A bish of a knightmare
Hi!
In one of my recent rapid games, I was faced with the beautiful task of delivering checkmate with knight and bishop. It's a checkmate procedure that I've known for a long time. I've studied it in detail, revised it often enough, and I also have a personal history with it. Next to this, I've seen it explained in a lot of different endgame monographs and videos, with differing levels of accuracy. I knew how to do it, so I pulled it off swiftly and without much further ado.
I'll present the game here. It's okay if the moves don't make too much sense right now. By the end of this post, you'll be able to see the logic behind the moves.
Normally, I'd write my thoughts down and analyse them the next day. However, given that I had this very specific checkmate on the table, a different yet laborious idea came to mind: a comprehensive, complete and conclusive treatise of the entire checkmate procedure.
On top of the material that I already had on this endgame, I amassed and consulted many different sources for their take on it: books, YouTube videos, websites, and games by high-rated players. Sometimes just to see which method they used, in what order they presented the material, and in several cases just what they said in the beginning of their treatment of the endgame. I found it hilarious to discover that even some of the strongest players out there have an incomplete understanding of this endgame. I thought that I knew basically all there is to know about this ending, but thanks to looking at some high-level games I also learned a few new things, even a few technical details that I've added as bonus sections to Sections 10 and 11.
The text you have before you is the accumulation of years of experience that I've gained as a chess-player and writer on and off the board. I hope that it will be your final answer to the question how to checkmate with knight and bishop.
Good luck!
Introduction: Should you study this endgame?
1. What people say about it
2. Strong players who botched the ending
3. My own experience
4. How to teach a checkmate procedure
5. Checkmating with two bishops
6. Complementing the bishop
7. Before we get started
8. Delivering checkmate from the Box
9. The Cage
10. The Barrier
11. The Safe Corner
12. Pushing the king to the edge
13. Centralise your pieces
14. Summary of the technique
15. Play better than the big boys & girls
16. Conclusion
17. Glossary
18. Bibliography
Introduction: Should you study this endgame?
If you take the views of many prolific writers and content creators, you might quickly get the feeling that it's not worth studying this endgame. The overall impression that you get is that it's an investment of a lot of time for only a very minimal return. The late IM Jeremy Silman, author of many iconic chess tomes such as How to Reassess Your Chess and The Amateur's Mind, and a personal hero of mine for saving the chess scene in Harry Potter and the Philosopher's Stone, consciously omitted checkmating with knight and bishop from his monumental endgame treatise Silman's Complete Endgame Course, because it's not likely to crop up all that often in your games:
I personally have had this position once in my whole career. That's right, just once! My good friend (and well-known chess author) IM John Watson has never had it at all! On top of that, Bishop and Knight vs. King is not at all easy to learn, and mastering it would take a significant chunk of time. Should the chess hopeful really spend many of the precious hours he's put aside for chess study learning an endgame that he'll achieve (at most) only once or twice in his lifetime?
- Jeremy Silman, Silman's Complete Endgame Course, "Part Five / Endgames for Class 'B' (1600-1799)"
To begin with, it's verifiably true that the endgame doesn't appear that often in practice. In my database, which consists of roughly two million games played by significantly strong players, the pawnless knight+bishop ending happened in only 440 games. This is less than one in 4000 games, and most players wouldn't play 4000 classical OTB games over the course of their lifetime.
So, should you study this endgame?
Let's start with the numerous caveats that have to be made with regards to Silman's statement. Silman's wish is for you to spend your time in a result-oriented and efficient way, and this is of course to be lauded. However, it must be observed that many players are likely to resign once they drop a piece, which decreases the likelihood of the endgame occurring. The notable exception to this is when the defender is higher rated. And especially these higher-rated players will be happy to be rewarded with an undeserved half point for their stubborn refusal to throw in the towel. If people refused to resign too quickly, it stands to reason that this endgame should crop up much more frequently.
Next: in case you find yourself having to play this endgame in real life and find yourself unable to succeed, you'll almost certainly encounter backlash in two forms. First of all, you'll be remembered by the public opinion as an amateur who can't pull it off. And second, after your first failure you'll be very likely to study it anyway. You could've saved yourself half a point by being on time, and you'll likely keep investing potential half points by not doing the work.
Of course, there are differences between players and what they want to get out of the game. Some people just play chess for fun and don't really care that much about spending their time mastering some of the more advanced procedures, while others are really strongly into improving. There's a spectrum of varying degrees, but ultimately everyone has an inclination towards one of the two (CC's Personality quiz opposes studious and playful), and both of these inclinations are completely valid.
Regardless of your inclination, studying the checkmating procedure with knight and bishop has something for everyone to benefit from. The playful one can pull it off as a party trick to show off and impress their friends. For the aspiring student, it's basically a matter of prestige to be able to do it, and knowing it might spare them an embarrassment that could follow them around for a lifetime.
As Naroditsky indicates, "you can feel more like a professional player," and that goes for anyone no matter where on the spectrum between playful and studious you find yourself.
Some masters have already gone back home red-faced with embarrassment after failing or showing a poor technique in the execution of this checkmate.
- Jesús de la Villa, 100 Endgames You Must Know, Chapter 13: "Other material relations"
I have seen how many chessplayers, including very strong ones, either missed learning this technique ar an appropriate time or had already forgotten it.
- Mark Dvoretsky, Dvoretsky's Endgame Manual, Chapter 14: "Other Material Relations"
To add a little extra weight to these two quotes: there are numerous grandmasters who have failed to pull it off. Some of them have even more reason to feel embarrassed because of this because of their legendary status with the community. And there are even some GMs who managed to add to their resume that they failed it twice.
