Bishop and Knight Mate — the Missing Part

Anyone who has studied chess endgames has probably seen the characteristic W-manoeuvre of the knight in the bishop-and-knight versus king endgame. What almost every explanation glosses over, however, is how to get into the starting position for that manoeuvre. Usually, this is dismissed with a casual "drive the enemy king into the corner". This article is about that missing part: how to reach the starting position in the first place.

The Typical Mate

The typical bishop-and-knight mate after finishing the W-manoeuvre looks like this:

Other mates are possible, if the attacking side did not completely follow the W-manoeuvre, for example this one:

The knight can also give check from a6.

Then there is also this mate:

Again, the knight can stand on a6 instead. The same is true for the king, but the mate is then only possible, if the other side helps by moving into the corner.

All positions have in common that the mate can only be forced in a corner controlled by the bishop. White has a light-squared bishop here, so the black king must eventually be driven to either a8 or h1.

The black king's defensive strategy is to stay as close to the centre of the board as possible. Once that is no longer an option, it tries to head for the "wrong" corner — h8 or a1 here — where mate cannot be forced.

The Starting Position for the Mating Technique

Most explanations of this endgame start from the following position:

The bishop does not have to be on f5. It can stand on any square from which it can reach h7, taking g8 away from the king on the following move.

The knight then performs the familiar W-manoeuvre, while the white king stays on the 6th rank and advances step by step towards b6.

But how do we reach this starting position?

In fact, it is easiest to approach the problem backwards. We need to ask whether there is a position from which the starting position of the mating technique can be forced. There is — and I am going to call it the revolving door.

The Revolving Door

The revolving door looks like this:

The black king is trapped because it can never reach either of the two exits, e8 or h5. As soon as it approaches one of them, one of the two minor pieces steps in and closes the gap.

In theory, the knight can do this as well, but the bishop makes things much easier. Wherever the bishop happens to be, it can always reach a square from which it controls one of the escape squares in a single move. This is, of course, assuming that the knight is not in the way.

Once one escape square has been blocked, the enemy king needs at least three moves to reach the other one. That gives the attacking side two moves to manoeuvre the knight into position — f7 here.

First Problem Case: Bishop on b1

If the bishop happens to be on b1, with White to move, the best way to continue is not quite so obvious:

Normally, we want to put the bishop on the a4-e8 diagonal to close the escape route. From b1, however, that diagonal is inaccessible.

A computer will actually play Ba2 here, allowing the king to escape. With best play, that reaches mate four moves faster than my suggestion. The catch is that the faster line is so complicated that it is probably something only a computer would find over the board.

My suggestion is the much simpler Bg6:

This plugs the hole, and we can continue with our plan of manoeuvring the knight to f7.

Second Problem Case: Bishop on a2

Above, I said that the bishop can close the escape route on e8 from any square in a single move. In principle, that is also true when the bishop is on a2, again with White to move:

The move that keeps the king trapped in the revolving door is Bf7:

The bishop does indeed seal off e8, but at the cost of a serious blunder: the position is stalemate. So that clearly will not do.

The same problem squares arise if the black king tries to escape via h6. The roles are simply reversed.

In practice, these cases are mostly theoretical. For tactical reasons, the attacking side will generally avoid placing the bishop on the edge of the board in the first place.

Rotating the Position

Most players will prefer to drive the king along the back rank rather than along the a- or h-file. Fortunately, that is under our control. The following position can be rotated into the "right" orientation with a simple manoeuvre:

The knight reaches the desired square f7 via e5. From there it also controls h6. All the bishop has to do now is cover h7, leaving the king with no square other than f8.

Whether you want to spend these five moves to reach a more familiar position, or would rather learn how to finish the job from the rotated position as well, is up to you.

Changing the Move

Sometimes you reach the starting position with Black to move. Changing the move is easy:

Whatever direction the black king chooses, the bishop follows it, effectively taking the opposition. This forces the black king to step back in front of the knight. We then use the bishop to stop it escaping again in the same direction.

