Elementary Endgames in Chess

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Elementary Endgames in Chess

Some chess endgames are known to be won or drawn. Here are the simplest.

This page covers two types of elementary endgames:-

elementary checkmates and
elementary King and Pawn vs. King.
The elementary checkmates are Pawnless endgames where the strong side has just enough material to force checkmate. As long as there are no immediate captures, it does not matter where the pieces start. The strong side can always deliver mate by following a simple plan.
King and Queen vs. King

This is always an easy win. The King and Queen work together to force the lone King to the side of the board, then give checkmate. In the diagrammed position, White on the move can checkmate with Qa8+ or Qg8+. If Black is on the move, White checkmates with 1...Kc8 2.Qa8+ or 1...Ke8 2.Qg8+.
King and Rook vs. King

This is also an easy win. The King and Rook force the opposing King to the side of the board. In the diagrammed position, White mates with Rh8. If Black is on the move, White mates with 1...Kc8 2.Rb5 Kd8 3.Rb8+ or 1...Ke8 2.Rf5 Kd8 3.Rf8+.
King and two Bishops vs. King

Although slightly more difficult than the preceding mates, this is also an easy win. The King and Bishops first force the opponent's King to the side of the board, then into the corner, where mate follows. In the diagrammed position, White plays 1.Be3+ Kh7 2.Bf5+ Kh8 3.Bd4 mate. The action of the two Bishops on adjacent diagonals creates a barrier which the opposing King cannot cross.
King, Bishop, and Knight vs. King

Strictly speaking, this is not an elementary mate, because it is considerably more difficult to execute than the preceding mates. The main difficulty is that the worst case positions bump into the 50 move rule.
The winning plan is threefold. First, the King, Bishop, and Knight force the lone King to the side of the board. Then, the stronger side forces the King into the corner -- the best defense is for the King to flee to a corner that the Bishop can't attack. Finally, the pieces force the King into a corner that the Bishop can attack.
In the diagrammed position, the White Bishop travels on the white squares, so the Black King has been forced into a white-squared corner. White mates with 1.Kc7 Ka8 2.Bb7+ Ka7 3.Nc6+ (or 3.Nc8+).
In all of the above elementary mates, the strong side must be careful not to stalemate the lone King. In the last example, 2.Nc6 would have been a blunder because it stalemates Black.
Insufficient mating material

As we saw in the page on draws, King and Knight -or- King and Bishop cannot checkmate a lone King.
The situation with King and two Knights is more complicated. There are certain positions where the King and Knights checkmate the lone King, but to reach these positions the strong side must allow an intermediate position where the lone King is stalemated. This means that the strong side can force a win only if the weak side has a Pawn, where stalemate is no longer a possibility.
The Pawn's Square

The question often arises whether a King can catch a Pawn which is racing to promotion. There is a simple trick, known as the 'The Rule of the Square', to answer this question without calculating any variations.

The pawn's square is visualized by first drawing a diagonal line from the Pawn to the Pawn's promotion rank. The diagonal creates an imaginary square, half of which is shown in the diagram. If the opposing King is in this square, the King can catch the Pawn. If the King is not in the square, the chase is hopeless.
Can the Black King catch the White Pawn in the diagram? It depends on who is to move. If Black is to move, 1...Kg4 puts the King into the square and Black will catch the Pawn. The King's other legal moves would be a serious mistake. If White is to move, 1.c5 creates a new diagonal, where the corner of the square is on f5. Since the Black King cannot enter the square, the Pawn will Queen and the game will become an elementary endgame of King and Queen vs. King.
King and Pawn vs. King

The last elementary endgame is King and Pawn vs. King where the Pawn is supported by its King and is about to promote. The lone King guards the promotion square, making a last-ditch attempt to stop the Pawn.

In the diagrammed position, the result of the game depends on who is to move. White to move has no better than 1.e7+ Ke8 2.Ke6, where Black is stalemated. Black to move has no better than 1...Ke8 2.e7 Kf7 3.Kd7, where the Pawn will promote and the game will end with an elementary mate.

