Knight and Bishop Checkmate: How and Why

Is is necessary to know a checkmate that you will never need to execute? Aside from deliberate choices due to underpromotion, I have never had to checkmate with a knight and a bishop in a game. I was on the weaker side in a blitz game on Internet Chess Club 25 years ago and got a draw because my opponent did not know how to perform the mate. I saw one young student try and fail in a youth tournament, and then in the very next round have the ending again, this time with the lone king and another draw.

In one tournament that I won, my last round opponent had failed to execute the checkmate in the previous round, else he could have won the event with a draw against me.

Many players never face it.

In Silman’s Complete Endgame Course: Beginner to Master (2007), Jeremy Silman writes:

I heretically decided not to include Bishop and Knight vs. Lone King because it’s far from easy to master, and it occurs very rarely in over-the-board play. In fact, I only got it once in my entire career, while IM John Watson and IM John Donaldson never got it at all! Is such a rarity really worth the two or three hours it would take to learn it? I say no. (xv)

On the other hand, Thomas Engqvist in 300 Most Important Chess Positions (2018) considers it of such importance that three of the 300 are concerned with this checkmate. Acknowledging its rarity (“it will probably happen once or twice in your life”), Engqvist states:

I used to teach children this endgame at a very early stage and they should know how to do it before they reach an Elo rating of 1500 to get a good feeling for how knight and bishop can harmonise together like a bishop pair. (184)

Practicing positions with few pieces develops understanding and appreciation of each piece’s unique capabilities. As Vasily Smyslov stated in Vasily Smyslov: Endgame Virtuoso (1997), "the properties and peculiarities of the pieces are most clearly revealed in the endgame" (6). Most chess study positions involve knowledge and skills that will be applied to other positions.

Yesterday, using the useful “Table of Computer Database Results for Pawnless Endings” in Karsten Müller and Frank Lamprecht, Fundamental Chess Endings (2001), I set up the knight and bishop ending that is longest distance to checkmate and played it against Stockfish. After my first five moves, I reached this position and noted the wall created on the central squares by the bishop and knight.

Black to move

I also worked through the three positions in Engqvist’s book. The first two involve the technique I have learned, forgotten, and relearned (see "Bishop and Knight Checkmate"). The third position is presented to teach the technique in lessons for beginners on Lichess that I have criticized it as more difficult.

It comes from Andre Chéron, Lehr-und Handbuch der Endspiele (1964). With Engqvist’s encouragement, I decided it was worth learning. It was not as difficult as I had thought and I spent some time practicing against the computer.

Then, I searched ChessBase Mega 2024 for endgames that reached a knight and bishop against a lone king. There are many more than I expected. Finding one that ended in a draw, I started going through the game. At several points where I thought I saw an improvement, I played from that position against Stockfish. Then, I used Stockfish and tablebases to identify areas where my play could be improved.

This exercise showed me that knowing more than one technique for executing the checkmate had practical implications. In a game, one might find one of the techniques is much faster than the other.

Here are some positions from that game. I do not know how much time pressure existed when the player was unable to finish successfully. An internet search turned up tournament information that listed the Black player’s rating as 1850.

Black to move

Black can force checkmate in 8 moves. The game went on another 20.

Nine moves earlier, Black had a mate in 9.

Black to move

A few moves prior, Black had a mate in 15, did not play it perfectly, but made progress as White did not offer the best defense.

Black to move

The closest Black came to finishing was mate in seven.

Black to move

109...Be3 (or Bf4, Bg5, Bh6) should be played, forcing White to the a-file. 110.Ka3 Kc3 111.Ka2 Bc1 and the bishop occupies the critical diagonal. 112.Kb1 Nd3 113.Ka2 Kc2 114.Ka1 Bb2+ 115.Ka2 Nb4#.

Students wanting to learn this checkmate could start with positions where checkmate can be forced in three to six moves and build from there.

Some Knight Endings

After working through the 13 knight endings in Thomas Engqvist, 300 Most Important Chess Positions (2018) over the course of several days, I put together five endings to play with some of my students. Two were from Engqvist and the others were found using ChessBase 17's research feature.

Black to move

From Sulistya,M. -- Slingerland,C., Timisoara 1988

As I beat Stockfish 16 rather easily from this position after forcing an exchange of knights, I hoped my students would do the same. That they did not suggests we might do more work on endings with a pawn majority and no pieces.

