Chess/The Endgame

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Contents 1 Basic Checkmates 1.1 King and Queen vs. King 1.2 King and Rook vs. King 2 Minor Piece Checkmates 3 Pawn Endings 3.1 The Rule of the Square 3.2 The Opposition 3.3 Outside Passed Pawn 3.4 Protected Passed Pawn 4 Minor Piece endings 5 Rook endings 6 Queen endings 7 Endgame Studies and Puzzles 8 External Links

[edit] Basic Checkmates

These include positions that have no pawns. When one side is ahead in material and has pawns, the easiest winning plan is typically to queen one or more pawns and use them to checkmate.

The situations where one has a king and queen, or king and rook, versus a lone king occur very often and it is essential to know how checkmate is achieved in such cases. The other cases, with minor pieces (bishops and knights) are much more rare, but are covered here for completeness.

[edit] King and Queen vs. King

Delivering checkmate with a king and queen against a lone king is quite easy. The basic technique involves driving the king to the edge of the board, which the queen can do by herself. It's faster if you use your king and queen together, but this increases the probability of a stalemate, so beginners should do it without the king. The technique described below will accomplish the mate in about 10 to 15 moves.

Here's an example (see diagram on right):

1.Qb5

Cutting the black king off along the fifth rank.

1...Ke6

1...Kc7 2.Qa6 limits Black's king to the last two ranks.

2.Qc5 (see diagram)

During this phase, notice how White's queen always stays a knight's move away from the black king, and how no checks are necessary (or even desirable). Moves like 2.Qc6+? only allow Black's king more freedom after 2...Ke5.

2...Kf6 3.Qd5 Kg6 4.Qe5 Kf7

After 4...Kh6 5.Qg3 White's goal has been achieved: the black king is trapped on the edge. White will then bring his king to f6 to force mate.

5.Qd6 Kg7 6.Qe6 Kh7

Black's king is forced to the edge of the board no matter what he does, e.g. 6...Kf8 7.Qd7.

7.Qg4 Kh6 8.Kb2 (see diagram)

Now that Black's king is stuck, the white monarch comes in to finish off his adversary.

8...Kh7 9.Kc3

9.Qg5 doesn't spoil anything, but it isn't necessary. Unlike the king and rook vs. king mate, here Black's king doesn't have to be trapped in the corner.

9...Kh8 10.Kd4

10 Qg6=?? stalemate was what Black was hoping for. Beware of this trap!

10...Kh7 11.Ke5 Kh8 12.Kf6 Kh7 13.Qg7#.

A detailed analysis of this endgame based on the computer-generated database is in Analysis of KQK Endgame. This shows that for any "King and Queen vs. King" endgame, white to move can force checkmate in at most ten moves.

[edit] King and Rook vs. King

This mate takes longer to do than king and queen vs. king, because the king and rook have to work together to trap the opposing king on the edge (often in the corner). The most commonly taught technique involves confining the opposing king into a box using the rook, which is protected by its own king. Then, the box becomes smaller and smaller until the king is forced into the corner. From the diagram on the right:

1.Kc2 Ke5 2.Kd3 Kd5 3.Ra4 Ke5

After the king's position is improved, the box can be constructed:

4.Rd4

The box is d8-d4-h4.

4...Kf5 5.Re4 (see diagram)

Now it's e8-e4-h4.

5...Kf6 6.Kd4

The box can't be reduced immediately, so the king creeps closer.

6...Kf5 7.Kd5 Kf6

7...Kg5 8.Ke6 Kg6 9.Rf4 Kg5 10.Ke5 Kg6 11.Rf5 Kg7 12.Rf6 Kg8 13.Kf5 Kg7 14.Kg5 Kh7 15.Rg6 Kh8 16.Kf6 Kh7 17.Kf7 Kh8 18.Rg6# is similar.

8.Re5

Back to shrinking the box: the process repeats itself. Notice that just as in K+Q vs. K, no checks are necessary until the actual mate.

8...Kf7 9.Re6 Kg7 10.Ke5 Kf7 11.Kf5 Kg7 12.Rf6 Kh7 13.Rg6 Kh8 14.Kf6 Kh7 15.Kf7 (see diagram)

Something important to know: if it somehow transpires that White reaches this position but it's his turn to move, all he has to do is move the rook anywhere along the sixth rank (except Rh6+ of course!). Then, Black's king is forced to move to h8, and White gives checkmate with Rh6#.

15...Kh8 16.Rh6#.
The alternative method is based on the opposition of the kings (see below) with the rook being far away. From the same starting position as before:

1.Kc2 Ke5 2.Kd3 Kd5

Once again, White must improve the position of his king first. Now, once the kings are in opposition, he checks along the fifth rank to push the black king back.

