Endgames

In chess, the endgame (or end game or ending) refers to the stage of the game when there are few pieces left on the board.

The line between middlegame and endgame is often not clear, and may occur gradually or with the quick exchange of a few pairs of pieces. The endgame, however, tends to have quite different characteristics from the middlegame, and the players have quite different strategic concerns. In particular, pawns become more important; endgames often revolve around attempting to promote a pawn by advancing it to the eighth rank. The king, which has to be protected in the middlegame owing to the threat of checkmate, becomes a strong piece in the endgame. It can be brought to the center of the board and be a useful attacking piece.

Many people have composed endgame studies, endgame positions which are solved by finding a win for white when there is no obvious way of winning, or a draw when it seems white must lose.

Endgames can be classified according to the type of pieces that remain. Some common types of endgames are discussed below.

When does the endgame begin?

An endgame is when there are only a few pieces left. With the usual system for chess piece point value, Speelman considers that endgames are positions in which each player has thirteen or fewer points in material (not counting the king). Alternatively, an endgame is a position in which the king can be used actively, but there are some famous exceptions to that (Speelman 1981:7-8).

Alburt and Krogius give three characteristics of an endgame: (Alburt & Krogius 2000:12)

1.Endgames favor an aggressive king
2.Passed pawns increase greatly in importance
3.Zugzwang is often a factor in endgames and rarely in other stages of the game

Common types of endgames

Basic checkmates

These are positions in which one side has only a king and the other side has one or two pieces and can checkmate the opposing king, with the pieces working together with their king. A queen or a rook can easily checkmate a lone king. See Wikibooks - Chess/The Endgame for a demonstration of these two checkmates. Two bishops can easily checkmate a lone king, provided that the bishops move on opposite color squares. (Two or more bishops on the same color can not checkmate.) A bishop and knight can also checkmate a lone king, although the checkmate procedure is long (up to 33 moves with correct play) and is difficult for a player who does not know the correct technique.

Two knights cannot force checkmate against a lone king, but if the weaker side also has a pawn, checkmate is sometimes possible, because positions which would be stalemate without the pawn are not stalemate with the additional pawn. If the pawn is blocked by a knight behind the Troitzky line, the knights have a long theoretical win. There are some other positions when the pawn is past the Troitzky line in which the knights can force checkmate, but the procedure is long and difficult. In either case, in competition the fifty move rule will usually result in the game being drawn first.

King and pawn

King and pawn endgames involve only kings and pawns on one or both sides. Cecil Purdy said "Pawn endings are to chess as putting is to golf."

Getting a passed pawn is crucial (a passed pawn is one which does not have an opposing pawn on its file or on adjacent files on its way to promotion). Nimzovich once said that a passed pawn has a "lust to expand". An outside passed pawn is particularly deadly. The point of this is a decoy — while the defending king is preventing it from queening, the attacking king wins pawns on the other side.

Opposition is an important technique that is used to gain an advantage. When two kings are in opposition, they are on the same file (or rank) with an empty square separating them. The player having the move loses the opposition. He must move his king and allow the opponent's king to advance. Note however that the opposition is a means to an end, which is penetration into the enemy position. If the attacker can penetrate without the opposition, he should do so.

King and pawn versus king. Assume that white has the pawn. A draw results if the black king can reach the square in front of the pawn or the square in front of that. See King and pawn versus king for more discussion of this important ending.

Knight and pawn

Knight and pawn endgames feature clever maneuvering by the knights to capture opponent pawns. While a knight is poor at chasing a passed pawn, it is the ideal piece to block a passed pawn. Knights can't lose a tempo, so knight and pawn endgames have much in common with king and pawn endgames. An outside passed pawn can outweigh a central protected passed pawn, unlike king and pawn endgames. A knight blockading a protected passed pawn attacks the protector, while the knight blockading an outside passed pawn is somewhat out of action.

Knight and pawn versus knight. This is generally a draw since the knight can be sacrificed for the pawn, however the king and knight must be covering squares in the pawn's path. If White's pawn reaches the seventh rank and is supported by the king and knight, White usually wins (Fine and Benko 2003:7-8).

Bishop and pawn

Bishop and pawn endgames come in two distinctly different variants. If the opposing bishops go on the same color of square, the mobility of the bishops is a crucial factor. A bad bishop is one that is hemmed in by pawns of its own color, and has the burden of defending them.

Bishop and pawn versus bishop on the same color. Two rules given by Luigi Centurini apply:

The game is a draw if the black king can reach any square in front of the pawn that is not of the color of the bishop.
If the black king is behind the pawn and the white king is near the pawn, black can draw only if his king is attacking the pawn, he has the opposition, and his bishop can move on two diagonals that have at least two squares each (Fine and Benko 2003:152).

