Bishop-and-knight mate, queen against pawn, fortresses

White has king, bishop and knight; Black has a lone king. There is enough material to mate, but mating is not easy: a bishop-and-knight mate is only possible in a corner of the bishop's colour, and getting there can take more than thirty moves. In this position the black king is already close to the right corner.

This ending is rare, but it contains all the main skills of the endgame: the pieces working together, driving the king back, exact counting. And the fifty-move rule applies: if fifty moves pass with no capture and no pawn move, the opponent can claim a draw. So the technique has to be known in advance. In this chapter we also look at other endings that are hard to solve at the board: queen or rook against a pawn, and fortresses.

The bishop-and-knight mate

Bishop and knight mate only in a corner of the same colour as the bishop. In a corner of the other colour the mate cannot be forced: the bishop does not cover the corner square, and the enemy king escapes the net. So the technique has two parts. First, king, bishop and knight together drive the enemy king to the edge of the board. Then, if it has ended up in the “wrong” corner, it is chased along the edge to the right one.

The first part resembles the queen or rook mate from the chapter “First mates”. The attacking king goes to the centre, towards the enemy king, and stands opposite it. Bishop and knight take away the squares it would like to go to. Step by step the net tightens until the enemy king is at the edge. There is no need to hurry with checks: a check that takes no squares away only wastes time.

The second part is the hardest. The enemy king heads for the wrong corner, and at the edge its way back has to be cut off all the time. The classic technique is called the “W” manoeuvre: the knight travels over squares that trace the letter W on the board and, together with the bishop, keeps the king on the edge. All this time the attacking king stands opposite the enemy king and stops it from returning to the centre.

The key to this ending is coordination. The bishop covers squares of one colour, the knight changes the colour of its square with every move, the king covers the squares around itself. None of the pieces can manage alone: together they build a net in which the enemy king has fewer and fewer squares. If the pieces work separately, the enemy king breaks out to the centre, and everything starts again.

Danger lurks at the very end too. When the enemy king is squeezed into the corner, it has one or two squares left, and a careless move easily takes away the last one. If there is no check at that moment, it is stalemate. So on the final moves, check before every move: does the enemy king still have at least one move?

Are fifty moves enough? From the hardest position mate takes 33 moves with exact play, so there is a margin. But it is small: if you wander about with the pieces without a plan, the moves will run out before the mate. So the technique has to be known in advance: there is no time to invent it at the board.

Queen against pawn

Another ending you need to know is queen against a pawn on the seventh rank. The opponent's pawn is one step from promotion, their king is next to it, and your king is far away. It seems the queen wins easily. But the result depends on which file the pawn is on. This ending often arises after a pawn race: one side queens first, and the opponent's pawn is already on the seventh rank.

Against a centre pawn or a knight pawn the queen wins. The method: with checks and attacks on the pawn the queen comes closer and forces the enemy king onto the promotion square, in front of its own pawn. While the king stands there, the pawn cannot move, and your king has one free move to come closer. So, move by move, the king approaches, until together with the queen it wins the pawn or mates.

Against a bishop pawn or a rook pawn this method does not work. Against a bishop pawn the enemy king goes into the corner instead of the promotion square, and taking the pawn gives stalemate. Against a rook pawn the king stands in the corner in front of the pawn with no moves, and any White move without check gives stalemate. With a pawn on the seventh rank on the c- or f-file, or the a- or h-file, and the attacking king far away, the result is usually a draw. A win is possible only if your own king can get close enough in time.

How close? That depends on the exact position of the pieces, and there is no general rule. Sometimes a single free move is enough for the king to get next to the pawn, and then the queen wins even against a bishop pawn. So in such a position calculate concretely: the general rule will not help here.

If the opponent's pawn is still on the sixth rank or further from the promotion square, the queen usually wins whatever the file: it has time to stop the pawn and bring up the king. What is dangerous is a pawn already one step from promotion and supported by its king.

See how to save the game against a bishop pawn. The white queen attacks the c2-pawn, but the black king heads for the corner: if the queen takes the pawn, it is stalemate.

The rule is simple: against a centre pawn or a knight pawn the queen wins; against a bishop pawn or a rook pawn it is usually a draw if the attacking king is far away. Before you give up a piece to get a pawn to the seventh rank, remember which file it is on: whether the game is won or drawn may depend on it.