The fact that it's covered in a book named 100 Endgames You Must Know should be the final nail in the coffin for this debate.
So, should you study this endgame?
With all the above points in the back of your head, my answer is a resounding yes.
Out of all the doable endgames against a lone king, the checkmating with knight and bishop is perhaps the most notorious one. It has a reputation of its own because of a combination of reasons, not the least of which is the reverence with which players and authors treat this endgame (1). The procedure requires a good degree of technical accuracy, with which even some very strong players have had troubles in the past (2). I have a personal history with this endgame, which I'll share in this blog as well (3).
Let's kick off with a list of quotes of the authors who have covered the checkmating procedure. The sentiment about the difficulty of the ending is hypnotically repeated:
This checkmate is very difficult, because the pieces lack harmonious teamwork.
- Siegbert Tarrasch, Das Schachspiel, "Das Endspiel" (quote translated from German)
One establishes that it's not easy to fulfil the rather arduous procedure.
- Max Euwe, Endspieltheorie und -praxis, Kapitel 1: "Das Mattsetzen des alleinigen Königs (aK)" (quote translated from German)
Indeed a very complicated checkmating, with all kinds of finesses like tempo moves and stalemate dangers, which already require a certain competence.
- Max Euwe, Schach von A-Z , Kapitel IV: "Der Angriff und die Kombination" (quote translated from German)
If you think winning with bishop and knight versus king is straightforward you might be in for a nasty shock when you reach it in a tournament game!
- Neil McDonald, Concise Chess Endings, Chapter 7: "Endgames without Pawns"
[T]his ending is quite difficult and not at all easy to master.
- Yasser Seirawan, Winning Chess Endings, Chapter One: "Basic Mates"
[T]he black sheep of all checkmates against a lone king. This ending has put many amateurs off because (...) it is not so easy in practical play.
- Jesús de la Villa, 100 Endgames You Must Know, Chapter 13: "Other material relations"
This is the only difficult mating combination. You may think it is easy, but it is not.
- Ian Snape, Chess Endings Made Simple, Chapter 1: "Pawnless Endgames"
This ending is quite tricky.
- Karsten Müller and Frank Lamprecht, Fundamental Chess Endings, Chapter 1: "The Basic Mates"
One does not simply checkmate with knight and bishop.
- Boromir, The Lord of the Rings: The Fellowship of the Ring
You get the drift by now. It's difficult, not easy, hard; it goes on and on. It almost feels like a fear campaign, and I'd only use this type of vocabulary if I'd actively wanted to discourage people to do something like chess. For the person who wishes to attempt it for the first time, it's not exactly reassuring. It serves to create a bogeyman out of the endgame, which leads to new players echoing the same rubbish.
Because that's what it is: utter nonsense.
Let's first establish some less discouraging vocabulary to refer to this endgame. It's challenging, fun, and rewarding on and off the board. If you can pull it off successfully and confidently, you might be able to gain the respect of your opponent and all those who watch you reel in the point.
2. Strong players who botched the ending
[E]ven titled players have occasionally struggled to win it, especially in quickplay finishes.
- Neil McDonald, Concise Chess Endings, Chapter 7
In the introduction I already mentioned that several GMs have botched this endgame. Of the 440 games with this ending, 44 ended in a draw. While the majority of these failed attempts happened in blitz games (29), there are several notable exceptions. Five of these examples happened in team matches; one even occurred in an Olympiad game.
Here I'll provide two very notable instances of strong players who botched the endgame.
Anna Ushenina
The first is a very famous example: then-World Women's Champion GM Anna Ushenina. She failed to bring home the full point in the FIDE Women's Grand Prix in May 2013. If the introduction hasn't convinced you that it's worth studying this endgame, then this example should put the question beyond any doubt. Make an effort to feel what she's going through in the video below and let that convince you:
You can feel that Anna Yuriyivna is going through. She feels that the whole world is watching her fail. She knows she'll be scorned for it, and she can feel the embarrassment and frustration building up.
The press conference must've been hell for Ushenina. Every time Ushenina looks up from her phone (you can even hear her typing), she has a "Shut up or I'll kill you" type of death stare that fits the emotion of wanting to vanish on the spot. She wants nothing to do with the press conference and is silent almost throughout. Throughout the video below, the only one who's able to smile at all was Olga Girya, the one who was outplayed and should've lost.
Nothing negative about Olga Alexandrovna: this is the sight of someone who's very relieved to have escaped with a draw. And nothing negative about Anna Yuriyivna here either: this isn't to bash her but rather to warn you. In her case I hope that if she ever encounters it, she can show that she knows how to do it and thereby redeem herself for it.
Hikaru Nakamura
Another person who you may or may not know is this individual called Hikaru Nakamura. He has been the very first chess-player to have ever reached 3400 in blitz on chess.com, and he's the current #2 on the World ranking of the FIDE rating list. Next to that, he's the Twitch-streamer with the highest number of followers (2M+).
Nakamura failed to deliver checkmate in a blitz game against Abdusattorov that happened live on stream. He claims that his brain isn't working, but I don't think that that's true. (Trigger warning: NSFW language in this clip):
The fact that he botched this endgame here was made rather worse by the fact that a few months prior, he scorned Polish CM Tomasz Jaskolka for not being able to pull it off.