Bishops on opposite colors

Endings with bishops of opposite color, meaning that one bishop works on the light squares, the other one working on dark squares, are notorious for their drawish character. Many players in a poor position have saved themselves from a loss by trading down to such an endgame. They are often drawn even when one side has a two pawn advantage since the weaker side can create a blockade on the squares which his bishop operates on. Interestingly the weaker side should often try to make his bishop bad by placing his pawns on the same color of his bishop in order to defend his remaining pawns, thereby creating an impregnable fortress.

Bishop and pawn versus bishop on the opposite color. White's bishop is practically useless and Black can normally draw if his king can reach any square in front of the pawn that is not of the color of White's bishop, or if his bishop can attack any square in front of the pawn (Fine and Benko 2003:184).

Bishop and two pawns versus a bishop on the opposite color. This combination is often a draw. (In most other endings, a two pawn advantage is an easy win). There are three general cases:

Doubled pawns. This is a draw if the black king can reach any square in front of the pawns that is not of the color of White's bishop.
Connected pawns. This is the most complex case, and the result depends on the ranks and files of the pawns and the colors and locations of the bishops. If one of the pawns is a rook pawn (on the a file or h file) the position is normally drawn. If the pawns are on the opposite color as Black's bishop, Black may be able to blockade the pawns and draw. If both pawns can safely reach the sixth rank, they win (if neither is a rook pawn).

Isolated pawns (on different files). The outcome depends on how widely separated the pawns are. In most cases if only one file separates the pawns the game is a draw, otherwise White wins. The reason is that if the pawns are more widely separated, Black's king must block one pawn while his bishop blocks the other pawn. Then the white king can support the pawn blocked by the bishop and win the piece. If only one file is between the pawns, Black can stop the advance of the pawns.

Bishop versus knight with pawns

Current theory is that bishops are better than knights about 60% of the time, in the middlegame and endgame. The more symmetrical the pawns are (i.e. Black's pawns are on the same files as White's pawns), the better it is for the knight. The knight is best suited at an outpost in the center whereas the bishop is strongest when it can attack targets on both sides of the board or a series of squares of the same color (Beliavsky and Mikhalchishin 1995:122).

Fine and Benko (Fine and Benko 2003:205) give four conclusions:

In general the bishop is better than the knight.
When there is a material advantage, the difference between the bishop and knight is not very important. However, the bishop usually wins more easily than the knight.
If the material is even, the position should be drawn. However, the bishop can exploit positional advantages more efficiently.
When most of the pawns are on the same color as the bishop (i.e. a bad bishop), the knight is better.

Bishop and pawn versus knight. This is a draw if the black king is in front of the pawn or sufficiently close. The black king can occupy a square in front of the pawn of the opposite color as the bishop and can't be driven away. Otherwise white can win (Fine and Benko 2003:206).

Knight and pawn versus bishop. This is a draw if the black king is in front of the pawn or sufficiently near. The bishop is kept on a diagonal that the pawn must cross and the knight can't both block the bishop and drive the black king away. Otherwise white can win (Fine and Benko 2003:209).

Rook and pawn

Rook and pawn endgames are often drawn in spite of one side having an extra pawn. (In some cases, two extra pawns are not enough to win.) An extra pawn is harder to convert to a win in a rook and pawn endgame than any other type of endgame except a bishop endgame with bishops on opposite colors. The great master Tartakower once jocularly said "All rook and pawn endings are drawn". (It may have been Siegbert Tarrasch who said this - see the article on Tartakower.) Rook endings are probably the deepest and most well studied endgames. They are the a common type of endgame in practice, occurring in about 10% of all games (including ones that don't reach an endgame) (Emms 1999:7).

Three rules of thumb regarding rooks are worth noting:

1.Rooks should almost always be placed behind passed pawns, whether one's own or the opponent's (the Tarrasch rule). A notable exception is in the ending of a rook and pawn versus a rook, if the pawn is not too far advanced. In that case, the best place for the opposing rook is in front of the pawn.

2.Rooks are very poor defenders relative to their attacking strength. So it is often good to sacrifice a pawn for activity. This is especially so in the following case

3.A rook on the seventh rank can wreak mayhem among the opponent's pawns. The power of a rook on the seventh rank is not confined to the endgame. The classic example is Capablanca–Tartakower, New York 1924

An important winning position in the endgame of a rook and pawn versus rook is the so-called Lucena position. If the side with the pawn can reach the Lucena position, he wins. However, there are several important drawing techniques such as the Philidor position, the back rank defense (rook on the first rank, for rook pawns and knight pawns only), the frontal defense, and the short side defense. A general rule is that if the weaker side's king can get to the queening square of the pawn, the game is a draw and otherwise it is a win, but there are many exceptions.

