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chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...
and other similar games, the endgame (or end game or ending) is the stage of the game when few
piece Piece or Pieces (not to be confused with peace) may refer to: Arts, entertainment, and media Games * Piece (chess), pieces deployed on a chessboard for playing the game of chess * ''Pieces'' (video game), a 1994 puzzle game for the Super NES * ...
s 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 . The king, which normally should stay hidden during the game should become active in the endgame, as it can help escort pawns to the promotion square, attack enemy pawns, protect other pieces, and restrict the movement of the enemy king. All chess positions with up to seven pieces on the board have been solved, that is, the outcome (win, loss, or draw) of best play by both sides is known, and textbooks and reference works teach the best play. Most endgames are not solved, and textbooks teach useful strategies and tactics for them. The body of
chess theory The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who wri ...
devoted to endgames is known as endgame theory. Compared to chess opening theory, which changes frequently, giving way to middlegame positions that fall in and out of popularity, endgame theory is less subject to change. Many
endgame studies In the game of chess, an endgame study, or just study, is a composed position—that is, one that has been made up rather than played in an actual game—presented as a sort of puzzle, in which the aim of the solver is to find the essentially uniq ...
have been composed, 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. In some compositions, the starting position would be unlikely to occur in an actual game; but if the starting position is not so exotic, the composition is sometimes incorporated into endgame theory. Chess players classify endgames according to the type of pieces that remain.


Categories

Endgames can be divided into three categories: # Theoretical endgames – positions where the correct line of play is generally known and well-analyzed, so the solution is a matter of technique # Practical endgames – positions arising in actual games, where skillful play should transform it into a theoretical endgame position # Artistic endgames (
studies Study or studies may refer to: General * Education ** Higher education * Clinical trial * Experiment * Observational study * Research * Study skills, abilities and approaches applied to learning Other * Study (art), a drawing or series of d ...
) – contrived positions which contain a theoretical endgame hidden by problematic complications. This article generally does not consider studies.


The start of the endgame

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.
Alexander Alekhine Alexander Aleksandrovich Alekhine, ''Aleksándr Aleksándrovich Alékhin''; (March 24, 1946) was a Russian and French chess player and the fourth World Chess Champion, a title he held for two reigns. By the age of 22, Alekhine was already a ...
said "We cannot define when the middle game ends and the end-game starts". With the usual system for
chess piece relative value In chess, a relative value (or point value) is a standard value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to assessing a position. Valuation systems almost always assign ...
, Speelman considers that endgames are positions in which each player has thirteen or fewer points in (not counting the
king King is the title given to a male monarch in a variety of contexts. The female equivalent is queen regnant, queen, which title is also given to the queen consort, consort of a king. *In the context of prehistory, antiquity and contempora ...
). Alternatively, an endgame is a position in which the king can be used actively, but there are some famous exceptions to that. Minev characterizes endgames as positions having four or fewer pieces other than kings and pawns. 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 Queen or QUEEN may refer to: Monarchy * Queen regnant, a female monarch of a Kingdom ** List of queens regnant * Queen consort, the wife of a reigning king * Queen dowager, the widow of a king * Queen mother, a queen dowager who is the mother ...
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". Alburt and Krogius give three characteristics of an endgame: # Endgames favor an aggressive king. #
Passed pawn In chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth ; i.e. there are no opposing pawns in front of it on either the same or adjacent files. A passed pawn is sometimes colloquially called a ''pas ...
s increase greatly in importance. #
Zugzwang Zugzwang (German for "compulsion to move", ) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal mov ...
is often a factor in endgames and rarely in other stages of the game. 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. 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: * better ; * open for attacking; * vulnerable king position; * misplaced pieces.


