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In chess and chess-like games, the endgame (or end game or ending) is the stage of the game when few pieces are 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 different characteristics from the middlegame, and the players have correspondingly different strategic concerns. In particular, pawns become more important as 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 act as a useful attacking piece.
Whereas chess opening theory changes frequently, giving way to middlegame positions that fall in and out of popularity, endgame theory always remains constant. Many people have composed endgame studies, endgame positions which are solved by finding a win for White when there is no obvious way to win, or a draw when it seems White must lose.
Usually in the endgame, the stronger side (the one with more material using the standard piece point count system) should try to exchange pieces (knights, bishops, rooks, and queens), while avoiding the exchange of pawns. This generally makes it easier to convert a material advantage into a won game. The defending side should strive for the opposite.
Chess players classify endgames according to the type of pieces that remain.
Endgames can be divided into three categories:
This article generally does not consider studies.
An endgame is when there are only a few pieces left. There is no strict criterion for when an endgame begins, and different experts have different opinions (Fine 1952:430). Alexander Alekhine said "We cannot define when the middle game ends and the end-game starts" (Whitaker & Hartleb 1960). With the usual system for chess piece relative 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). Minev characterizes endgames as positions having four or fewer pieces other than kings and pawns (Minev 2004:5). Some authors consider endgames to be positions without queens (e.g. Fine, 1952), while others consider a position to be an endgame when each player has less than a queen plus rook in material. Flear considers an endgame to be where each player has at most one piece (other than kings and pawns) and positions with more material where each player has at most two pieces to be "Not Quite an Endgame" (NQE), pronounced "nuckie" (Flear 2007:7-8).
Alburt and Krogius give three characteristics of an endgame: (Alburt & Krogius 2000:12)
Some problem composers consider that the endgame starts when the player who is about to move can force a win or a draw against any variation of moves (Portisch & Sárközy 1981:vii).
Mednis and Crouch address the question of what constitutes an endgame negatively. The game is still in the middlegame if middlegame elements still describe the position. The game is not in the endgame if these apply:
In endgames with pieces and pawns, an extra pawn is a winning advantage in 50 to 60 percent of the cases. It becomes more decisive if the stronger side has a positional advantage (Euwe & Meiden 1978:xvi). 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 (Dvoretsky & Yusupov 2008:134). 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. Also when all of the pawns are on the same side of the board, often the stronger side must exchange pawns to try to create a passed pawn.
In the endgame, it is usually better for the player with more pawns to avoid too many pawn exchanges, because winning chances are reduced if too few pawns remain. 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.
Max Euwe and Walter Meiden give these five generalizations:
Read main article: Checkmate
Many references have sections on basic, elementary, or fundamental checkmates. These are positions with a minimal amount of material in which checkmate can generally be forced. All sources agree on four types of positions: (1) king and queen versus king, (2) king and rook versus king, (3) king and two bishops versus king, and (4) king, bishop, and knight versus king. These references include Basic Chess Endgames, Ruben Fine & revised by Pal Benko, 2003, chapter 1; A Pocket Guide to Endgames, David Hooper, 1970, chapter 1; Practical Chess Endings, Paul Keres, 1973, chapter 1; Chess Endings for the Practical Player, Ludek Pachman, 1977, chapter 1; Batsford Chess Endings, by Speelman, Tisdall, and Wade, pp. 9-12; Pandolfini's Endgame Course, Bruce Pandolfini, 1988, chapters 1 and 2; Winning Chess Endings, by Yasser Seirwan, chapter 1; and Winning Chess Endgames, by Tony Kosten, 1987, chapter 1. Graham Burgess in The Mammoth Book of Chess, 2009, includes the first three of these, but does not cover the bishop and knight checkmate "since it is too difficult to be regarded as a basic mate".
In addition, the first of Fine's Basic Chess Endings, but not the revised edition, includes the unusual combination of a king and three knights versus a king. A few references also include the endgame of a king and two knights versus a king and a pawn, in which checkmate can be forced in some positions. These books include Chess Endings: Essential Knowledge, by Yuri Averbach, 1993, chapter 1 and Fundamental Chess Endings by Karsten Müller and Frank Lamprecht, 2003, chapter 1.
In conjunction with its king, a queen or a rook can easily checkmate a lone king, but a single minor piece (a bishop or knight) cannot. See Wikibooks - Chess/The Endgame for a demonstration of these two checkmates. Two bishops (plus their king) 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 (plus their king) 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 (see Two knights endgame), but if the weaker side also has other material, checkmate is sometimes possible.(Troitzky 2006:197-257) The winning chances with two knights are insignificant except against a few pawns. (Hawarth, Guy McC (2009). "Western Chess:Endgame Data". CentAUR.) The procedure can be long and difficult. In competition the fifty-move rule will often result in the game being drawn first. (While there is a board position that allows two knights to checkmate a lone king, such requires a careless move by the weaker side to execute.)