Rook and pawn versus rook. Generally (but not always), if black's king can reach the queening square of the pawn the game is a draw (see Philidor position), otherwise White wins (if it is not a rook pawn). The wining procedure can be very difficult and some positions require more than sixty moves to win, so the fifty move rule comes into play. If White's rook is two files from the pawn and the black king is cut off on the other side, White normally wins (with a few exceptions) (Fine and Benko 2003:294).

The most difficult case of a rook and pawn versus a rook is when White's rook is one file over from the pawn and black's king is cut off on the other side. Siegbert Tarrasch gave the following rules for this case: "For a player defending against a pawn on the fifth or even sixth ranks to obtain a draw, even after his king has been forced off the queening square, the following conditions must obtain: The file on which the pawn stands divides the board into two unequal parts. The defending rook must stand in the longer part and give checks from the flank at the greatest possible distance from the attacking king. Nothing less than a distance of three files makes it possible for the rook to keep on giving check. Otherwise it would ultimately be attacked by the king. The defending king must stand on the smaller part of the board." See the short side defense at Rook and pawn versus rook.

Queen and pawn

In Queen and pawn endings, passed pawns have paramount importance, because the queen can escort it to the queening square alone. The advancement of the passed pawn outweighs the number of pawns. The defender must resort to perpetual check. These endings are frequently extremely long affairs. For an example of a Queen and pawn endgame see Kasparov versus The World — Kasparov won although he had fewer pawns because his was more advanced. For the ending with a queen versus a pawn, see Queen versus pawn.

Queen and pawn versus queen. This combination is a win less frequently than the equivalent ending with rooks, and it is very difficult to play. According to Fine and Benko (Fine and Benko 2003:538), this ending is a draw unless the pawn is a bishop pawn or a center pawn (i.e. king pawn or queen pawn) and the pawn is in the seventh rank and is supported by its king. If the black king can get in front of the pawn, the game is a draw; otherwise it is best for Black to keep his king far away from the pawn. Black should keep checking until he runs out of check, and then pin the pawn. Based on computer analysis, Müller and Lamprecht (Müller and Lamprecht 2001:316) give a slightly different description. According to them, normally Black's king needs to be in front of the pawn. A rook pawn or knight pawn is a theoretical draw if the black king is in front or near the pawn or if the king is in the opposite corner. A knight pawn has more practical winning chances than a rook pawn. A bishop pawn or central pawn is a win if Black's king is not in front of the pawn. A bishop pawn has better winning chances than a central pawn.

Asymmetric positions

A rook is worth roughly two pawns plus a bishop or a knight. A bishop and knight are worth roughly a rook and a pawn, and a queen is worth a rook, a minor piece (bishop or knight) and a pawn. Three pawns are often enough to win against a minor piece, but two pawns rarely are.

However, with rooks on the board, the bishop often outweighs the pawns. This is because the bishop defends against enemy rook attacks, while the bishop's own rook attacks enemy pawns and reduces the enemy rook to passivity. This relates to Rule 2 with rooks (above).

A bishop is usually worth more than a knight. A bishop is especially valuable when there are pawns on both wings of the board, since it can intercept them quickly.

Endings with no pawns

Besides the basic checkmates, there are other endings with no pawns. Generally they do not occur very often in practice, but some of the more common ones follow.

A queen wins against a rook, but the "third rank defense" by the rook is difficult for a person to crack. The "third rank defense" is when the rook is on the third rank or file from the edge of the board, his king is closer to the edge and the enemy king is on the other side. The winning move is the counter-intuitive withdrawal of the queen from the seventh rank to a more central location, Qf4, so the queen can make checking maneuvers to win the rook if it moves along the third rank. And if the black king emerges from the back rank, ...Kd7, then Qa4+ Kc7, Qa7+ forces Rb7, with a standard win heading towards Philidor position.

A queen normally wins against a bishop and knight, but there is one drawing fortress position forming a barrier against the enemy king's approach. Another position is more artificial: the queen's king is on a1 confined by Ba3 and Nc3 protected by their king (Müller and Lamprecht 2001:339-41).

A queen generally has a theoretical win against two bishops, but many ordinary positions require up to 71 moves (a draw can be claimed after 50 moves under the rules of competition, see fifty move rule); and there is one drawing fortress position for the two bishops (Müller and Lamprecht 2001:339-41).

