THE BISHOP AND KNIGHT MATE

Everybody "knows" the basic Bishop-and-Knight mate, but few can actually demonstrate it. Some experts recommend studying the mating process because it is a model of the combined powers of the two pieces, whereas other experts discourage amateurs from studying it because it arises so seldom in actual play.

The Bishop-and-Knight mate should be explored because certain aspects of it carry over to a wide range of practical endings, especially the way the two pieces cooperate to rope off entire sections of the board. Since space is a factor not only in the endgame, knowing how to coordinate these two pieces is useful in other phases of the game as well.

You don't have to devour every detail to learn how to play this ending. You can assimilate the key ideas simply by examining the formations and patterns presented here. To strengthen your grasp of those ideas, work out the sample variations and notes. And if you're still thirsty for variations, turn to the standard texts (Averbakh or Cheron, for example).

A Word of Advice

In some positions you may not be able to force mate in fewer than 330 moves, and you may exceed the 50-move drawing rule (if no capture or pawn move occurs in 50 moves, the game is a draw). At first, don't worry about accuracy. Instead, try to develop an overview of the subject. Once you know what has to be done, then you can learn the precise way to do it. Don't make the mistake of trying to know everything before you know something.

How Mate Is Forced

To force checkmate you must drive the lone King to a corner square that is the same color as the squares controlled by your Bishop. With a light-square Bishop, mate can be forced only in the h1 or a8 corner; with a dark-square Bishop, only in the a1 or h8 corner. The term "right corner" is used for a corner in which mate can be forced; "wrong corner" for the other kind.

Two Typical Mating Patterns

In diagram 1 the Knight could also be on d7 and the Bishop on any square along the g2-b7 diagonal. In diagram 2 the Knight could also be on a6 or d7.

Diag. 1... Diag. 2... Diag. 3...

It is easy to mate once the King is trapped in the right corner. The problem is to force it there in the first place. Although this might require precise maneuvering, you can make the job easier by thinking in terms of specific schemes. For example, diagram 3 shows a simple forcing situation: Black must retreat.

Three Related Nets

Before you can drive the King into the right corner, you must restrict its movement. For this you may find it helpful to remember three interrelated nets and their mirror images. The nets are shown in the diagrams, their mirror images in notation.

1st Mirror
W: Kg7, Bc2, Nc4
B: Kg5

2nd Mirror
W: Be2, Ne4
B: Kh4

3rd Mirror
W: Kf2, Bf1
B: Kh2

These three nets (and their respective mirrors) are related in that each is a stage in the same confirming process: in all three the lone King clearly has no escape. The 1st net can usually be created even without your opponent's realizing it. From there you maneuver your King closer, square by square, tightening the 1st net into the 2nd net (or its mirror). Finally, by the same gradual maneuvering, you squeeze the 2nd net into the 3rd (for its mirror). As you try it, you will sometimes find it useful to waste a move by moving the Bishop along the last diagonal it had to control! (I'll explain this later).

Three Corresponding Triangles

Notice that each net is a right triangle. The 1st net is the triangle b1-h1-h7, the 2nd net d1-h1-h5, and the 3rd net f1-h1-h3. Notice also that the Bishop occupies the hypotenuse (the side opposite the right angle) of each triangle in succession: first the b1-h7 diagonal, then the d1-h5 diagonal, and finally the f1-h3 diagonal. Indeed, the crux of the whole restricting process is to transfer the Bishop from the 1st hypotenuse to the 2nd and finally to the 3rd. (The rudiments of this system can be tracked back to 1780, but it wasn't published as a system until 1923.) The following analysis demonstrates the whole process, from the 1st net to mate. Try to follow the general course of play without getting lost in particulars. The main line of play is in dark type, the notes in parentheses.