Eventually — more precisely, after three moves — it is White to move, and Black has only f8. White then plays Bf5, and Black is forced by zugzwang to move to f8.

On the first move, the bishop can also move to any other square that keeps the black king from escaping, but thinking of this as "taking the opposition" makes the idea easy to remember.

Now let's practice this against Stockfish. The goal is to reach one of the starting positions: put your knight directly in front of the enemy king and place the bishop so that it can drive the king out of the corner on the next move:

Avoiding Stalemate

Stalemate traps are particularly nasty in the bishop-and-knight versus king endgame because it is not always obvious at a glance which squares the enemy king still has available.

In the following position, you might be tempted to play 1. ♘b4??, aiming to bring the knight to c2.

That would be a fatal mistake, because Black would be stalemated:

The problem is that the bishop points into the revolving door, taking b1 away from the king. That gives us a simple rule for avoiding stalemate in this phase: once the king is trapped in the revolving door, the bishop must not point towards the corner.

So 1. ♗e2 would have been the safer move, leaving the king an escape square before we start manoeuvring the knight towards one of the target squares b3 or c2.

Objectively, 1. ♘e3 is best, of course, because the knight can then reach c2 on the very next move without giving stalemate. But with 1. ♗e2, you know for certain that stalemate cannot occur.

Building the Revolving Door

What comes immediately before the revolving door? Is there a position from which we can force it with a simple manoeuvre?

Let's look at the basic shape of the revolving door once more, this time without the knight and bishop:

With White to move, the black king can only have come from e8 or g8, because every other possible escape square is controlled by the white king.

If the black king came from e8, there must have been some reason why it went into the corner instead of escaping via d8 or d7. The position might have looked like this:

Because the two escape squares d8 and d7 are different colours, both the knight and the bishop must have contributed. Neither piece can control squares of both colours at the same time.

And what if the black king came from g8? Then it was already trapped. That line therefore gets us nowhere.

This leads to an important conclusion: the revolving door can only be built with the help of both minor pieces, bishop and knight. The long-range bishop can influence the king from a distance, but the knight has to be close to the action to have any influence at all.

Two rooks can trivially drive the enemy king to the edge on their own (staircase mate). Two bishops can do the same with the help of their king. But with king, bishop and knight, there is no comparably intuitive technique.

So there is no easily reachable position from which the revolving door can simply be forced. But the preceding analysis is still useful. In practice, against a strong opponent, the starting position for the mating technique will very often be reached through the revolving door. It is therefore worth storing the revolving door in your pattern-recognition toolbox as an immediate winning position.

Of course, you may already reach a position in which the W-manoeuvre works on the way to the revolving door. In that case, there is obviously no point in building the revolving door first. You will only start recognising such positions intuitively as your playing strength improves. And since your opponents will usually be stronger too, they will tend to avoid these positions themselves. Since you can only win or lose one point in a chess game, however, it makes sense to focus on the forced winning method against best defence.

Centralising the Pieces

Let's approach the problem from the other direction instead, starting from the worst possible position.

Our pieces are sitting uselessly in the corner, far from the action, while the black king occupies the deserted centre. We want to change that.

The first goal is simply to bring all three pieces into the centre (e4, e5, d4, d5) and then see which direction the enemy king chooses when it is forced to move.

This should be straightforward, especially because the engine in the diagram above is quite happy to give up the centre. Human opponents may not be quite so cooperative.

When driving the king away, we can make use of a simple principle that applies to all elementary endgames, but is especially valuable in bishop-and-knight versus king: don't give check — use zugzwang instead.

The white king already controls e4 and e5. We could now play Be3+ or Bf3+, adding d5 to the list. But that is the square the black king currently occupies, so it has to leave it anyway.

It is more effective to use Nf3 or Ne2 to control the square to which the black king can still move. Because of zugzwang, it has to vacate d5, allowing the white king to occupy the centre with Ke4 or Ke5.