Two knights can generally draw against a queen by setting up a fortress.

A rook versus a minor piece (bishop or knight) is generally a draw. A rook plus a minor piece versus a rook is usually a draw; as is a queen and a minor piece versus a queen. A queen versus a rook and a minor piece is generally a draw. Of course, there are positions that are exceptions to these general rules.

Fine's rule

In his landmark book Basic Chess Endings, Reuben Fine inaccurately stated that in endgames without pawns, at least the advantage of a rook (or equivalent material) is required to win, with two exceptions in which less of an advantage is sufficient (chapter IX of the first edition). The advantage of a rook corresponds to a five-point material advantage using the traditional relative value of the pieces (pawn=1, knight=3, bishop=3, rook=5, queen=9). The two exceptions noted by Fine are (1) the double exchange — two rooks versus any two minor pieces, and (2) four minor pieces versus a queen. (Fine and Benko 2003:585). It turns out that there are several exceptions, but they are endgames that rarely occur in actual games (except for perhaps a queen versus a rook).

A four-point material advantage is often enough to win in some endings without pawns. For example, a queen wins versus a rook (as mentioned above, but 31 moves may be required); as well as when there is matching additional material on both sides, i.e.: a queen and any minor piece versus a rook and any minor piece; a queen and a rook versus two rooks; and two queens versus a queen and a rook. Another type of win with a four-point material advantage is the double exchange — two rooks versus any two minor pieces. There are some other endgames with four-point material differences that are generally long theoretical wins, but the fifty move rule comes into play in competition because in general more than 50 moves are required: two bishops and a knight versus a rook (68 moves); and two rooks and a minor piece versus a queen (82 moves for the bishop, 101 moves for the knight).

A three-point material advantage can also result in a forced win, in some cases. For instance, some of the cases of a queen versus two minor piece are such positions (as mentioned above). In addition, the four minor pieces win against a queen.

There are some long general theoretical wins with only a two- or three-point material advantage but the fifty move rule usually comes into play because of the number of moves required: two bishops versus a knight (66 moves); a queen and bishop versus two rooks (two-point material advantage, can require 84 moves); a rook and bishop versus a bishop on the opposite color and a knight (a two-point material advantage, requires up to 98 moves); and a rook and bishop versus two knights (two-point material advantage, but it requires up to 222 moves!). The number of moves given are the number of moves to convert the endgame to a simpler endgame (or checkmate), and are from Fundamental Chess Endings, by Müller and Lamprecht; and Secrets of Pawnless Endings, by John Nunn.

Finally, there are some other unusual exceptions to Fine's rule involving underpromotions. Some of these are (1) a queen wins against three bishops of the same color (no difference in material points), up to 51 moves are required; (2) a rook and knight win against two bishops on the same color (two point difference), up to 140 moves are needed; and (3) three bishops (two on the same color) win against a rook (four point difference), requiring up to 69 moves, and (4) four knights win against a queen (85 moves). This was proven by computer in 2005 and was the first ending with seven pieces that was completely solved.

General remarks on these endings

Other than the basic checkmates with a queen and with a rook, the endgames without pawns occur rarely in actual games. Therefore a chess player should concentrate on endings with pawns after learning the basic checkmates.

Note: many of these endings are listed as a win in a certain number of moves. That assumes perfect play by both sides, which is rarely achieved if the number of moves is large. Also, finding the right moves may be exceedingly difficult for one or both sides. When a forced win is more than 50 moves long, some positions can be won within the 50 move limit (for a draw claim) and others can't. Also, generally all of the combinations of pieces that are usually a theoretical draw have some non-trivial positions that are a win for one side. Similarly, combinations that are generally a win for one side often have non-trivial positions which result in draws.

General

In general, the player with a material advantage tries to exchange pieces and reach the endgame. In the endgame, the player with a material advantage should usually try to exchange pieces but avoid the exchange of pawns. There are some exceptions to this: (1) endings in which both sides have two rooks plus pawns – the player with more pawns has better winning chances if a pair of rooks are not exchanged, and (2) bishops on opposite color with other pieces – the stronger side should avoid exchanging the other pieces.

In the endgame, it is better for the player with more pawns to avoid too many pawn exchanges, because they should be won for nothing. Also, endings with pawns on both sides of the board are much easier to win. A king and pawn endgame with an outside passed pawn should be a far easier win than a middlegame a rook ahead.

With the recent growth of computer chess, an interesting development has been the creation of endgame databases which are tables of stored positions calculated by retrograde analysis (such a database is called an endgame tablebase). A program which incorporates knowledge from such a database is able to play perfect chess on reaching any position in the database.