King and pawn endgames involve only kings and pawns on one or both sides. International Master Cecil Purdy said "Pawn endings are to chess as putting is to golf." Any endgame with pieces and pawns has the possibility of simplifying into a pawn ending (Nunn 2010:43).
In king and pawn endings, an extra pawn is decisive in more than 90 percent of the cases (Euwe & Meiden 1978:xvi). 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. The tactics of triangulation and zugzwang as well as the theory of corresponding squares are often decisive.
Unlike most positions, king and pawn endgames can usually be analyzed to a definite conclusion, given enough skill and time. An error in a king and pawn endgame almost always turns a win into a draw or a draw into a loss - there is little chance for recovery. Accuracy is most important in these endgames. There are three fundamental ideas in these endgames: opposition, triangulation, and the Réti manoeuvre (Nunn 2007:113ff).
Müller & Lamprecht, diagram 2.11
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Read main article: King and pawn versus king endgame
This is one of the most basic endgames. A draw results if the defending king can reach the square in front of the pawn or the square in front of that (or capture the pawn) (Müller & Lamprecht 2007:16,21). If the attacking king can prevent that, the king will assist the pawn in being promoted to a queen or rook, and checkmate can be achieved. A rook pawn is an exception because the king may not be able to get out of the way of its pawn. The other pawns are also exceptions (see diagram far right).
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 cannot lose a tempo, so knight and pawn endgames have much in common with king and pawn endgames. As a result, Mikhail Botvinnik stated that “a knight ending is really a pawn ending.” (Beliavsky & Mikhalchishin 2003:139)
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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 the pawn reaches the seventh rank and is supported by its king and knight, it usually promotes and wins. In this position, White to move wins: 1. b6 Nb7 2. Ne6! Na5 3. Kc8! N-any 4. Nc7#. If Black plays the knight to any other square on move 2, White plays Kc8 anyway, threatening b7+ and promotion if the knight leaves the defense of the b7 square. Black to move draws starting with 1... Nc4 because White cannot gain a tempo (Fine & Benko 2003:112-14).
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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.
The diagram on the right, from Molnar-Nagy, Hungary 1966, illustrates the concepts of good bishop versus bad bishop, opposition, zugzwang, and outside passed pawn. White wins with 1.e6! (vacating e5 for his king) Bxe6 2.Bc2! (threatening Bxg6) 2...Bf7 3.Be4! Be8 4.Ke5! Seizing the opposition (i.e. the kings are two orthogonal squares apart, with the other player on move) and placing Black in zugzwang - he must either move his king, allowing White's king to penetrate, or his bishop, allowing a decisive incursion by White's bishop. 4...Bd7 5.Bxg6!
Centurini
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Centurini, 1856
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Two rules given by Luigi Centurini in the 19th century apply:
The position in the second diagram shows a winning position for White, although it requires accurate play. A knight pawn always wins if the defending bishop only has one long diagonal available (Fine & Benko 2003:155-56).
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This position was reached in a game from the 1965 Candidates Tournament between Lajos Portisch and former World Champion Mikhail Tal. White must defend accurately and utilize reciprocal zugzwang. Often he has only one or two moves that avoid a losing position. Black was unable to make any progress and the game was drawn on move 83 (Nunn 1995:169).
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Read main article: opposite-colored bishops endgame
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.
Current theory is that bishops are better than knights about 60 percent of the time in the endgame. The more symmetrical the pawn structure, the better it is for the knight. The knight is best suited at an outpost in the center, particularly where it cannot easily be driven away, 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 & Mikhalchishin 1995:122).
Fine and Benko (Fine & Benko 2003:205) give four conclusions:
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This is a draw if the defending king is in front of the pawn or sufficiently close. The defending king can occupy a square in front of the pawn of the opposite color as the bishop and cannot be driven away. Otherwise the attacker can win (Fine & Benko 2003:206).
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This is a draw if the defending 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 cannot both block the bishop and drive the defending king away. Otherwise the attacker can win (Fine & Benko 2003:209).
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. Rook endings are probably the deepest and most well studied endgames. They are a common type of endgame in practice, occurring in about 10 percent of all games (including ones that do not reach an endgame) (Emms 2008:7). These endgames occur frequently because rooks are often the last pieces to be exchanged. The ability to play these endgames well is a major factor distinguishing masters from amateurs (Nunn 2007:125). When both sides have two rooks and pawns, the stronger side usually has more winning chances than if each had only one rook (Emms 2008:141).
Three rules of thumb regarding rooks are worth noting:
An important winning position in the rook and pawn versus rook endgame 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.
