kf8 3.Bh7 Ke8 4.Ne5! Kd8 5.Ke6 Ke

6.Nd7

Taking the f8 square away

6…Kd8 7.Kd6 Ke8 7.Bg6+ Kd8 8. Nc5 Kc8 9.Bf5+ Kd8 10.Ne6+

And we come to the previous driving maneuver where the King gets mated in if it goes to e8.

Problem no.9 - White to Move

(Magic position after 1.Nf7+ Kg8 2.Bb1 Kf8 3.Bh7 Ke8 4.Ne5! Kd8 5.Ke6 Kc7 6.Nd7 Kc6 7.Bd3 Kc7 8.Be4 Kd

9. Kd6

Taking the c7 square away while keeping an eye on e7.

9…Ke8 10.Bg6+ Kd8 11.Nc5 and we are back on track with our previous lines. (e.g. 11…Kc8 12.Bf5+ Kd8 13.Ne6+ Kc8 14.Kc6 Kb8 15.Nc5 etc.)

Position no.10 - White to Move and Mate in 10

1.Bg6 Kc8 2.Nc5 Kd8 3.Nb7+ Kc8 4.Kc6 Kb8 5.Kb6 (An alternative is 5.Bf5) Kc8 6.Bf5+ Kb8 7.Be6 Ka8 8.Nc5 Kb8 9.Na6+ Ka8 10.Bd5++

Conclusion

It is my hope that these concepts and strategies help the reader gain a better understanding of the bishop and knight mate. Keep in mind that there is no magic learning bullet here. If you really want to learn this mate I suggest that you work on all the exercises presented to you in this article, and practice with another player or computer. This will help you assimilate these concepts, and find what works best for you over the board. 

References

Averback, Yuri “Chess Endings: Essential Knowledge” Pergamon Press, 1982

Fine, Reuben “Basic Chess Endings” Random House, 2003

Hooper, David “A Pocket Guide to Chess Endgames” Great Britain, G.Bell and Sons Ltd 1973

Keres, Paul “Practical Chess Endings” New York, Doubleday & Company, Inc. 1974

Kopec, Danny “Basic Chess Endings” (DVD)

Lasker, Edward “Chess: The Complete Self-Tutor”  London, B.T. Batsford Ltd, 1972

Pandolfini, Bruce “Pandolfini’s Endgame Course” Simon & Schuster 1988

Portisch, Lajos; Sarkozy, Balazs “Six Hundred Endings” Hungary, Pergamon Press 1981

Sala Ponce, Lorenzo “Teoria y Practica de los Finales” Barcelona, Hispano Europea 1999

Vassaux, Guillermo “Iniciacion a la Estrategia” Guatemala, Federacion Nacional de Ajedrez 1996