A year prior, he made an attempt to explain the checkmating to his audience. But if you pay close attention, you might get the impression that even in this video he doesn't really know how it works:
And there are more videos of Nakamura openly displaying that he has very little clue how it works. At around 0:27 in the video below, he starts shouting Bd5 (which puts the bishop in the way of the king), looks very puzzled at Bd3 (which is in fact the right move, and Nakamura would have known this if he had in fact studied the endgame), then he starts to opt for Bc4 which is again the wrong move because the bishop is well-placed on b3:
To be fair, I did find an example in which he managed to pull off the win. However, he deliberately stacked the deck in his favour in this game for show:
What doesn't quite speak in his favour either is that this game was played all the way back in 2007. Since that moment he apparently never became any better at performing this endgame, and he became the laughing stock when he failed to get it done against Abdusattorov. This mishap was cited by Alireza Firouzja when he pulled it off against Denis Lazavik, and by WFM Alessia Santeramo when she urged you to study it in this YouTube Short and this YouTube tutorial.
I'm happy to share the view of his fans that Nakamura is a contemporary legendary chess-player, but in this particular endgame he's spectacularly failed to impress me so far. I hope that he will have actually studied the endgame by now so he doesn't have to put up such a facade for his viewers again.
How can I make this about me?
- Any narcissist in any conversation
When I was 11 years old, I was shown the following position at my chess club:
This picture showed me the perfect synergy of the two bishops: each covers squares of the colour that the other can't reach, and together they're able to form a solid barrier that the enemy king can never cross. I saved this position in my memory, set up my board at home, and tried to bring the position to its rightful conclusion. I managed to do it, albeit not in the most economic way possible.
Understanding this checkmating is very useful in itself, and has relevance for checkmating with knight and bishop. In Section 5 I'll be going over it briefly but sufficiently to show how it's done, and to illustrate some of the techniques that will come in handy for checkmating with knight and bishop.
I had been told by someone from my school that I wouldn't be able to checkmate with two knights and a bishop. I took that to mean that it was impossible unless the opponent would cooperate, and subsequently never attempted to try it out for myself.
When I was presented with some ancient textbooks when I was 14, I found out that I had been gaslit (although I didn't know that term back then). It became clear that not only was the checkmate indeed possible, it was doable even with a knight less than my schoolmate had tried to sell me. Sadly I've never been able to show that guy how it was done because by the time I learned the first principles of the procedure, that person had already left the school.
The first time I had it on the board in some form was in a youth team match. Although there were still some pawns left on the board, my opponent pressured me beforehand to try my strength at it and get it done. During the rapid game that I started this blog with, I thought back to this first encounter with the checkmating in a classical OTB game:
Save for the few times that I wanted to practice it (i.e.: show off that I can do it), I've had this endgame on the board in a classical OTB game two more times, one time as the defender. I managed to obtain the maximum result of two wins and a draw out of those three games; the game I drew was thanks to my opponent getting confused. I still have those two wins, but unfortunately I'm no longer able to retrieve the one in which I drew. There are plenty of examples in which stronger players botched the ending in a rather similar fashion, so it's not such a huge loss.
The one game in which I got my pawnless checkmating was a very special one because it was a game I played against my dearest coach. I lost the initial notation sheet, so I only have the fragment of the game that boiled down to it.
I had never studied this endgame with my coach at all, but he was very proud to see me get the job done. His remark after this game was one that has stuck with me for forever:
Pupils are just like monkeys. First you teach them how to climb, and then they toss the coconut in your face.
- My dearest coach
The procedure to checkmate with knight and bishop is fun and challenging, because it demands a few things. First of all, you have to learn how the knight moves. If Andrea Botez has contributed anything lasting to the world of chess, it's to put this question in the forefront of everyone's minds; if you're in doubt, you can read this blog about it.
Checkmating with knight and bishop is a rather more advanced procedure. It's as challenging as it is because a) it demands a fair deal of your skills to get your three pieces to work together, and b) you're bound to the 50 move rule so you can't afford to make too many mistakes. We'll go into detail with this coordination in Part III; here in Part II we'll familiarise ourselves with the fundamental basic knowledge that you'll need to pull it off. I'll present my way to teach checkmate methods (4), then apply it to checkmating with two bishops, which is a procedure that's vital to know for checkmating with knight and bishop (5). We'll then establish how we can compensate for the bishop's absent counterpart (6) and cover a few extra points that will come in handy before we get started (7).
For the purpose of consistency, let's establish right here that throughout the explanation:
- we assume the white pieces,
- we have a light-square bishop, and
- we want to deliver checkmate in the a8-corner.
4. How to teach a checkmate procedure
What we call the opening is often the end. And to make a checkmate is to make a beginning. The checkmate with knight and bishop is where we start from.
- T.S. Elliot
Let's say you're not one of the authors of Section 1 and you actually want to spark the interest of your students. When you teach new players how to play chess, you don't typically start with explaining very advanced concepts. You start with the basics (the board, the pieces, the mechanics of capturing, attack, defence, and check) before you explain checkmate. how does the board look? Then you teach how the rook moves, because the rook is the easiest and most straightforward (literally) piece to understand. You follow up with the bishop, then the queen, and then the rest of the pieces. You start easy and then slowly increase the level of difficulty.
Checkmate is a thing that you only teach after you've covered the movement of all of the pieces, attack, capturing, defence, and check. The very first checkmate that you teach is the Ladder Mate (or Staircase Mate), because it shows you a situation with overkill material against a lone king.