Starting from the 1st net:
1. Bc2 (to drive the lone King back, if possible to the h1 corner) 1...Ke3 (staying close to the center) 2. Kc1 (to be able to play Kd1 preventing Black from reaching e2) 2...Ke2 3. Bg6 (a waiting move forcing Black to give ground) 3...Ke3 4. Kd1 Kf2 (4...Kf3 5. Kd2 Kf2 6.Bh5 and White will soon establish the 2nd net by shifting his Knight to e4 and the Bishop to g4 or e2) 5. Kd2 Kf3 6. Kd3 Kg4 (staying as far as possible from the h1 corner and preventing the Bishop from reaching h5 to shorten the hypotenuse; on 6...Kf2 7. Bh5 tightening the net) 7. Ke3 Kh4 (still guarding h5) 8. Kf4 Kh3 9. Bh5 (mission accomplished: the Bishop controls the hypotenuse of the 2nd triangle and has narrowed Black's territory) 9...Kg2 (trying to run away; but on 9...Kh4 10. Be2 Kh3 11. Ng5+ or Nc5 and 12. Ne4 establishing the minor image of the 2nd net) 10. Nc5 (or Ng5) Kf2 11. Ne4+ Kg2 (on other King moves White replies the same way) 12. Bg4 (arriving at the 2nd net; now While moves his King in, squeezing Black into the 3rd net) 12...Kf1 13. Kf3 (or Ke3) Ke1 14. Ke3 Kf1 15. Kd2 Kg2 16. Ke2 Kg1 (if 16...Kh2 17. Kf2 Kh1 18. Bh3 Kh2 19. Ng5 Kh1 20. Bg2+ Kh2 21. Nf3 mate) 17. Bh3 (seizing the hypotenuse of the final triangle) 17...Kh2 18. Bf1 Kg1 19. Ng5 (preparing to guard h2) 19...Kh1 (on 19...Kh2 20. Kf2 Kh1 21. Bg2+ Kh2 22. Nf3 mate) 20. Kf2 (obviously not 20. Nf3 stalemate) 20...Kh2 21. Nf3+ Kh1 22. Bg2 mate. These variations clearly depict how the three pieces work harmoniously.

Starting from the Wrong Corner

The nets are foolproof, but sometimes the lone King avoids the nets and retreats to a wrong corner. We therefore need a method of driving the King from a wrong corner to a right one. This is done by gradually controlling square after square along the outer row. Here White can systematically drive Black to either a8 or h1. White's King is ideally placed on f6, equidistant from both light-square corners. By rotating the board, you can see that if the wrong corner were a8, White's King should start on c6; if it were a1, the King should start on c3; and if it were h1, the King should start on f3.

The first square White must control is h8, either by Nf7 or Ng6. To drive Black's King to h1, White should play Ng6; to drive it to a8, White should play Nf7. Let's look first at driving the King to a8.

1. Nf7+ Kh7 (on 1...Kg8 White still plays 2. Be4) 2. Be4+ Kg8 (since White wants to play Bh7 to guard g8, the next square along the outer row, he must waste a move) 3. Bf5 (as I indicated above, you can waste a move in this ending by moving the Bishop along the last diagonal it had to control: in this case, the bl-h7 diagonal) 3...Kf8 4. Bh7 (next White must maneuver his Knight to guard f8) 4...Ke8 5. Ne5 (preventing escape via d7 and repositioning the Knight to guard f8 from d7).

Black can now move closer to the wrong corner by Kf8 or make a run for it by Kd8. Sample variations for each possibility follow.

A: Passive Defense

5...Kf8 6. Nd7+ Ke8 7. Ke6 Kd8 8. Kd6 Ke8 (on 8...Kc8 9. Nc5, and if 9...Kd8 10. Bg6 Kc8 11. Bh5 or f7 Kd8 12. Nb7+ continues the confining process; if 9...Kb8 10. Kc6 Kc8 11. Nb7; if 10...Ka7 11. Kc7 and the Black King is trapped) 9. Bg6+ (White eats up another square along the back row) 9...Kd8 10. Nc5 (preparing to guard d8 from b7, but not from e6 which would interfere with the Bishop) 10...Kc8 (since White wants to play Nb7, he needs to waste a move with his Bishop) 11. Bf7 (or Bh5) Kd8 (or 11...Kb8 12. Kc6 and the Black King will be trapped as in an earlier variation) 12. Nb7+ Kc8 13. Kc6 Kb8 14. Kb6 Kc8 (or 14...Ka8 15. Nc5 Kb8 16. Be6 Ka8 17. Bd7 Kb8 18. Na6+ Ka8 19. Bc6 mate) 15. Bc6+ Kb8 16. Nc5 Ka8 17. Bd7 (wasting a move and mating in two).

Now let's consider Black's alternative.

