Understanding The Bishop and Knight Mate By Louis Alejandro Lima
nd
2 Edition Copyright 2006-2008©
Note Special thanks to Brent Hefley for reviewing the first edition of this article when published on www.schemingmind.com . I would also like to thank the many readers who contacted me with feedback after posting this article on my site: http://chesstactics.wordpress.com
Introduction The Bishop and Knight Mate is the most difficult of the so called elementary mates. Certainly there is nothing “elementary” about this mate, as some positions require thirty five moves to realize, and the techniques can be rather laborious to acquire for beginner players. Furthermore, this mate rarely surfaces in practical play. So why learn it if you are unlikely to ever face it over the board? I think mastering this mate can help the learner develop skills and concepts that are useful in other parts of the game, for example: a. Piece Coordination 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 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 and technically fluent. b. Endgame Concepts Several endgame techniques useful for other endgame areas can be learned from the Bishop and Knight Mate including zugzwang, the opposition, temporizing, and stalemating. c. Other Concepts and Skills Students of this endgame can learn the importance of centralization, the importance of controlling key squares and diagonals, as well gain an overall appreciation for the natural abilities of the bishop and the knight. This mate can also help increase both visualization and calculational abilities.
Goal The goal in the bishop and knight mate is to checkmate in the same corner as the color of the bishop. (See Diagrams 1 and 2)
Diagram 1 – Mating Net
(The red squares show alternative mating squares for the bishop)
Diagram 2 – Mating Net
(The red squares show alternative mating squares for the knight)
The above diagrams are examples of end positions we want to aim for, although it sometimes happens that the defender makes a gross error on the edge of the board, and gets caught while being driven to the right corner. (See diagrams 3 and 4 on next page)
Diagram 3 – Mating Net
(The red squares show alternative mating squares for the bishop)
Diagram 4 – Mating Net
(The red squares show alternative mating squares for the knight)
We must be alert all the way, especially in the last stages, as we do not want to stalemate our opponent. (See diagrams 5 and 6 on next page)
Diagram 5 – Stalemate
Diagram 6 – Stalemate
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 suddenly 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 Step 1. Square Deprivation The attacker takes squares away from the defending king until it is driven to one of the four edges of the board. In the initial position the defender can choose to roam just about anywhere on the board. We can aim towards confining it to a limited group of squares. Once we achieve this, we then proceed to confine him to an even smaller number of squares, until the king is incarcerated in one of the four edges of the board. Step 2. Driving We drive the king 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. Step 3. Checkmate We checkmate the defending king. This sounds obvious, but careless moves can easily stalemate our opponent in this stage. Careful repositioning of the pieces is necessary to checkmate, and without letting the king out of the mating net.
Concepts and Techniques This section outlines nine concepts and techniques related to the Bishop and Knight Mate. Credit is given where possible, but it is difficult to accurately credit the original source since 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. If the reader has any information regarding this mate kindly e-mail me at
[email protected] #1 - Deletang’s Triangles This method was systematized by Daniel Deletang, a Frenchman living in Argentina in the 1920’s. According to a blog in the Kibitzer’s Corner, Mr. Deletang was a chess amateur belonging to Club Argentino who in 1923 published his system of triangles. In his book “Iniciacion a la Estrategia”, Guillermo Vassaux suggests that Mr.Deletang based his triangles on past analysis as well. Mr. Deletang might have been a chess amateur, but as GM Andy Soltis once said “The best chess teachers are often just interested amateurs”, In my opinion, Deletang’s method is still one of the simplest to grasp over the board for beginner players. 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 – Black King on f3 Place the White king, bishop and knight in such a way that the Black king cannot escape if it was given an unlimited number of consecutive moves.
Problem no.2 – Black King on g2 Place the White king, bishop and knight in such a way that the Black king cannot escape if it was given an unlimited number of consecutive moves.
Problem no.3 – Black King on h1 Place the White king, bishop and knight in such a way that the Black king cannot escape if it was given an unlimited number of consecutive moves.