Black to move

This one is in Engqvist and from a game I cannot locate in databases: Gebhardt -- Bellman, Levelezes 1996. It is a good one to practice with. Stockfish evaluates Black's advantage as less than a pawn. I was lucky to get a draw with Stockfish 16 while playing Black. Well, not actually luck; I used the takeback feature.

White to move

In Pohjala,H.--Sulskis,S., Jyvaskyla 2013, White missed a chance for equality from this position. Against Stockfish on the iPad, I was able to hold the draw. Maybe I'll see if I can do the same against Stockfish 16 on my computer.

White to move

This position arose in Rossetto,H.--Stein,L., Amsterdam 1964 and Black won after a long struggle. The engine says the position is equal. I have not tested myself against the machine with this one.

Black to move

Black is slightly better and went on to win from this position in Lasker,E.--Nimzowitsch,A., Zurich 1934. Engqvist has this one in his book. Stockfish does not find fault with 35...h5, which all of my students played, but it seems the me that White might have more difficulties if that pawn holds back a bit.

Go to the Source

Three of the past four days, endings with a knight against pawns have been the focus as I am racing through Thomas Engqvist, 300 Most Important Chess Positions (2018). One of the positions and some of the analysis is from Yuri Averbakh and Vitaly Chekhover, Knight Endings, trans. Mary Lasher (1977). As this book was one of many that I acquired the year prior to turning 64, I pulled it from the shelf and began reading it (see "64 Endgame Books"). I skimmed the first two chapters and then looked at the analysis Engqvist referenced. 

Engqvist reaches position 41 in Knight Endings via a variation from a game played in Paris in 1848. This game is not in ChessBase Mega 2024, nor on chessgames.com, nor, as near as I can tell, anywhere else in online databases. But Engqvist offers a clue to help my search for the game: "Kieseritzky remarked that the ending was very interesting" (153).

Thanks to Chess Archaeology, it only took a minute to locate La Régence: Journal des Échecs, which Lionel Kieseritzky edited. It turns out that the source of the ending was the first game in the first issue. 

The journal offers a diagram after White's move 65. Engqvist played several training games from the position after 65...Ke5 more than twenty years before writing 300 Most Important Chess Positions. His analysis of this game, which Black could have drawn and in which both players made errors is instructive.

I played this position against the computer a couple of times on Friday and then read Engqvist's analysis more carefully yesterday. I also learned to read Kieseritzky's unusual notation: 65...E65 66. E47 E66 and entered the entire endgame into my database from the journal.

Some Easier Practice

While skimming the first chapter of Knight Endings, I paused on this statement by Averbakh and Chekhover: "Starting from any point on the board, a knight on move, can stop any pawn that has not gone beyond the fourth rank" (2).

Accordingly, I created an exercise to play against the computer. Stockfish on the iPad offered minimal resistance and was not worth the effort. I could have come to my office and used Stockfish 16 resident in Fritz, but was on the couch in the living room with my dog on my lap, so I tried using Lichess. This effort resulted in a game where I had to find a few only moves, but my composition was not as challenging as I hoped.

White to move

Almost any move works here, but I opted to only move the knight.

1.Nf7 b4 2.Nd6 Kd5

White to move

This position makes a better composition as only one move works.

3.Nf5 Ke4 4.Nd6+ Kd5 5.Nf5 Kc4 6.Ne3+ Kd3

White to move

7.Nd1

Only move, as are the next three. But they are not difficult.

7...Kc2 8.Ne3+ Kd3 9.Nd1 Kc2 10.Ne3+ Kc1 11.Nc4 b3 12.Ne5 Kc2

White to move

13.Nc4 Kc3 14.Na3

14.Nb6 and 14.Ne3 also work because 14...b2 would walk into a fork. I opted for the elementary 14.Na3 because of a known pattern.

14...b2 15.Nb1

The game went on until move 28, but there are no difficulties.

Principle of Development

The first task of a chess player at the beginning of a game is rapid development. This means that a player should deploy the maximum number of pieces on squares where they are not vulnerable and work together with other pieces. They should be deployed with attention to the opponent's efforts to accomplish the same.

There are other ways to define the principle of development (see "What is Development"). The paragraph above is an effort to present the essence of the oldest definition of the principle that I have found in print. That definition is a translation of writing by Domenico Lorenzo Ponziani (although credited to Ercole del Rio by the translator). It was published in English 17 years before Paul Morphy was born (see "Principle of Development: Early History").