Your student will quickly be ready for their second checkmating technique: the checkmate with king and queen against king.
Whenever I'd teach checkmates, I'd start with showing the goal (checkmate), and then work my way backwards one step at a time. I'll do a quick breakdown:
Step 1: The checkmate.
Step 2: Deliver the checkmate:
Step 3: The king is trapped at the edge. Approach with your king:
Step 4: The pieces are out in the open. Use your queen only, and apply the "knight leap distance" sequence to force the king to the edge:
There are numerous benefits to learning checkmating in a retrograde fashion. You'll learn that the whole procedure is a series of different steps or phases, and that each new phase is marked by a key position which you have to connect to the next by a sequence of moves. This very basic form of schematic thinking will be useful later in your chess career, and also comes in handy later in this blog. But the most important thing is that at every step of the way, you'll know exactly what to work for. And you know that every move that you play should help you further your plans.
In teaching checkmating with other material configurations, it makes sense to apply this same retrograde method of teaching, and we'll use that method here to teach how to checkmate with knight and bishop.
5. Checkmating with two bishops
A bishop gains in value when its partner is still on the board since their actions complement each other.
- GM Bryan Smith, "The Art of the Two Bishops"
As indicated, we'll first cover the checkmating with two bishops. Checkmating the lone king can only happen in one of the corners of the board. It doesn't really matter which one: the most convenient corner will do.
Step 1: The checkmate
The checkmate in the diagram above is the archetypal checkmate with king and two bishops. Our king body-checks the enemy king, one bishop delivers check against the king in the corner, and the other bishop covers the escape route.
Step 2: Driving the king into the corner
In order to checkmate the king with two bishops, we have to escort the enemy king into one of the corners. At the same time we have to deny him the opportunity to escape. In gameviewer form, it looks like this:
The checkmating shows an important part of the procedure: the bishops alternate in denying the enemy king its escape routes.
Step 3: Driving the king to the edge of the board
You can see how greatly the two bishops assist each other in taking away escape routes when they're right next to one another.
Step 4: Aligning the bishops
Logically, the final step in the learning of this checkmate is to align the bishops such that they can set Step 3 in motion. This requires almost no example, but I'll provide one anyway for convenience sake:
To recapitulate in the order in which they occur on the board:
- Step 4: Align the bishops next to each other
- Step 3: Drive the king to the edge by taking away his squares.
- Step 2: Escort the king into the corner
- Step 1: Checkmate.
What else you need to know:
- Don't hang your bishops.
- Don't approach the target edge with the king closer than two ranks or files.
- Watch out for stalemate!
- Don't let the enemy king escape.
Botvinnik's arch-rival David Bronstein once thought 45 minutes after the opening moves 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6, before deciding on the exchange 4.Bxc6. Afterwards he was asked what made him think so long about this theoretically known continuation. Bronstein replied laconically that with the exchange of his bishop for the knight he had weakened 32 light squares, and that he had wanted to stop and think how he could deal with this weakening in the further course of the game!
- Herman Grooten, Chess Strategy for Club Players, Chapter 9: "Strong and weak squares"
Since the bishop can only cover squares of one colour, it always needs companions to chase and checkmate the enemy king. The most obvious allies to control squares of both colours would be the other bishop and the queen. In this endgame, however, we only have a knight and a king to cover for the bishop that we're missing.
Let's see how each of these pieces can cover for the opposite squares tho those the bishop can control.
The knight
By its way of moving, the knight has a few peculiarities that are worth noting. First of all, it alternates between light and dark squares with every move that it plays:
What follows from this is that a knight is unable to lose a tempo. It'll always take an even number of moves for the knight to land on the same square, and the enemy king can back-and-forth during this time.
Second, it can reach every square on the board. Have a look at this excerpt, taken from a training session between Daniil Dubov and Ian Nepomniachtchi:
N.B.: I took this pattern off the Wiki page on the knight tour.
The king
The king is the slowest moving piece, but it can reach every square on the board. Its use for this endgame is limited to close combat, but it can fulfil that role well enough.
How to combine the pieces with the bishop
We saw in Section 5 that two bishops can create a barrier that the enemy king is unable to cross. We can do the same with knight, bishop and king. Although the piece configuration is different, the essence of what we need to do is the same. The knight and king have to cover enough dark squares around the bishop's diagonal to make sure that the enemy king is unable to escape.
Let's look at the following position:
White's knight and king are placed such that they cover enough squares around the bishop's diagonal to prevent the enemy king from escaping. We'll come back to this position in Section 10, but for now, pay note that the knight is standing on the same colour as the bishop, and the king is on the opposite colour.
If we advance the pieces two ranks up, we can see that the knight and the bishop together can cover enough ground to deprive the enemy king of its freedom:
This piece configuration is very important for the checkmating with knight and bishop. We'll come back to it in Section 9. Suffice to say here that both Dvoretsky's Endgame Manual and 100 Endgames You Must Know use this exact position as a starting point for their discussion of the checkmate procedure (save for the position of the black king, but the relevant point is that he's locked in and can't escape).
I'll add another position for your convenience:
The king and the bishop keep the king trapped in the corner. We'll discuss this position in Section 8.
Checkmating with a bishop and a knight is easy, but not mechanical.
- Jesús de la Villa, 100 Endgames You Must Know, Chapter 13.
You read that right: over 4000 words and we haven't even started yet. But still this is important to get out of the way. As it is, I have some prior notions to share, along with several practical bits of advice that I'm happy to extend to help you in the practice of this endgame.