Answer to Problem 1 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. One solution is placing the White king on g2, the knight on c4, and the bishop on c2. (See Diagram 7)
Diagram 7 – Possible Answer to Problem 1
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. Answer to Problem no. 2 Here the job is a lot of easier, and kudos if you discovered that the White’s king is not even necessary. (See diagram 8 on next page)
Diagram 8 – Possible Answer to Problem 2
Answer to Problem no. 3 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. The Black king can only move from h1 to g1 as seen in Diagram 9. Trapping the king with the bishop and knight is not so effective here as we would be stalemating Black’s king. (See Diagram 9)
Diagram 9 – Possible Answer to Problem 3
Deletang’s technique works in the following manner: 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 the knight and bishop. 3. The bishop takes the lead and moves to the second diagonal (in this case, the d1h5 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 completes 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 shortly be looking at some concrete examples. For now, let us continue exploring other concepts and techniques related to Deletang’s triangles. # 2 – Hooper’s Cordons In his book “A Pocket Guide to Chess Endgames” David Hooper’s talks about setting up cordons around the defending the king. His description and examples are identical to Deletang’s triangles. However, the idea of cordons can be useful in practice. Although a cordon does not completely seal the defending king, it takes 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:
Diagram 10 – Hooper’s Cordons
Here white does not have a perfect triangle that seals the black king’s escape to the queenside. Theoretically the black king could travel to the queenside via e8, but this is not realistic as it would require several moves, giving white ample time to reposition its pieces. 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 take Diagram 10 as an example with black to move. 1…Kf4 White’s knight and bishop cannot be touched by Black’s king, so they are most effective if left there for the moment. Therefore, Black strives to limit White’s king, which is the only piece free to move without disturbing the cordon. 2.Ke6 Kg5 3.Kf7 Kh6 4.Bc2 There are several right moves here, but 4.Bc2 positions the bishop to relocate to d1 at the right moment to set up Deletang’s second triangle. Notice that we have yet to reach the first of Deletang’s triangles, since the Black king can theoretically escape via g5-f4-e5. Thus 4.Bc2 can be seen as the beginning of the upgrade from the “cordon” to the “triangle”. 4…Kg5 5.Nd2 (The knight repositions itself at the right moment …) 5…Kh6 6.Nc4 Kg5 7.Kg7 and we have reached the first of Deletang’s triangles.
Problem no.4 –Exercise on Effective Piece Placement Place the the Black king anywhere on the twelve highlighted squares. 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.
# 3 - Zugzwang and Temporizing Moves Problem no.5 –White to Move
White would like to make a move with the king which would force 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 Deletang’s technique, 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 and must make an inferior one. In this case the Black king cannot longer stay in the h5-a5 file and must move back. Later on we will be looking at other instances of temporizing moves. # 4 – 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 turn to problem no.5 after 1.Bg6 to see an example of the roles pieces play. 1… Kg4 2.Kh6 Kh4 3.Bh5 Kg3 4.Kg5 (The longer 1…Kg4 2.Kf6 Kh4 3. Kf5 Kg3 4.Bh5 Kh4 5.Kg6 Kg3 6.Kg4 is also possible) and we have succeeded in closing the second triangle. Noticed how the knight did not make a single move in this sequence!
If Black now tries to make a move like 4…Kh3 , then White has time to reposition his knight to d3. If instead black plas 4…Kf2 white’s king can move forward with 5.Kf4 Ke1 6.Ke3 Kf1. There are various winning routes for white here. Returning to diagram 5, after 1.Bg6 Kg4 2.Kh6 Kh4 3.Bh5 Kg3 4.Kg5 Kh3, White could play 5.Kf4 instead of repositioning the knight on c4. 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.6 -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 reaching the last triangle 13…Kg1 14.Bh3 Kh1 15.Bg2+ Kg1 16.Nf3 voila!) 11.Ng2+ Kh3 12.Bf3 Kh2 13.Kg4 Kg1 14.Kg3 Kf1 and we have pushed the defending king back to one available square. 15.Bg4! a temporizing move. 14…Kg1 15.Be2 robbing more squares 15…Kh1 16.Nf4 carefully repositioning the pieces.. 16…Kg1 17.Nh3+ Kh1 18.Bf3 mate. # 5 – IM Danny Kopec’s Theory of Good Formations In his excellent DVD “Basic Chess Endings” IM Danny Kopec discusses the concept of good minor piece formations in the Bishop and Knight Mate. Mr.Kopec describes how these formations are effective in that they set up an effective barrrier against the defending king. Diagram 11 and 12 show two examples of good minor piece formations. 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 utilize our king to encircle Black’s king, much in the same way as Deletang’s and Hooper’s technique.