Morphy is usually credited as the "first player to understand the importance of swift development in open games", as Thomas Engqvist puts it in 300 Most Important Chess Positions (2018), 13. Engqvist offers 30 key positions from 24 games to articulate the concept of development in practical ways (13-32). There should be no question that Morphy's games illustrate well the principle of rapid development. They also show, as Engqvist elucidates well, how to sacrifice material to gain a decisive advantage against a player who neglects the principle.

I have spent that past ten days working through these 30 key positions as part of an effort to read the whole of Engqvist's book in 60 days (see "60 Days, 300 Positions: Day One"). This morning I reviewed all thirty positions after spending some time (too little) on numbers 26-30. I noted the key ideas that Engqvist offers through these positions, questioning how much was absent from Ponziani's articulation of the principle.

Engqvist includes center control, which I do not see in Ponziani's statement. He also shows Morphy's preference for avoiding "unproductive one-move threats" (14). Some of the most challenging positions in the first section of the book feature positions from modern grandmaster practice where the idea is to interfere with the opponent's harmonious development. The translation of Ponziani states, 

Whoever, at the beginning, has brought out his Pieces with greater symmetry, relatively to the adverse situation, may thence promise himself a fortunate issue in the prosecution of the battle.
J.S. Bingham, The Incomparable Game of Chess (1820), 32.

In the context, I suspect that harmony might make more sense than the word symmetry, but I have not examined Ponziani's Italian. Nonetheless, it is clear that the notion of attentiveness to the opponent's development exists in Ponziani's formulation.

William Steinitz is often credited with articulating the principles underneath Morphy's play. But, clearly other chess writers before Steinitz mentioned the principle of development. As for Morphy being the first to understand rapid development, I offer this position, which would be in my collection of 300 most important positions.

White to move

White has already sacrificed two pawns and here often plays 10.Qb3, sacrificing a rook for a winning attack. Black's best chance is 10...d5 11.Bxd5 O-O, as was played in Meyer,H. -- Ubbens,MH., 1926. Gioachino Greco is credited with the position and has both 10...Bxd4 and 10...Bxa1 for Black. In fact, Greco copied this position from the manuscripts of Giulio Cesare Polerio, or perhaps a book by Alessandro Salvio (see "Greco Attack Before Greco").

Searching ChessBase Mega 2024 for the position turns up nine games with 10.Qb3 prior to the first with 10.Ba3, which might be an improvement (see "Corte -- Bolbochan 1946").

After 10...Bxa1 in Polerio's composition, we have a position that I like to show students in conjunction with this position from Morphy's Opera Game.

White to move

In both cases, White is behind a considerable amount of material but completely winning because Black's pieces lack mobility. It seems clear to me that Polerio and to an even greater extent Greco understood the pitfalls in neglecting the principle of development. It remained for the leading players of the so-called Italian school a century later to articulate the principle.

Nonetheless, Morphy's games remain the clearest early examples.

Interesting Exercise

This pawn structure arises after the Spanish Exchange and a similar one, but with Black’s doubled pawns on the f-file, can arise from the Caro-Kann. Opening theory states that Black cannot allow liquidation of all the pieces because the pawn ending would be lost. Max Euwe offers analysis of how to play the pawn ending in an obscure book. Thomas Engqvist presents the analysis in 300 Most Important Chess Positions (2018).

White to move

Naturally, after reading through Engqvist’s analysis, I played the game against Stockfish. My best result after several efforts has been a draw. I lost, used the takeback feature, and tried again. In repeated efforts, I’ve blundered and lost more than I have tracked, but completed two games with draws.

The win is elusive and worth pursuing for what I can learn about pawn endings.

Today is the ninth day of my 60 day quest to go through all of Engqvist’s book at the rate of five positions per day. Yesterday, I spent a fair amount of time looking at games from which positions 21-25 were or could have been derived. For instance, one position featured a novelty played by Hikaru Nakamura in 2011. Several other players have followed his lead and I played through some of those games.

Today’s position is the 16th in the section on pawn endings. I have been alternating between openings and endings. I will finish the development section tomorrow.

Edit: after multiple efforts, I dove back into the analysis in 300 Most Important Chess Positions. I have been struggling against the engine from the wrong position. Black's a-pawn should be on a6. How much difference does this make?