Of all the fundamental piece endgames, bishop and knight versus king is the hardest because these two pieces together control fewer squares than any other mating force. That is why it is especially important not to waste tempi checking the king off a square that it will have to leave anyway.

Some people recommend placing the pieces in the centre in such a way that the bishop and knight occupy squares of the same colour:

Now, black can really make progress with 1. ♔f5. But only, if the black king has moved into the same quarter of the board as the white king in the first place, and that cannot be easily forced. Black can instead try to move into the same quarter as the knight:

In this position, there is no simple king move that makes progress. One of the pieces has to leave the centre.

With the help of an endgame tablebase, you will see that the second position is actually worse for black than the first position. But white has to find the faster mate (faster by two moves), and not many humans will be able to do so with ease.

Take-away: Do not waste time targeting a specific setup of your pieces in the centre.

Driving the King to the Corner

Now we come to the hardest part: driving the enemy king into a corner.

With a light-squared bishop, the ideal corners are a8 and h1, where we can deliver mate directly. The other corners, a1 and h8, are the "wrong" corners; there we have to build the revolving door and then force the king along the edge into one of the good corners.

The rule "the enemy king will try to escape to the corner the bishop does not control" is repeated so often that a strong defence often consists simply of doing the opposite and heading for the other corner. In many positions, that is actually the best defence, as in the following example:

This position arises from the basic setup after 1. ♗h7 ♔e8 2. ♘e5, and is probably familiar to anyone who knows the W-manoeuvre.

The black king has only two moves: 2... ♔d8 and 2... ♔f8. Counter- intuitively, 2... ♔d8, heading towards the corner controlled by the bishop, is the tougher defence because it opens an escape route via c7.

The king can actually escape as far as c6, but bishop, knight and zugzwang then combine to drive it back to the back rank.

Opposition

There is no simple, mechanical system for driving the king to the edge, so you need a mixture of calculation and pattern recognition. The key is to recognise positions in which the enemy king is forced to retreat, or at least prevented from moving back towards the centre.

The most obvious such pattern is opposition.

To create opposition, or any of the other patterns we will see, our king should never be more than two squares away from the enemy king. Keeping that distance is always a priority.

When our king stands directly opposite the enemy king, the latter cannot move towards us on the next move. That is useful most of the times, when driving the king towards the edge. One obvious exception arises, when maintaining the opposition would lead to move repetition. Another exception is described in the section about the wall below.

The Scissors

The simplest pattern that actually pushes the king backwards is what I call the scissors. Daniel Naroditsky used the more technical term piece-assisted opposition for the same idea:

The black king is caught between the blades of a pair of scissors and is forced one rank backwards.

Important: if you force the king into the scissors on the edge of the board, it is stalemate!

If the black king moves diagonally, the white king simply follows. For example:

After 1... ♔d7, this exact move does not work because the bishop is in the way. The white king should still follow by surrounding the bishop, choosing one side or the other.

In either case, we arrive at the next pattern: the wall. The resulting positions differ according to whether the two kings are in opposition.

The Wall

The king and bishop stand side by side, creating a wall of four controlled squares in front of them.

The Wall with Opposition

With the kings in opposition, the black king will usually have two possible escape routes.

The route via f8 and g7 does not work, at least not immediately: 1... ♔f8 2. ♔f6, and the hole closes again.

Important: this is not yet a revolving door, because Black is to move and can still escape via d8. Instead of 2. ♔f6, 2. ♘f5 and 2. ♘h5 also work.

Most players would therefore choose 1... ♔d7, intending to escape via c7 and b6. Which of the two defensive options is better depends on the exact position, particularly on where the knight is placed.

The wall with opposition arises naturally whenever the attacking side sets up the scissors and the enemy king approaches the edge diagonally.

The Wall without Opposition

This version occurs when the defending king steps out of the scissors and the attacking king has to follow it around the bishop.

The situation is essentially the same as with opposition. The difference is that the black king is now closer to the escape square on the bishop's side.