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Elementary Endgames in Chess
Some chess endgames are known to be won or drawn. Here are the simplest.
This page covers two types of elementary endgames:- elementary checkmates and elementary King and Pawn vs. King. The elementary checkmates are Pawnless endgames where the strong side has just enough material to force checkmate. As long as there are no immediate captures, it does not matter where the pieces start. The strong side can always deliver mate by following a simple plan. King and Queen vs. King This is always an easy win. The King and Queen work together to force the lone King to the side of the board, then give checkmate. In the diagrammed position, White on the move can checkmate with Qa8+ or Qg8+. If Black is on the move, White checkmates with 1...Kc8 2.Qa8+ or 1...Ke8 2.Qg8+. King and Rook vs. King This is also an easy win. The King and Rook force the opposing King to the side of the board. In the diagrammed position, White mates with Rh8. If Black is on the move, White mates with 1...Kc8 2.Rb5 Kd8 3.Rb8+ or 1...Ke8 2.Rf5 Kd8 3.Rf8+. King and two Bishops vs. King Although slightly more difficult than the preceding mates, this is also an easy win. The King and Bishops first force the opponent's King to the side of the board, then into the corner, where mate follows. In the diagrammed position, White plays 1.Be3+ Kh7 2.Bf5+ Kh8 3.Bd4 mate. The action of the two Bishops on adjacent diagonals creates a barrier which the opposing King cannot cross. King, Bishop, and Knight vs. King Strictly speaking, this is not an elementary mate, because it is considerably more difficult to execute than the preceding mates. The main difficulty is that the worst case positions bump into the 50 move rule. The winning plan is threefold. First, the King, Bishop, and Knight force the lone King to the side of the board. Then, the stronger side forces the King into the corner -- the best defense is for the King to flee to a corner that the Bishop can't attack. Finally, the pieces force the King into a corner that the Bishop can attack. In the diagrammed position, the White Bishop travels on the white squares, so the Black King has been forced into a white-squared corner. White mates with 1.Kc7 Ka8 2.Bb7+ Ka7 3.Nc6+ (or 3.Nc8+). In all of the above elementary mates, the strong side must be careful not to stalemate the lone King. In the last example, 2.Nc6 would have been a blunder because it stalemates Black. Insufficient mating material As we saw in the page on draws, King and Knight -or- King and Bishop cannot checkmate a lone King. The situation with King and two Knights is more complicated. There are certain positions where the King and Knights checkmate the lone King, but to reach these positions the strong side must allow an intermediate position where the lone King is stalemated. This means that the strong side can force a win only if the weak side has a Pawn, where stalemate is no longer a possibility. The Pawn's Square The question often arises whether a King can catch a Pawn which is racing to promotion. There is a simple trick, known as the 'The Rule of the Square', to answer this question without calculating any variations. The pawn's square is visualized by first drawing a diagonal line from the Pawn to the Pawn's promotion rank. The diagonal creates an imaginary square, half of which is shown in the diagram. If the opposing King is in this square, the King can catch the Pawn. If the King is not in the square, the chase is hopeless. Can the Black King catch the White Pawn in the diagram? It depends on who is to move. If Black is to move, 1...Kg4 puts the King into the square and Black will catch the Pawn. The King's other legal moves would be a serious mistake. If White is to move, 1.c5 creates a new diagonal, where the corner of the square is on f5. Since the Black King cannot enter the square, the Pawn will Queen and the game will become an elementary endgame of King and Queen vs. King. King and Pawn vs. King The last elementary endgame is King and Pawn vs. King where the Pawn is supported by its King and is about to promote. The lone King guards the promotion square, making a last-ditch attempt to stop the Pawn. In the diagrammed position, the result of the game depends on who is to move. White to move has no better than 1.e7+ Ke8 2.Ke6, where Black is stalemated. Black to move has no better than 1...Ke8 2.e7 Kf7 3.Kd7, where the Pawn will promote and the game will end with an elementary mate. Previous Page -- Next Page Back to Basic Concepts