Read main article: Rook and pawn versus rook endgame
Fine & Benko, diagram 646| a | b | c | d | e | f | g | h | ||
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Generally (but not always), if the defending king can reach the queening square of the pawn the game is a draw (see Philidor position), otherwise the attacker usually wins (if it is not a rook pawn) (see Lucena position) (Fine & Benko 2003:294). The winning procedure can be very difficult and some positions require up to sixty moves to win (Speelman, Tisdall & Wade 1993:7). If the attacking rook is two files from the pawn and the defending king is cut off on the other side, the attacker normally wins (with a few exceptions) (Fine & Benko 2003:294). The rook and pawn versus rook is the most common of the "piece and pawn versus piece" endgames (Nunn 2007:148).
The most difficult case of a rook and pawn versus a rook occurs when the attacking rook is one file over from the pawn and the defending 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 endgame.)
The context of this quote shows it is a comment on the fact that a small advantage in a rook and pawn endgame is less likely to be converted into a win. Mark Dvoretsky said that the statement is "semi-joking, semi-serious" (Dvoretsky & Yusupov 2008:159). This quotation has variously been attributed to Savielly Tartakower and to Siegbert Tarrasch. Writers Victor Korchnoi (Korchnoi 2002:29), John Emms (Emms 2008:41), and James Howell (Howell 1997:36) attribute the quote to Tartakower, whereas Dvoretsky (Dvoretsky 2006:158), Andy Soltis (Soltis 2003:52), Karsten Müller, and Kaufeld & Kern (Kaufeld & Kern 2011:167) attribute it to Tarrasch. John Watson attributed to Tarrasch "by legend" and says that statistics do not support the statement (Watson 1998:81-82). Benko wonders if it was due to Vasily Smyslov (Benko 2007:186). Attributing the quote to Tarrasch may be a result of confusion between this quote and the Tarrasch rule concerning rooks. The source of the quote is currently unresolved. Benko noted that although the saying is usually said with tongue in cheek, it is truer in practice than one might think (Benko 2007:189).
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 endgame.
Read main article: Queen and pawn versus queen endgame
Müller & Lamprecht, diagram 9.12A| a | b | c | d | e | f | g | h | ||
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The queen and pawn versus queen endgame is the second most common of the "piece and pawn versus piece" endgames, after rook and pawn versus rook. It is very complicated and difficult to play. Human analysts were not able to make a complete analysis before the advent of endgame tablebases (Nunn 2007:148). This combination is a win less frequently than the equivalent ending with rooks.
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The difference in material between a rook and a minor piece is about two points or a little less, the equivalent of two pawns.
If both sides have pawns, the result essentially depends on how many pawns the minor piece has for the exchange:
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In an endgame, two minor pieces are approximately equivalent to a rook plus one pawn. The pawn structure is important. The two pieces have the advantage if the opponent's pawns are weak. Initiative is more important in this endgame than any other. The general outcome can be broken down by the number of pawns.
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Without pawns this is normally drawn, but either side wins in some positions. A queen and pawn are normally equivalent to two rooks, which is usually a draw if both sides have an equal number of additional pawns. Two rooks plus one pawn versus a queen is also generally drawn. Otherwise, if either side has an additional pawn, that side normally wins (Fine & Benko 2003:566-67).
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If there are no pawns, the position is usually drawn, but either side wins in some positions. A queen is equivalent to a rook and bishop plus one pawn. If the queen has an additional pawn it wins, but with difficulty. A rook and bishop plus two pawns win over a queen (Fine & Benko 2003:563).
Philidor, 1777
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D.Ponziani, 1782
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Johann Berger 1914 (Fine & Benko diagram 1053)
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Fine & Benko diagram 1054
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There are many cases for a lone piece versus pawns. The position of the pawns is critical.
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Besides the basic checkmates, there are other endings with no pawns. They do not occur very often in practice. Two of the most common pawnless endgames (when the defense has a piece in addition to the king) are (1) a queen versus a rook and (2) a rook and bishop versus a rook. A queen wins against a rook, see Queen versus rook. A rook and bishop versus a rook is generally a theoretical draw, but the defense is difficult and there are winning positions (see rook and bishop versus rook endgame).
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 (see chess piece relative value). 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.
Endgame tablebases have made some minor corrections to historical endgame analysis, but they have made some more significant changes to endgame theory too. (The fifty-move rule is not taken into account in these studies.) Major changes to endgame theory as a result of tablebases include (Müller & Lamprecht 2001:8,400-406):
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| 1 | 1 | ||||||||
| a | b | c | d | e | f | g | h | ||
In May 2006 a record-shattering 517-move endgame was announced (see first diagram). Marc Bourzutschky found it using a program written by Yakov Konoval. Black's first move is 1. ... Rd7+ and White wins the rook in 517 moves. This was determined using the easier-to-calculate depth-to-conversion method, which assumes that the two sides are aiming respectively to reduce the game to a simpler won ending or to delay that conversion. Such endgames do not necessarily represent strictly optimal play from both sides, as Black may delay checkmate by allowing an earlier conversion or White may accelerate it by delaying a conversion (or not making one at all). In September 2009, it was found that the distance to mate (not conversion) in a similar position to the Bourzutschky-Konoval position was 545 (see diagram). The same researchers later confirmed that this (along with variations of it) is the longest 7-man pawnless endgame, and that, with pawns, the longest 7-man endgame is the one depicted in the second diagram. White takes 6 moves to promote his pawn to a Knight, after which it takes him another 543 moves to win the game.