The quote from De la Villa is important to observe. The fact that it's not mechanical is the one thing that differentiates this endgame from checkmating with queen, rook or two bishops, and the only thing that may make it feel less straightforward. Instead, it requires that you coordinate your pieces well.
Necessary prior knowledge you need to know to learn this endgame
- How to checkmate with two bishops (see Section 5)
- How the knight moves
- The concept of Zugzwang
Schematic thinking
Schematic thinking is the method thinking in different phases. This method of thinking is important in many endgames, and it's especially the case in checkmating procedures.
Checkmating with knight and bishop also consists of several phases. Each phase is defined by a starting key position and a target key position, and it's your job to advance the endgame towards the next phase. Outside making sure that the enemy king can't escape from your clutches, there is hardly anything that you need to calculate.
Pattern recognition
Pattern recognition and calculation are not the same, and the two shouldn't be confused to mean the same thing. The ending is marked by a strong dose of pattern recognition, but requires almost no calculation.
- You can only force checkmate in a corner that the bishop can attack. Let's call this the Mate Corner; the other corner will be the Safe Corner.
- The enemy king wants to stay away from the Mate Corner. That's typically the centre, or the Safe Corner.
- The king and the knight should cover squares around the bishop's diagonal, as can be seen in the positions of Section 6. For this, the knight should be on the same colour square as the bishop.
- It's most useful to have the king on the outside of the diagonal:
Conducting your pieces
Knowing how to use your pieces is critical in bringing home the full point. So let's get the most important points down here:
- Don't move the knight too much!
The knight is best capable to fulfil its job as a substitute bishop by standing still, on the same colour as the bishop as indicated above. It should only move if it has to: to drive the king away from the wrong corner, to complete one of the constructions that we've seen in Section 6, or to deliver mate. In other cases, it stands still on the right square. - Beware of stalemate!
Most stalemates and king escapes occur because of players not knowing when to move the knight and when to leave it alone. - The bishop can make tempo moves.
The bishop is a long-range piece that can easily restore its original position. There are positions in which it's essential to put the opponent in Zugzwang, and a bishop move usually makes the most sense to accomplish this. - The king does most of the heavy weightlifting.
With the knight stationary on a central square and the bishop only able to cover half of the squares, it will be up to the king to do most of the bodychecking. - Most checks are unnecessary.
In many cases you don't need to give check. Your pieces have to cover the squares where the king wants to go to, not where he is. On the next turn he'll move anyway.
If it sounds like a lot to keep in mind: don't worry. We'll get this down when we go over the technique and the exercises.
We're ready to get started with the endgame, but before we do, I'll explain something about the methods that we'll use. As it is, there are essentially two known methods to win this endgame: Delétang's Triangles (henceforth referred to as Delétang), and the W-manoeuvre. I'll cover both of these methods as we go. There is a reason why I think that it's necessary to know about both these methods. The usefulness of knowing the W-manoeuvre is evidenced by the fact that virtually every treatise on this ending covers this. However, the method of Delétang is less well-known, even though it's arguably even more important.
In almost all coverages I've read on the checkmating with knight and bishop, the instructors mention that the defending king should turn towards the Safe Corner. They support this statement with the sole observation that the king can't be checkmated in that corner and mating will therefore take longer, and they then treat the entire matter properly addressed. What they invariably fail to explain or demonstrate is what you're supposed to do if the opponent hints at running towards the Mate Corner.
The consequence of this is that many people simply don't know about any other techniques than the W-manoeuvre. They falsely believe that they know how to do it, and then fail to pull it off once you refuse to comply to their prior knowledge. It's basically the same as surprising your opponent in the opening and getting them into unfamiliar terrain: suddenly your opponent has to show what they really understand about how the game goes. As became clear when I watched the clips from Section 2, Nakamura is one of these people who may have never heard of Delétang. And he's far from the only one:
To my knowledge, there are only a few sources that even mention Delétang: ChessNetwork's YouTube instruction, the Gambiter website (which is a huge mess and is likely a literal copy of the Wikipedia article), and De la Villa's 100 Endgames You Must Know. De la Villa doesn't explain the method, but does mention that it's very valuable. I can confirm this by pointing our that in the game at the top of this blog, I solely used Delétang to get the job done.
We'll work this endgame in retrograde phase order, as explained in Part II. First we'll assume that the king is already trapped in the vicinity of the Mate Corner. We'll familiarise ourselves with the final moves and the checkmate patterns that we can deliver from the Box (8). We'll then take it one step back and see how we can force the king into the Box from the Cage (9), followed by the transition from the Barrier into the Cage (10). Naturally, the enemy king isn't too happy to cooperate. If he must, he'll often seek refuge in the Safe Corner, from which we'll learn how to expel him (11). And if he can, the enemy king will run into the open field, to which we'll have to put an end (12). How to proceed will become clearest once we've centralised our pieces (13).
I've dissected the endgame into small subsections to help you understand the schematic thinking and to make the study of the endgame more easily digestible. I recommend that you study these different sections one at a time, and only proceed to the next section if you're confident that you understand it well enough.
8. Delivering checkmate from the Box
Life's like a Box of chocolates, you never know whether you get to checkmate with knight and bishop.
- Forrest Gump
We start with the easiest and most rewarding part of the entire procedure: finishing it off.
The starting position of this section shows the smallest of the three Delétang Triangles: a construction that I've dubbed "the Box" to distinguish it from the other two Triangles.