Rook against pawn

A similar question is settled in the ending of rook against pawn. The rook is stronger than the pawn, but if the pawn has advanced far with its king's support while the attacking king is far away, any result is possible: a win for the rook, a draw, even a win for the pawn. Here counting moves decides.

The rook wins easily if the attacking king gets in front of the pawn in time: then the rook picks up the pawn, and all that is left is the rook mate from the chapter “First mates”. If the king is too late, the rook must cut off the enemy king from the pawn and attack the pawn from behind. The defending side, on the contrary, keeps its king next to the pawn and tries to stop the rook from either cutting off the king or getting behind the pawn.

This ending has an unexpected trick too: promoting to something other than a queen. If a queen on the promotion square is attacked at once or gives stalemate, a knight sometimes saves the game. Such cases were covered in the chapter “The pawn”. There is one rule: before promoting, look at what happens after it.

Fortresses

Extra material does not always win. Sometimes the defending side builds a position that cannot be broken, however hard the opponent tries. Such a position is called a fortress. A fortress does not demand precise play from the defender: it is enough not to dismantle it yourself. The word comes from warfare: such a position falls neither to an assault nor to a long siege.

The best-known example is the wrong bishop. White has a bishop and a rook pawn, but the promotion square is of a different colour from the bishop. If the black king has reached the corner in front of the pawn, it cannot be driven out: the bishop does not cover the corner square, and the king cannot force the enemy king out of the corner without stalemate. The extra bishop and pawn do not win.

The black king moves between h8 and g8 or h7, and White can do nothing. If the pawn goes to h7, the king stands on h8, and White is left only with stalemate. So when defending against a rook pawn with a bishop, check the colour of the promotion square first: if the bishop does not cover it, head for the corner.

If the bishop does cover the promotion square, it is the other way round: the enemy king is driven out of the corner, and the pawn queens. So with a rook pawn the colour of the bishop decides the result before the pawn has even moved. The attacker should think in advance about which bishop to keep when trading: with the “right” bishop the rook pawn wins, with the “wrong” one it often does not.

A similar fortress occurs with pawns. If all the pawns are blocked and the kings cannot get past the squares covered by the enemy pawns, neither side can win. The extreme case, with pawns locked against each other across the whole board, was covered in the chapter “Castling and draws”: such a position is dead, and the game is drawn at once.

There are fortresses with pieces too. A rook and a pawn sometimes hold against a queen if the rook is protected by the pawn and the king stands nearby. A bishop or a knight can hold off the enemy king and pawns if the pawns stand on squares the piece controls. The common sign of a fortress: the attacker has no way to create a new weakness or to break through with the king.

Engines find fortresses hard. An engine sees the extra material and shows a big advantage, but however long it searches, it finds no way to convert it. If the engine's evaluation does not change for many moves in a row and the position goes nowhere, you may be looking at a fortress. For example, if in a wrong-bishop position the black king is already in the corner and the white king is still on e1, this course's engine rates it at about five pawns in White's favour. Theory has long known that it is a draw.

Knowing fortresses is useful to both sides. The defender looks for them when material is short: sometimes it is better to give up a pawn or even a piece and reach a position that cannot be broken. The attacker, on the contrary, must notice in time that the opponent is building a fortress and stop them while that is still possible. A pawn pushed one square earlier, or a piece not traded at the right time, often decides whether there will be a fortress or not.

How do you train these endings? Learn the bishop-and-knight mate once against the engine, then repeat it every few months so as not to forget the technique. Play queen against pawn for both sides with pawns on different files: the rule will stick by itself. And look for fortresses in your own games: in every lost ending, ask whether there was a way to build a position the opponent could not have broken.

The rules of this chapter in short. The bishop-and-knight mate happens only in a corner of the bishop's colour, and the technique must be known in advance. The queen beats a centre pawn or a knight pawn on the seventh rank, while against a bishop pawn or a rook pawn with the attacking king far away it is usually a draw because of stalemate. Rook against pawn is a matter of counting moves. A fortress saves you when material is short: look for one in defence and stop one being built when you attack.

What's next

The endgame part is over. The last part of the course is about mastery: how to calculate variations, how to review your own games and how to play in tournaments. We begin with calculation — the next chapter.