B: Active Defense

5...Kd8 6. Ke6 Kc7 (6...Ke8 transposes to the passive line after 7. Nd7, and 6...Kc8 creates possibilities similar to the text) 7. Nd7 Kc6 (on other responses White can play the same 8th move) 8. Bd3! (Black is trapped after all) 8...Kc7 (or Kb7) 9. Bb5 (Most texts recommend Be4, but Bb5 is more systematic) 9...Kd8 (on any other move White plays Kd6) 10. Nb6 (or Nf6) Kc7 11. Nd5+ (and White has the 2nd net!). A sample conclusion: 11...Kd8 12. Kf7 (or Kd6) Kc8 13. Ke7 Kb7 14. Kd7 Kb8 15. Ba6! Ka7 16. Bc8 Kb8 17. Nc3 (or Nb4 or Ne7) 17...Ka8 18. Kc7 Ka7 19. Nb5+ Ka8 20. Bb7 mate.

Going back to the starting position (last diagram), here are sample variations showing how White wins if he decides to drive the Black King to h1: 1. Ng6+ Kg8 2. Bd5+ Kh7 3. Be6 Kh6 4. Bg8 Kh5 5. Ne5 and now either (A) 5...Kh6 6. Ng4+ Kh5 7. Kf5 Kh4 8. Kf4 Kh5 9. Bf7+ Kh4 10. Ne3 Kh3 11. Bg6 Kh4 12. Ng2+ Kh3 13. Kf3 Kh2 14. Kf2 Kh3 15. Bf5+ Kh2 16. Ne3 Kh1 17. Bg4 Kh2 18. Nf1+ Kh1 19. Bf3 mate; or (B) 5...Kh4 6. Kf5 Kg3 7. Ng4 Kf3 8. Bc4 Kg3 9. Be2 Kh4 10. Nf6 Kg3 11. Ne4+ and we've arrived at the 2nd net.

The W Maneuver

A particularly intriguing possibility is the Mahler W maneuver. Although it is not a main line, the W maneuver is worth examining because it shows beautiful interaction among the pieces (and it makes a useful mnemonic device).

In one satisfying variation all three pieces trace W's: the King by moving over the squares e5, d6, c5, and b6; the bishop covering d5, c6, b5 and a6; the Knight traversing f4, e6, d4, and c6.

1. Ke5 Kd8 2. Kd6 (tracing the first half of the King's W) 2...Ke8 3. Bd5 Kd8 4. Bc6 (the first half of the Bishop's W) 4...Kc8 5. Nf4 Kd8 (on 5...Kh8 6. Kc5; if then 6...Kc7 or Kc8 7. Ne6+ transposes to the main line, and if 6...Ka7 7. Kb5 Kb8 8. Kb6 Kc8 9. Ne6 Kb8 10. Bd7 Ka8 11. Nc7+ Kb8 12. Na6+ Ka8 13. Bc6 mate) 6. Ne6+ (the first half of the Knight's W) 6...Kc8 7. Kc5 Kb8 8. Kb6 (completing the King's W) 8...Kc8 (or Ka8) 9. Bb5 Kb8 10. Ba6 (completing the Bishop's W) 10...Ka8 11. Nd4 Kb8 12. Nc6+ (completing the Knight's W) 12...Ka8 13. Bb7 mate!

How to Start

Most of the time your pieces will not be so nicely placed as they are in the analyzed examples, so you need to know how to prepare your forces for action. Unless the position clearly suggests a better plan, start by moving all three pieces to the center; specifically, your King to a central square not the color of your Bishop, the Bishop to a central square next to the King, and the Knight to the other side of the King, so that the three pieces form a straight line (say, Nc4, Kd4, Be4).

This approach is especially helpful when you have no idea what to do. Since a central arrangement can be achieved without much trouble, create random positions and practice trying to centralize the pieces. By grappling with it on your own you should get a better idea of how the pieces work together.

Conclusion

The key patterns that underlie the Bishop-and-Knight mate are strikingly powerful, but they are entirely absent from most textbooks. While a single article cannot give you perfect technique, I hope this one at least displays how the Bishop, Knight, and King can function as a unit. I stress this point because interaction is what chess is all about. Never forget that the value of a piece is measured by its relation to other pieces.

THE ABCs OF CHESS
by Bruce Pandolfini, National Master
Chess Life & Review, October, 1979


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