3.Ra5+ (see diagram)

Black has no choice but to give ground.

3...Kc6 4.Kd4 Kb6

4...Kd6 5.Ra6+ immediately cuts Black off the sixth rank.

5.Rg5 Kc6 6.Rh5 Kd6

6...Kb6 7.Kc4 Kc6 8.Rh6+ is the same sort of thing.

7.Rh6+ Ke7 8.Kd5 Kf7 9.Ke5 Kg7 10.Rb6 Kf7 11.Ra6 Ke7 12.Ra7+ Kd8 13.Ke6 Kc8 14.Kd6 Kb8 15.Rg7 Kc8 16.Rh7 Kb8 17.Kc6 Ka8 18.Kb6 Kb8 19.Rh8#.

Using either method, it should take about 15-20 moves to deliver the mate. Theoretically, it should take no longer than 16 moves to checkmate, but depending on the position, one might have to use a mixture of the two techniques to do this.

[edit] Minor Piece Checkmates

If white has only one minor piece against a lone king, it is not possible to arrange the pieces so that the black king is checkmated. If white has three pieces, the mate is easy. As we shall see, with two bishops white's job is relatively easy, with a bishop and knight it is somewhat harder, and with two knights it is typically impossible.

The diagram at left shows a mate in 6 with two bishops.

1. Bc2 Kf1 2. Bd2 Kg1 3. Kg3 Kf1 4. Bd3+ Kg1 5. Be3+ Kh1 6. Be4#

If black plays 3. ... Kh1, instead of Kf1, white responds with the line: 4. Be1 Kg1 5. Bf2+ Kh1 6. Be4#, or 5...Kf1 6. Bd3#

The bishops coordinate by taking adjacent diagonals, thus cutting off the opposing king.

In the diagram position with Black to move, White can "gain a move" by triangulating his king:

1...Kd1 2. Kf4 Ke1 3. Ke4 Kd1 4. Kf3 Ke1. Now the diagram position is reached with White to move, and play proceeds as above. Black's king, hemmed in by the two bishops, cannot escape from the d1-e1 box.

In order to mate with a bishop and knight, white must force black's king to the corner that is the same color as his bishop - in this case the a8 square. This is not so easy to do, because the bishop and knight do not coordinate well in cutting off the opponent's king. Mate can always be forced unless black can win a white piece, but, even with best play, the mate may take over 30 moves.

In the position at right, much of the hard work has already been done. Black is being pressed in the direction of the a8 corner. Nevertheless, nine more moves are required to mate.

1. Kd6 Kc8 2. Ke7 Kb7 3. Kd7 Kb8 4. Ba6 Ka7 5. Bc8 Kb8 6. Ne7 Ka7 (or 6. ... Ka8 7. Kc7 Ka7 8. Nc6+ Ka8 9. Bb7# ) 7. Kc7 Ka8 8. Bb7+ Ka7 9. Nc6#

When white has two knights against a bare king, it is impossible to mate without cooperation from black. The diagram at left illustrates his predicament. The black king is cornered, but white has no way to force checkmate. Moving either Nf3, or moving Nh3 all lead to stalemate. White can try for 1. Ne4 Kg1 2. Nf3+ Kh1?? 3. Nf2#, but instead black plays 2. ... Kf1 3. Nd4 (otherwise black can play Ke2, and white must corner him again) 3. ... Ke1 and white still has a challenge to confine the black king.

If black has one pawn, white may be able to win by cornering the black king with a king and one knight, and avoiding stalemate by letting black to advance his pawn, while the other knight administers mate. This is more likely to succeed if the black pawn is not far advanced, and needs at least three moves to become a queen. Alexey Troitsky, the famous endgame study composer, produced an extensive analysis of this endgame and composed several endgame studies with two knights against one pawn. Some positions require as many 70 moves without a pawn move or capture. This endgame has some historic interest - it was included in the amendment of the "50 move draw rule" to exclude those positions in which it could be demonstrated that more moves were required. (The exception to this rule has since been rescinded; the rule now dictates that either player may claim a draw after 50 moves without a pawn move or capture, regardless of the position on the chessboard.) The ending of two knights versus one pawn has occasionally occurred in practical tournament play.

[edit] Pawn Endings

Two important concepts in endgames only involving the kings and pawns are the rule of the square and the opposition.

A passed pawn is a pawn that cannot be stopped from queening by an opponent's pawn. If both sides have one or more passed pawns, then the player with a protected passed pawn (protected by another pawn) is likely to have an advantage. If neither side has a protected passed pawn, then the player with an outside passed pawn (farthest from the other pawns) will most likely win.