Today's Position

White to move

This position is not among the five that I considered today from Thomas Engqvist, 300 Most Important Chess Positions (2018), which I am working through at the rate of five positions per day. The position does come from a game from which Engqvist extracted three positions, but it was this moment in several games that captured most of my time this morning.

This position seems to have arisen for the first time in Gelfand,B. -- Karpov,A., Sanghi Nagar 1995 and at least twice more that year.

Gelfand played 9.Nd2 and lost after a long struggle. In Anatoly Karpov, How to Play the English Opening (2007), it references 9.Ne1, first played in Gulko,B. -- Sadler,M., Lucerne 1997 as an improvement for White (47). Nonetheless, ChessBase Mega has two White wins, two draws, and four Black wins after 9.Ne1. One of the draws is Engqvist's source game.

After 9.Nd2, White has three wins, a draw, and two losses. Why is 9.Ne1 an improvement?

Process

On the sixth day of my quest to study 300 carefully selected chess positions in 60 days, another speed bump was thrown in my way. I have worked through 15 pawn endings and now find myself at the 12th opening position. Thomas Engqvist, 300 Most Important Chess Positions (2018), writes, “At higher levels there are many subtleties when in the process of developing the pieces” (19). He proceeds to narrate an account of how Mark Taimanov developed the Sicilian variation that bears his name. This narrative sent me to look at his 1972 loss to Anatoly Karpov, and then to a book he wrote on the variation.

Other books, too, might be on the docket as I decide how much time should be given to this one position.

As I wrote in “Ten Books to Achieve 1800+”, I started playing the Sicilian Defense in the 1970s. In the late 1990s, I became enamored with the Kalashnikov variation and sought to memorize the critical lines, inevitably finding myself in trouble when White played a move outside my book knowledge. In 2003, I took up the French, which is not a better defense for Black. In fact, it might be worse. But, my approach to understanding the opening was altered.

Memorization of lines grows out of comprehension of the ideas, rather than the reverse. Now, Engqvist pushes me to comprehend the ideas in some move order nuances of Sicilian lines that I often reach via the French when White opts to play something other than 2.d4.

After writing and posting the above, I continued with the next positions in Engqvist's book. Three of today's five positions are from a single game (a feature I like about Lev Alburt and Al Lawrence, Chess Training Pocket Book II (2008)--one of the 300 positions series). Engqvist's analysis references some by the winner of the game, and his book of selected games has been ordered.

Corresponding Squares

My quest to learn 300 chess positions in 60 days is proving time consuming. Most of the time that I could spare today was expended laboring to understand number 37. The first day was a review of some pawn endings that I know: positions 151-155 in Thomas Engqvist, 300 Most Important Chess Positions (2018). My quest is an effort to read all of this book in less than two months. On the second day, I reviewed some Paul Morphy positions that I know well. An obscure line in the Slav Defense captured my interest yesterday. Today, I went back into endgames with numbers 156-160 in Engqvist. Number 157 is a much analyzed study by Emanuel Lasker (some books employ the version published by Gustavus Reichhelm after Lasker and he discussed Lasker’s composition).

First, I set up Lasker’s position on my iPad and spent some time analyzing it. Then, I played against the engine, backing up and trying again when I failed. I have worked with this position in the past and knew the basic ideas, but have not developed well my ability to calculate the whole series of corresponding squares. Looking for help drove me into other books on the shelf. I confirmed that Jeremy Silman, Silman’s Complete Endgame Course (2007) lacks the position. I know that corresponding squares are mentioned early in Mark Dvoretsky, Dvoretsky’s Endgame Manual (2003) and the concept is trumpeted in Paul Keres, Practical Chess Endings (1974). I opted to check John Speelman, Endgame Preparation (1981) and was pleased with the instruction.

Speelman offers a digested version of what he found in Yuri Averbakh and Ilya Maizelis, Pawn Endings (1974), which I consulted later in the day. My process was to read some in Speelman, and then construct a position derived from Lasker/Reichhelm. First, I sought to find positions with Black to move that were winning for White. With all the pawns fixed as in Lasker’s study, I placed the Black king on a8. Where must I place the White king for the position to be winning if Black is on the move?

Black to move

Then, I repeated the process with Black’s king on b8. After several such efforts, I went back to Reichhelm’s version of the original study and played against the computer. Then, additional modifications and more play against the engine.

This version was one of the easier ones.

White to move

After many hours of play against the engine and study of several books, I have the sense that I am beginning to scratch the surface of this difficult position.