This is something the attacking side needs to consider when deciding which way to go around the bishop. The knight must be able to close the escape route, and that is usually easier if the attacking king goes around the bishop on the side away from the knight.

As a rule of thumb, try to build as broad a barrier as possible in front of the enemy king, taking away as many squares as you can.

The other escape route is usually unattractive. After 1... ♔c7 2. ♗c6, the black king is trapped in the scissors again. After 1... ♔c8 2. ♗c6, it is already severely restricted.

Ironically, the natural-looking 2. ♔c6, maintaining the opposition, is less effective: after 1... ♔c8 2. ♔c6 ♔d8 3. ♔d6 ♔e8, White has a hard time trapping the king again.

The Umbrella

This pattern can also be a powerful weapon:

The pattern of squares controlled by the king and bishop looks a bit like an umbrella blown inside out by the wind, with the king and bishop forming the handle.

Together, they build a five-square wall in front of the enemy king. On each flank, there is a potential breakout gap, but this can often be plugged by the knight. If you shift the position sideways closer to the edge, one side is even completely closed off.

Here, there are two possible continuations: 1... ♔f7 2. ♗f5 and 1... ♔d7 2. ♗d5. So the white bishop simply follows the black king, and you end up back at the wall we already looked at.

If the black king already has an eye on one of the two gaps, White will usually try to plug the hole with the knight:

Here, 1... ♔c7 2. ♘c4 could follow. If the knight cannot seal the gap, you have to look for another option.

Despite the impressive barricade built by the king and bishop, however, you should not forget that — just like with the wall — the opponent's king cannot necessarily be pushed further towards the edge, at least not immediately.

Shouldering

In the following position, White has built the wall, but the black king is threatening to escape on the bishop's side:

White cannot actually prevent 1... ♔g5 here, because the knight is too far away to intervene. But whenever the black king heads for this escape route, the right response is shouldering, here with 1. ♔d5:

Shouldering means placing the king diagonally next to the bishop.

If the black king now tries to escape with 1... ♔g5, heading via f4 towards e3 or g3, we simply play 2. ♔e5, and the wall is back:

Originally, the king was two squares from the edge. Now it is only one square away.

1... ♔e7, 1... ♔f7 and 1... ♔g7 would all have the same effect: the black king has been pushed closer to the edge.

There are, of course, other configurations in which you can cut off the enemy king. But the scissors, shouldering, umbrella and the wall are easy to recognise and all highly effective.

I will not explain the W-manoeuvre itself. There are already countless guides to it. But you can practise everything we have covered so far against the engine:

Reload the page to get a new random position.

If you want to practise building the revolving door specifically, use the following exercise. The task is considered complete as soon as the revolving door has been reached:

There is one caveat, though: this is not an especially good endgame to train against an engine. The engine always chooses the best move, and that move is much more likely to match our expectations — namely, to allow itself to be driven into the "wrong" corner fairly readily, giving us the chance to build the revolving door.

So it is worth practising this endgame against humans as well — or, if necessary, against yourself. The aim is to learn how to convert the position even when the defence is less than optimal.

Conclusion

With king, bishop and knight, the basic route to checkmate is:

1. Centralise your pieces.
2. Use the scissors, shouldering and the wall to drive the enemy king towards the edge.
3. Use the same patterns to drive the king into a corner.
4. If necessary, build the revolving door and use the W-manoeuvre to drive the king into the corner controlled by the bishop.
5. Checkmate.

Step 2 is the hardest. A simple checklist helps:

1. Bring your king within two squares of the enemy king.
2. Opposition? Except when it causes repetition or leads to an easy escape.
3. Scissors?
4. Shouldering?
5. Wall or umbrella?

If none of these ideas works, it is almost always best to improve the knight's position. Sooner or later, this approach should allow you to drive the enemy king into a corner.

The implementation of the interactive chess diagrams on this page is based on the library cm-chessboard.