We see the enemy king safely trapped in the Mate Corner. The bishop covers the light-square diagonal, and the king covers enough dark squares around the diagonal to prevent the king from escaping. All we need to do is to take away his two final squares b8 and a8, and do so without stalemating the opponent. For this, both moves will have to come with check:
There is an important variation of the Box in which the bishop covers the escape square c8 from the other side. This position often comes about when you follow the W-manoeuvre, explained in Section 11:
So, the way this phase works is thus:
- We trap the king inside the Box.
- We take away the final two squares with check.
We are all living in cages with the door wide open, except black's king in the position above.
- George Lucas
The Cage is the blueprint position of how a knight and bishop can work together. White doesn't need the king to keep the enemy king trapped, as can be seen from the marked squares.
Note that the bishop is standing close to the edge of the board, and that the knight is on the same square colour as the bishop, close-by so that it can cover dark squares around the bishop's diagonal.
If you remember well, the Cage is the construction that Nakamura set up in his game against Leon Hoyos (see Section 2).
The plan in this phase is to transition the Cage configuration into the Box configuration. We'll be using the king to infringe upon black's king's playground:
In the final position of the excerpt above, the enemy king's space has already been significantly reduced. We've arrived at an important moment in the Delétang method, which can best be understood with the gameviewer below:
It's important to hammer home the point that the knight remained stationary throughout this entire section. The only exception for this was when the enemy king was already trapped inside the Box Triangle, and the king was able to take over the control of the important escape route.
Rhine's Stalemate Trap
Another fair warning why you shouldn't move the knight too much is a position that was discovered by Frederick Rhine in 2000:
To recapitulate what we did in this phase:
- First, we used the king to chip away at the enemy king's playground.
- Second, we moved the bishop onto the next diagonal when the enemy king was inside the Box.
- Third: we moved the knight to fulfil a new role, only when we knew that the Box was secure.
There is really no insurmountable barrier save your own inherent weakness of purpose and the one in the diagram above.
- Ralph Waldo Emerson
The Barrier is the largest of the three Delétang Triangles. Because the enemy king still has lots of room to move, it takes all three of our pieces to keep him trapped within the confines of this Triangle.
If you compare the Barrier position to the Cage position, you'll see that our minor pieces are two ranks further away from the Mate Corner. In this phase, our objective will thus be to move our pieces up those two ranks, so that we can apply the technique that we learned in Section 9. This process is slightly more complicated than what we did in Section 9. Nakamura didn't know how this phase goes, so if you can master this section, you'll be able to boast that as far as the public record goes, you're better at this ending than Hikaru Nakamura.
This is a method that ChessNetwork opted for in their YouTube tutorial.
The Snowplough
In the final position above, the enemy king has two squares available on the e-file: e8 and e7. He will bide his time for forever unless we force him out of there. Here you can use a technique that Chessable author laudic aptly calls the "Snowplough" technique:
All of these lines end up in the Cage, which was our objective in this Section.
To recapitulate how we transitioned from Barrier to Cage:
- We used our king and bishop to shrink the king's playground by means of the Snowplough method.
- When the enemy king was within the Cage, we closed the door by moving the bishop to the next diagonal.
- The knight remained stationary and only moved when it needed to take up a new position.
Bonus: Judit Polgár Teaches Chess
As a small bonus, let me present an excerpt from Judit Polgár, who is celebrating her 49th birthday at the time of me writing these words. She used a neat little trick to accelerate the process. What makes this even more fantastic is that in a blindfold game against Ljubomir Ljubojevic when she was 17 years of age. It goes against my advice to not move the knight too much, but it's certainly worth a look.
In the game, Polgár was playing with the black pieces, and this happened on the other side of the board with colours reversed. However, for the sake of consistency I've modified the position to match our piece configuration:
There's nothing more dangerous than a king in the Safe Corner.
- Roy Spim, "Roy and Hank Spim: Mosquito hunters" (Monty Python's Flying Circus, Episode 21: "Archaeology Today")
We've established that it's not possible to checkmate the enemy king in the corner that the bishop can't attack, and I've subsequently dubbed this the Safe Corner (a term I borrowed from De la Villa's 100 Endgames You Must Know). It follows logically that we have to drive the king out of the Safe Corner.
We can't drive the king away from the Safe Corner with our own king or with our bishop, so that's a job that our knight will have to perform:
After we've taken away the Safe Corner from the enemy king, we have two ways to proceed. The first is to transpose into the Barrier:
However, the second method is the most famous element of this ending, and in many cases the only thing that they've ever heard about this endgame at all:
The "W-manoeuvre"
The "W-manoeuvre" has received its name by the shape of the movement of the knight, although the only two sources that I can find who mention its W-shape are Fundamental Chess Endings and 100 Endgames You Must Know. As Averbakh mentioned in Chess Ending: Essential Knowledge, this pattern was already known in 1749 by Philidor. It's being taught by virtually every source on this checkmate pattern that I could find (with the exception of ChessNetwork's tutorial, which only explains Delétang, and the Gambiter web page, which explains both). For the complete list of sources that I consulted for this: see the Bibliography at the end. And credit where it's due: Nakamura also mentions it.
This W-manoeuvre, although not too difficult to remember, has seen a great number of flinches and fails. Anna Ushenina is perhaps the best known example of this, but notably GM Vidit Santosh Gujrathi also found himself having troubles remembering the key move in an OTB encounter. He later managed to correct his mistake and did pull off the win in the end, but by the closest margin possible: he was exactly one move away from exceeding the 50 move rule!