The fifty-move rule is ignored in the calculation of these results and lengths.
Endgames can be classified by the material on the board. The standard classification system lists each player's material, including the kings, in the following order: king, queen, bishops, knights, rooks, pawn. Each piece is designated by its algebraic symbol.
For example, if White has a king and pawn, and Black has only a king, the endgame is classified KPK. If White has bishop and knight, and Black has a rook, the endgame is classified KBNKR. Note that KNBKR would be incorrect; bishops come before knights.
In positions with two or more bishops on the board, a "bishop signature" may be added to clarify the relationship between the bishops. Two methods have been used. The informal method is to designate one color of squares as "x" and the other color as "y". An endgame of KBPKB can be written KBPKB x-y if the bishops are opposite-colored, or KBPKB x-x if the bishops are same-colored. The more formal method is to use a four digit suffix of the form abcd:
Thus, the aforementioned endgame can be written KBPKB_1001 for opposite-color bishops, and KBPKB_1010 for same-color bishops.
In positions with one or more rooks on the board and where one or both players have one or both castling rights, a castling signature may be added to indicate which castling rights exist. The method is to use a one to four character suffix formed by omitting up to three characters from the string KQkq.
Thus the endgame where White has bishop and rook and Black has a rook can be written KBRKR if no castling rights exist or KBRKR_kq if White may castle on the king's side and Black may castle on the queen's side. In case the position also has two or more bishops the castling signature follows the bishop signature as in KBBNKRR_1100_kq.
GBR code is an alternative method of endgame classification.
The Encyclopedia of Chess Endings - ECE by Chess Informant had a different classification scheme, somewhat similar to the ECO codes, but it is not widely used. The full system is a 53-page index that was contained in the book The Best Endings of Capablanca and Fischer. The code starts with a letter representing the most powerful piece on the board, not counting kings. The order is queen, rook, bishop, knight, and then pawn. (Figurines are used to stand for the pieces.) Each of these has up to 100 subclassifications, for instance R00 through R99. The first digit is a code for the pieces. For instance, R0 contains all endgames with a rook versus pawns and a rook versus a lone king, R8 contains the double rook endgames, and R9 contains the endings with more than four pieces. The second digit is a classification for the number of pawns. For instance, R30 contains endgames with a rook versus a rook without pawns or with one pawn and R38 are rook versus rook endings in which one player has two extra pawns.
The table below lists the most common endings in actual games by percentage (percentage of games, not percentage of endings; generally pawns go along with the pieces). (Müller & Lamprecht 2001:11-12, 304)
| Percent | Pieces | Pieces |
|---|---|---|
| 8.45 | rook | rook |
| 6.76 | rook & bishop | rook & knight |
| 3.45 | two rooks | two rooks |
| 3.37 | rook & bishop | rook & bishop (same color) |
| 3.29 | bishop | knight |
| 3.09 | rook & knight | rook & knight |
| 2.87 | king & pawns | king (and pawns) |
| 1.92 | rook & bishop | rook & bishop (opposite color) |
| 1.87 | queen | queen |
| 1.77 | rook & bishop | rook |
| 1.65 | bishop | bishop (same color) |
| 1.56 | knight | knight |
| 1.51 | rook | bishop |
| 1.42 | rook & knight | rook |
| 1.11 | bishop | bishop (opposite color) |
| 1.01 | bishop | pawns |
| 0.97 | rook | knight |
| 0.92 | knight | pawns |
| 0.90 | queen & minor piece | queen |
| 0.81 | rook | two minor pieces |
| 0.75 | rook | pawns |
| 0.69 | queen | rook & minor piece |
| 0.67 | rook & pawn | rook |
| 0.56 | rook & two pawns | rook |
| 0.42 | queen | pawns |
| 0.40 | queen | rook |
| 0.31 | queen | two rooks |
| 0.23 | king & one pawn | king |
| 0.17 | queen | minor piece |
| 0.09 | queen & one pawn | queen |
| 0.08 | queen | two minor pieces |
| 0.02 | bishop & knight | king |
| 0.01 | queen | three minor pieces |
Read main article: Chess endgame literature
There are many books on endgames, see Chess endgame literature for a large list and the history. Some of the most popular current ones are:
Endgame topics
Specific endgames