Diagram 11 – Example of a Good Formation
Diagram 12 – Example of a Good Formation
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.”
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 why things work the way they do, rather than rote-memorization. # 6 – 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. Utilizing diagram 13 we can show one of several ways to drive the Black king off the center: 1.Kc3 The king moves towards the center and takes the d4 square away from Black’s king. 1…Kd5 Black’s king refuses to leave the center. 2.Nf2 On its way to e4… 2…Ke5 3.Ne4 Kd5 4.Bc2 A temporizing move… 4… Ke5 5.Kc4 Kf5 6.Kd4 and we have successfully driven the defending king off the center.
Diagram 13 – Centralizating Our Pieces
# 7 – Paul Keres’ Position for Driving the King to the Corner Problem no.7 - White to Move
In his book “Practical Chess Endings”, Paul Keres outlines an effective method for driving the king to the edge of the board once centralization has been achieved. In problem no.7 above White to move plays 1.Nb3 and Black’s king cannot 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. # 8 – The Magic Position Problem no.8 - White to Move
(The yellow squares show alternative placements for the bishop, while the red squares show alternative placements for the knight)
Perhaps most challenging situations occurs 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. The technique is aimed at taking squares away from the defending king. 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. 9 5…Kc7 For 5…Ke8 see Problem no.10 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, Black tries to limit White’s king mobility and stay as far away from the mating square as possible (in this case a8.) 8.Be4 Takes the c6 square away from the Black king. 8…Kc8 For 8…Kd8 see Problem no.11
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 and 10.Bh1. 10.Bg6 is in the spirit of immediately taking the e8 square from the defending king. 10.Nf6 also takes e8 away and the mate takes place in twelve moves. 10…Kc8 11.Nc5 The knight repositions to take control of the b7 square and check the king if it attempts to go to d8. 11…Kd8 12.Nb7+ Notice the knight’s zig zag maneuver f7-e5-d7-c5-b7. GM Alexandra Kosteniuk refers to it as the “W” maneuver in her podcast/online video from www.chesskillertips.com (CKT 039: B+N vs K). This makes it easy for students to remember the technique. 12…Kc8 13.Kc6 Kb8 14.Kb6 Takes away the a7 square 14…Ka8 15.Bf5 Kb8 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. Na5 Ka8 19.Bc8 Kb8 20.Ba6 Ka8 21.Bb7+ Kb8 22.Nc6 mate.
Problem no.9 - White to Move (Magic position after 1.Nf7+ Kg8 2.Bb1 Kf8 3.Bh7 Ke8 4.Ne5! Kf8)
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 (If 10…Kd8 11.Ne6+ Kc8 [11…Ke8?? Bg6 mate]12.Kc6 Kb8 13.Nc5 Ka7 14.Bc8 etc) 11.Be6 Ka7 12.Kc7 Ka8 etc; or 11.Kc6 Ka8 12.Bc8 Kb8 13.Ba6 Ka7 14.Kb5 Ka8 15.Kb6 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 14. Kc7 Ka8 and now the easiest is closing the triangle with 15.Bc8 Kb8 and just reposition the knight to give a timely mate (e.g. 16.Nd7 Ka8 17. Ne5 Kb8 18.Nc6+ Ka8 19.Bb7 mate.
Problem no.10 - White to Move (Magic position after 1.Nf7+ Kg8 2.Bb1 Kf8 3.Bh7 Ke8 4.Ne5! Kd8 5.Ke6 Ke8)
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.11 - 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 Kd8)
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 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++
References Books
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 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
DVD
Kopec, Danny “Basic Chess Endings”
www.chesskillertips.com CKT 039: B + N vs K (Online Video)
http://www.chessvideos.tv/forum/about802.html Checkmating with B+N by Josh Specht (Online Video/Podcast)
Internet
Practice Online Engines
http://www.chessposter.com/chess_problems/mate_king_and_bishop_knight.htm
http://www.chessvideos.tv/bishop-knight-checkmate.php