This section requires accuracy at a very specific moment. So if you choose to learn this method (and I highly recommend that you do), then pay attention:
We've successfully driven the king out of the Safe Corner, and he's forced to flee in the general direction of the Mate Corner. Let's proceed.
The king has left the edge. This is the precise moment at which many players flinch, including Ushenina. If you learn and remember this moment, and what to do, you'll be able to say that you'd have done better than a reigning world champion.
White has to play an absolute only move here:
From this final position, the process repeats.
If at the final position of the above fragment you noted that this is the alternate version of the Box of Section 8, with the bishop covering the escape square from the other side: well done! That's precisely it! I'll leave it up to you to find the checkmate in three moves.
Now, why was this called the W-manoeuvre?
That'll be because of the movements of the knight in order to arrive at the Mate Corner. Chesscom doesn't allow nice straight lines for knight leaps, but it'll do:
To recapitulate, we got the king out of the Safe Corner with the following steps:
- Cover the corner square with the knight
- Cover the adjacent square with the bishop
- Ushered the enemy king into the Barrier, or
- Used the W-manoeuvre to prevent the king from escaping and drive him into the Mate Corner
12. Pushing the king to the edge
I'm gonna run right to, to the edge with you
Where we can checkmate your lone king
- Lady Gaga, "The Edge of Glory"
We've already come a very long way. We've learned how to deliver checkmate, we know how to keep the enemy king trapped in the vicinity of the Mate Corner, chip away at the enemy king's terrain, and expel the enemy king out of the Safe Corner.
We've only a few questions left to ask and answer:
- How do we get the king to the edge of the board?
- What if the king "plays dumb" and attempts to flee to the right corner first?
Incidentally, you know the answer to the first question already. With the bishop and the knight in place, they already cover a lot of ground around the king, so you can use your king's bodycheck and your bishop's tempo moves to force the enemy king to give up the terrain. This is the one part that De la Villa describes as "not mechanical," so it's senseless to discuss every flavour of this position.
The second question, the importance of which I explained in the introduction to Part III, is especially important for your practical game. If you find yourself on the defending side, you can revert to this idea. Delétang isn't well-known, and you're fully entitled to try to exploit such gaps in your opponent's knowledge (and you can rest assured that if your opponent does know this method, they'd have likely won anyway). Run towards the Mate Corner for a move or two, then change course, and see if your opponent will get confused. It saved me half a point in the third game I mentioned above in Section 3.
We start this section with all our pieces centralised: the bishop and the knight on the same colour square, and our king pontifically on the opposite colour. Naturally, the enemy king will have to be somewhere, and this will very likely be near the Safe Corner. The reason for this is that if the king flees to the right corner first, you'll be able to trap him inside one of the Delétang Triangles (most often the Barrier, which we've studied in Section 10). From a central square, the knight will only be two leaps away from its position in any Barrier Triangle, which is more than enough time.
Let's get going with the position at the start of this section. Based on how you know our pieces should behave, hardly any move needs any specific explanation anymore: we trap the king inside the Barrier in case he tries to run, and we happily allow him into the wrong corner because we can flex our muscles.
What you'll hopefully be able to see in the short example above is that both methods are used, depending on where the enemy king chooses to run.
From the centralised position, we drive the king to the edge with this strategy:
- We can use our bishop and king as a Snowplough to force him to the edge.
- If the king runs towards the Mate Corner, we trap him by setting up the Barrier, and use Delétang's Method from that point on.
- If the king runs towards the Safe Corner, we push the king into the Safe Corner.
Occupying and controlling the centre in chess is not an end; it is a means.
- George Orwell, 1984
The final step is again a very easy one: we have to put our pieces in the centre. A few guidelines are sufficient to be able to do this right:
- The knight and bishop go to the same colour square, and the king goes to an opposite colour.
- The bishop controls the central squares from a distance first. The other pieces follow afterwards.
A short example:
If you spotted that on move 8, white could have gone 8.Bd5 and set up the Barrier: well done!
With this, we've covered everything that I know about checkmating with knight and bishop. This will be a sort of TLDR-section; in which I'll go over the entirety of the technique once more (14). I'll follow this up with a set of exercises (15), and end with my conclusion (16) as well as a glossary of terms (17) and the list of sources that I've used throughout this blog (18).
Perhaps the best test of a person's intelligence is their capacity for making a summary.
- Lytton Strachey
With the sheer volume of text that I produced for this blog, a TLDR would is quite necessary. So this would be the go-to. It may also serve as a quick review flyer, or a set of Flash Cards. This time, however, I'll go in chronological order.
Centralise your pieces:
- The knight and bishop go to the same colour square, and the king goes to an opposite colour.
- The bishop controls the central squares from a distance first. The other pieces follow afterwards.
Drive the king to the edge
- We can use our bishop and king as a Snowplough to force him to the edge.
- If the king runs towards the Mate Corner, we trap him by setting up the Barrier, and use Delétang's Method from that point on.
- If the king runs towards the Safe Corner, we push the king into the Safe Corner.
Drive the king out of the Safe Corner
- We cover the corner square with the knight
- We cover the adjacent square with the bishop
- We set up the Barrier, or
- We use the W-manoeuvre to drive the king into the Mate Corner
From Barrier to Cage:
- We used our king and bishop to shrink the king's playground by means of the Snowplough method.
- When the enemy king was within the Cage, we closed the door by moving the bishop to the next diagonal.
- The knight remained stationary and only moved when it needed to take up a new position.