[edit] The Rule of the Square

The Rule of the Square is used to determine whether or not a passed pawn can queen when it is not supported by its own king and the enemy king is chasing it. The idea is shown by the diagram on the right:

One side of the square is the line that extends from the pawn to the square on which it queens. The rule says: if the enemy king can reach the square of the pawn, then it can capture the pawn; if not, the pawn can queen without the aid of its own king. Remember that if the pawn is on its starting square, it can make a double step, so the square is the same as if the pawn has advanced one square. The rule is valid for all pawns, including rook's pawns.

So, in the diagram, if it's White's turn to move, then Black's king is outside the square and White can queen: 1.e6 Kb5 2.e7 Kc6 3.e8Q+.

If Black is to play, the pawn can't escape the king: 1...Kb5! (moving into the square) 2.e6 Kc6 3.e7 Kd7 4.e8Q+ Kxe8 =.

The rule assumes that there is nothing stopping the king from taking the shortest route to chase the pawn. If there are pawns that might get in the way of the king then the rule does not apply:

The position is the same as the first one, except that now there is a black pawn on c6. This pawn gets in the way of its own king, so that even if it's Black's turn to move he still loses: 1...Kb5 (1...c5 2.e6! and Black's king cannot get into the c8-c6-e6-e8 square) 2.e6 Kb6 3.e7 Kc7 4.e8Q.

The rule of the square can form a basis for tactics. In the position on the right, Black to move played 1...Kb4, entering the square of White's f-pawn. He thought that this would be good enough for a draw, but White played 2.d6!. After 2...cxd6 3.f5 the effect of White's sacrifice is clear: he has decoyed Black's pawn to the a3-f8 diagonal, where it obstructs Black's king. Now White simply promotes the pawn and wins. Black had no other choice but to take White's d-pawn on his second move as otherwise it would have queened. Please note that 2.f5 Kc5 3.f6 Kd6 4.Kb2 Kd7 5.Kc3 Ke8 6.Kd4 Kf7 7.Ke5 wins as well.

[edit] The Opposition

When the two Kings stand next to each other so that there is one square between them, they are said to oppose each other (or to be in opposition). Because the rules of chess say that the King can't step to a square next to the opposite King, there is an invisible wall between the Kings that makes it impossible for them to advance forwards.

The player who is not to move in such situation is said to have the opposition. Since his opponent can't move his King forwards, he has to move it sideways or backwards, and after that the other player gets to advance his King forwards, which is usually advantageous for him.

Let's consider the very simple position on the right that illustrates the opposition:

If Black is to move, White has the opposition. Black can't move his King forwards, so he might play 1...Kd6 (1...Kf6 is the same in mirror image). Now the f5-square becomes available for the white King, so White's next move is 2. Kf5. If Black now moves his King to e7, White responds by moving his King to e5, when a position similar to the starting position has arisen, with the exception that the white King has advanced one square forwards and thus forced the black King to retreat one square.

Now you might wonder what is the advantage of having the opposition. Let's add a Pawn to the previous position, and we get an example of how to queen the Pawn with the aid of the opposition (see diagram on right):

Now Black plays 1...Kd6, as in the previous example. White's first move is also the same, 2.Kf5, advancing his King forwards. The play might go on 2...Kd7 3.Kf6 Kd6. Now it seems that Black has the opposition, but we shouldn't forget that White doesn't have to move his King. Therefore the right move is 4.e4, when Black has to concede the opposition. Now White wins after 4...Kd7 5.e5 Ke8 6.Ke6 Kd8 7. Kf7 Kd7 8.e6+ Kd6 9.e7 and the Pawn queens next move.

This position might look like a simple win with White to move as well. However, in this case, the game is drawn. Black has the opposition, and he can use it to block the Pawn (if he is careful and doesn't blunder the opposition away). Play could begin with 1.Kf4 Kf6 2. e4 Ke6!. This is the only move that holds the draw. In this kind of position, when the defending King can't oppose the enemy King, he must never move backwards. Instead he always has to move sideways, and always to the file on which the opponent's Pawn stands. If Black had now played 2...Ke7?, White would have gained the opposition with 3.Ke5, and won the game as in the previous example. After 2...Ke6 White has no way to force the Pawn through as long as Black carefully keeps the opposition. The play could continue 3.e5 Ke7 4.Kf5 Kf7 5.e6 Ke8 6.Kf6 Kf8 7.e7 Ke8 8.Ke6 stalemate.

You need more than just a pawn and the opposition to win though. Take the position at right. Unlike the previous one, White's king is behind the pawn, and this is enough to ensure black a draw. Assuming black to move (so white has the opposition) the game might continue 1. ... Kd7 2. Kc5 Kc7 3. d6+ Kd7 4. Kd5 Kd8 5. Kc6 Kc8 6. d7+ Kd8 7. Kd6 stalemate.