From Cage to Box:
- First, we used the king to chip away at the enemy king's playground.
- Second, we moved the bishop onto the next diagonal when the enemy king was inside the Box.
- Third: we moved the knight to fulfil a new role, only when we knew that the Box was secure.
Checkmate within the Box:
- We trap the king inside the Box.
- We take away the final two squares with check.
A full example
It only fits to end this section with a full example. This example is taken from Tarrasch's Das Schachspiel:
Other tips:
- Be careful for stalemate
- The king has to do the heavy work
- The bishop can use tempo moves
- Don't use the knight too much
15. Play better than the big boys & girls
Even the greatest heroes have their flaws.
- Ken Burns
This section has three goals. The primary goal is to put your knowledge to the test in a playful form by solving a set of exercises. The second is to boost your ego and self-esteem because you'll be correcting some of the mistakes that titled players made. And lastly, doing the exercises in this section will hopefully encourage you to not to follow in their footsteps (at least as far as this endgame is concerned).
The exercises are placed in a loose order. I felt that it was rather senseless to take the 50 move rule into account with the exercises, because the point here is to find the right moves.
1: Ushenina's critical miss 1
For further practice:
There are plenty of resources to practice the endgame. The easiest tool is the ending drill on chesscom, linked below, but you can also set up a position and play it out against an engine. Practice it regularly,
https://www.chess.com/endgames/checkmates/bishop-and-knight-mate/challenge.
When I started this blog, I hadn't expected it to become as long as it ended up being, but there was too much good stuff to not include in the blog. I wanted to do a thorough job of it and make it the complete post on checkmating with knight and bishop that I believe it has become.
I hope that the length of this blog didn't hold you back, and that it was as enlightening, educative, and entertaining for you to read as it was for me to write. If anything, I hope that you'll be convinced that this ending is fun to learn and to play, that you know this ending rather much better now than you did before, and that you won't be intimidated by it from this point onwards. With this blog you'll have a reference source that you can always consult if the need arises.
If you've made it all the way through to the end: congratulations, and my sincere thanks.
Good luck!
50-move rule
The rule that the game will be declared a draw if for 50 consecutive moves no irreversible changes to the position (captures, pawn moves, en passant possibilities, castling rights) have been made.
Barrier
The largest of the Delétang Triangles. See Section 10.
Box
The smallest of the Delétang Triangles. See Section 8.
Cage
The middle of the Delétang Triangles. See Section 9.
Delétang Method
The method of driving the enemy king inside three Triangles (Barrier, Cage, Box) that become progressively smaller as the procedure advances. See Sections 8-10.
Mate Corner
The corner that the bishop can reach. The enemy king can only be checkmated in this corner. See Section 8.
Safe Corner
The corner that the bishop cannot reach. Checkmate cannot be forced upon the enemy king in the Safe Corner. See Section 11.
Snowplough
The method of using the bishop and king to drive the enemy king towards the edge of the board. A specific form of Zugzwang. See Section 10.
Stalemate
What happens if you're not careful.
Tempo move
A move that aims to put the opponent in Zugzwang.
W-manoeuvre
A knight manoeuvre to force the enemy king outside the Safe Corner and into the Mate Corner. See Section 11.
Zugzwang
The situation in which the side to move has no good moves and can only worsen their position. Used as an attacking device throughout the checkmating procedure.
Books:
Yuri Averbakh, Chess Ending: Essential Knowledge
Mark Dvoretsky, Dvoretsky's Endgame Manual
Max Euwe, Endspieltheorie und -praxis
Max Euwe, Schach von A-Z
Neil McDonald, Concise Chess Endings
Karsten Müller & Frank Lamprecht, Fundamental Chess Endings
John Nunn, Understanding Chess Endgames
Yasser Seirawan, Winning Chess Endings
Ian Snape, Chess Endings Made Simple
Siegbert Tarrasch, Das Schachspiel: Systematisches Lehrbuch für Anfänger und Geübte
Jesús de la Villa, 100 Endgames You Must Know
Jesús de la Villa, The 100 Endgames You Must Know Workbook
YouTube:
https://www.youtube.com/watch?v=oRK7XLhGz_c
https://www.youtube.com/watch?v=YFF5ibgB6eA
https://www.youtube.com/watch?v=pzAHQp20-gY
https://www.youtube.com/watch?v=sn2kiHh7s9w
https://www.youtube.com/watch?v=jZwiKHJKt54
https://www.youtube.com/watch?v=OkC37JlWzCc
https://www.youtube.com/watch?v=-BSEIhDsT9E
https://www.youtube.com/shorts/SpjpLpeEk1Q
https://www.youtube.com/watch?v=7QY-JJcRDqg
https://www.youtube.com/watch?v=r3EqM17jvOc
https://www.youtube.com/watch?v=aCQ0yUSWey4
Other online sources:
https://www.chess.com/blog/nova-stone/do-the-pawns-really-go-first-in-chess
https://www.chesspersonality.com/
https://www.chess.com/blog/learn-chess/how-knights-move-at-different-elos
https://www.chess.com/article/view/the-art-of-the-two-bishops
https://en.wikipedia.org/wiki/Knight%27s_tour
https://gambiter.com/chess/endgame/Bishop_and_knight_checkmate.html
https://en.wikipedia.org/wiki/Bishop_and_knight_checkmate
https://www.chessable.com/profile/laudic/
https://www.chessable.com/course/2033/
https://www.chess.com/endgames/checkmates/bishop-and-knight-mate/challenge