Even if one side has a pawn advantage, his king is in front of the pawn, and he has the opposition, it may not be enough to win. A notable exception is shown at right, namely the rook pawn. Unlike the previous case, there is nothing white can do to force black out of the corner - thus his pawn can never queen.

[edit] Outside Passed Pawn

The position at right is a good example of an outside passed pawn. It is not that the pawn is at the edge of the board - it is the fact that this pawn is far away from the other pawns, and acts as a decoy. It is often the case that in positions with an equal number of pawns that an outside passed pawn is sufficient advantage to win.

Take the position at right as an example. White advances his passed pawn, and when the black king is far away, he captures all the black pawns, and queens his remaining pawn.

1. f5 Kd6 2. f6 Ke6 3. Kxc5 Kxf6 4. Kb6 Ke6 5. Kxa6 Kd7 6. Kb7 and the pawn queens.

[edit] Protected Passed Pawn

White's c pawn is a protected passed pawn - enough to win in this position, even when black has an outside passed pawn. White could easily fritter away this advantage, and even lose, after 1. c6+?? Kc7 2. Kc5 f5 3. Kd5 f4 4. Ke4 Kxc6 5. Kxf4 Kd5 6. Ke3 Kc4 (the outside passed pawn prevailed). The correct strategy is for White to threaten the f pawn with his king, and then trade the c pawn for the f pawn in such a way that he gets the opposition. Black cannot counter by attacking White's other pawns, because then the c pawn will queen.

1. Ke5 Ke7 2. c6 Kd8 3. Kf6 Kc7 4. Kxf7 Kxc6 5. Ke6 Kc7 6. Kd5 Kb6 7. Kd6 Kb7 8. Kc5 Ka6 9. Kc6 wins both pawns

Probably better is the fighting alternative 1. Ke5 Kc6 2. Kf6 Kd5 3. Kxf7 Kc4 4. c6 Kb3 5. c7 Kxa3 6. c8/Q Kxb4 7. Qe6 but white has no trouble stopping the black pawns and mating.

(Note: In principle, the above strategy is right. However, in this position, White has a win even after 1.c6. After 1...Kc7 2. Kc5 f5, White can play 3.Kxb5 and still has time to stop Black's f-pawn, winning the game easily. Uday B)

If the protected passed pawn is not so far advanced, it confers less of an advantage. The position at right, which has most of the pieces moved back two rows, actually provides Black with a slight advantage, but not enough to win against best defense. Black uses his outside passed pawn as a decoy, and then queens his b pawn, while white queens his c pawn.

1. Ke3 Kc4 2. Ke2 (trying to stop black from penetrating) f4 3. Kd2 f3 4. Ke3 f2 5. Kxf2 Kd3 6. Kf3 Kc2 7. c4 Kxb2 8. c5 Kxa3 9. c6 b2 10. c7 b1/Q 11. c8/Q

Black is a pawn up in an ending with queens on the board. Black has an opportunity to play for a win, but such endings are generally drawn.

[edit] Minor Piece endings

[edit] Rook endings

[edit] Queen endings

[edit] Endgame Studies and Puzzles

In this position who is winning? Or assuming correct play by both players what will be the result of the game? Before answering consider the next two diagrams.

In diagrams 2 and 3 white has a clear plan, promote his pawn to a queen, however black can stop that. White cannot immediately push his pawn. In diagram 2 if white pushes his pawn with a7+ black can play Ka8 and the game is drawn. In diagram 3 if white plays pawn to a7 it will also be a stalemate. So white must dislodge the black king from the a8 and b8 squares. White can't do that, no matter what white does with the king black can simply move back and forth between a8 and b8 therefore the game is drawn. A lot of times you will be offered a trade of material that results in an end game, or you may want to figure out if its best for you to offer a trade to enter the end game. You may play a game of chess and in doing so do a long calculation where diagram 1 is as far as you can calculate. In which case you do not need to do anymore calculations because you already know that its a draw! By understanding the outcome of positions without needing to calculate all the different variations you can make accurate evaluations of trades that may be decisive. There are several details that must be kept in mind for this position drawn. White cannot have any other pawns, if he does then black is lost. Also, the black king must be able to get to the corner for the board, if possible the white king will shield the black king away and white will win.

[edit] External Links

• Interactive King + Queen vs King Checkmate
• Interactive King + Rook vs King Checkmate
• View endgames involving the King+Knight+Pawn vs. King+Knight+Pawn
• View endgames involving the King+Pawn vs. King+Pawn
• View endgames involving the King+Queen+Pawn vs. King+Queen+Pawn
• View endgames involving the King+Rook+Pawn vs. King+Rook+Pawn
• View endgames involving the King+Bishop+Pawn vs. King+Bishop+Pawn

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