General considerations

In endgames with pieces and pawns, an extra pawn is a winning advantage in 50 to 60 percent of cases. It becomes more decisive if the stronger side also has a positional advantage. In general, the player with a 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. 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 chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth ; i.e. there are no opposing pawns in front of it on either the same or adjacent files. A passed pawn is sometimes colloquially called a ''pas ...
. In the endgame, it is usually better for the player with more pawns to avoid many pawn exchanges, because winning chances usually decrease as the number of pawns decreases. 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. Usually in the endgame, the stronger side (the one with more using the standard piece point count system) should try to exchange pieces (
knights A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the ...
,
bishops A bishop is an ordained clergy member who is entrusted with a position of authority and oversight in a religious institution. In Christianity, bishops are normally responsible for the governance of dioceses. The role or office of bishop is ca ...
,
rooks Rook (''Corvus frugilegus'') is a bird of the corvid family. Rook or rooks may also refer to: Games *Rook (chess), a piece in chess *Rook (card game), a trick-taking card game Military *Sukhoi Su-25 The Sukhoi Su-25 ''Grach'' (russian: � ...
, and
queens Queens is a borough of New York City, coextensive with Queens County, in the U.S. state of New York. Located on Long Island, it is the largest New York City borough by area. It is bordered by the borough of Brooklyn at the western tip of Long ...
), 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. Usually the first person to make a queen in the endgame wins if the opponent is unable to promote the turn immediately after. With the recent growth of
computer chess Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysi ...
, a 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: # In
king King is the title given to a male monarch in a variety of contexts. The female equivalent is queen regnant, queen, which title is also given to the queen consort, consort of a king. *In the context of prehistory, antiquity and contempora ...
and
pawn Pawn most often refers to: * Pawn (chess), the weakest and most numerous piece in the game * Pawnbroker or pawnshop, a business that provides loans by taking personal property as collateral Pawn may also refer to: Places * Pawn, Oregon, an his ...
endings, an extra pawn is decisive in more than 90 percent of the cases. # 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. # The king plays an important role in the endgame. #
Initiative In political science, an initiative (also known as a popular initiative or citizens' initiative) is a means by which a petition signed by a certain number of registered voters can force a government to choose either to enact a law or hold a ...
is more important in the endgame than in other phases of the game. In rook endgames the initiative is usually worth at least a pawn. # Two connected
passed pawn In chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth ; i.e. there are no opposing pawns in front of it on either the same or adjacent files. A passed pawn is sometimes colloquially called a ''pas ...
s are very strong. If they reach their sixth they are generally as powerful as a rook.


Common types of endgames


Endings with no pawns


Basic checkmates

Many endings without pawns have been solved, that is, best play for both sides from any starting position can be determined, and the outcome (win, loss, or draw) is known. For example, the following are all wins for the side with pieces: # king and queen against a king—A queen, with its king, can easily
checkmate Checkmate (often shortened to mate) is any game position in chess and other chess-like games in which a player's king is in check (threatened with ) and there is no possible escape. Checkmating the opponent wins the game. In chess, the king is ...
a lone king. # king and rook against a king # king and two bishops of opposite colour against a king # king, bishop, and knight against a king See Wikibooks – Chess/The Endgame for a demonstration of the first two checkmates, which are generally taught in textbooks as basic knowledge. The last two are sometimes taught as basic knowledge as well, although the procedure for mate with bishop and knight is relatively difficult and many tournament players do not know it.


Other endings with no pawns

The ending of king and
bishop A bishop is an ordained clergy member who is entrusted with a position of authority and oversight in a religious institution. In Christianity, bishops are normally responsible for the governance of dioceses. The role or office of bishop is ...
versus king is a trivial draw, in that checkmate is not even possible. Likewise for king and
knight A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the Christian denomination, church or the country, especially in a military capacity. Knighthood ...
versus king. Two knights cannot force checkmate against a lone king (see
Two knights endgame The two knights endgame is a chess endgame with a king and two knights versus a king. In contrast to a king and two bishops (on opposite-colored squares), or a bishop and a knight, a king and two knights cannot checkmate against a lone king (howe ...
). 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. If the weaker side also has material (besides the king), checkmate is sometimes possible. The winning chances with two knights are insignificant except against a few pawns. () The procedure can be long and difficult. In competition, the
fifty-move rule The fifty-move rule in chess states that a player can claim a draw if no has been made and no pawn has been moved in the last fifty moves (for this purpose a "move" consists of a player completing a turn followed by the opponent completing a tur ...
will often result in the game being drawn first. The endgame of king and three knights against king will not normally occur in a game, but it is of theoretical interest. The three knights win. 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 pawnless chess endgame#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 The rook and bishop versus rook endgame is a chess endgame where one player has just a king, a rook, and a bishop, and the other player has just a king and a rook. This combination of is one of the most common pawnless chess endgames. It is gene ...
).


King and pawn endings

King and pawn endgames involve only
kings Kings or King's may refer to: *Monarchs: The sovereign heads of states and/or nations, with the male being kings *One of several works known as the "Book of Kings": **The Books of Kings part of the Bible, divided into two parts **The ''Shahnameh'' ...
and pawns on one or both sides.
International Master FIDE titles are awarded by the international chess governing body FIDE (''Fédération Internationale des Échecs'') for outstanding performance. The highest such title is Grandmaster (GM). Titles generally require a combination of Elo rating and ...
Cecil Purdy Cecil John Seddon Purdy (27 March 1906 – 6 November 1979), often referred to as "C. J. S. Purdy", was an Australian chess player and writer. He was awarded the titles International Master in 1951 and Grandmaster of correspondence chess in ...
said, "Pawn endings are to chess as putting is to golf." Any endgame with pieces and pawns has the possibility of into a pawn ending. In king and pawn endings, an extra pawn is decisive in more than 90 percent of the cases. Getting a
passed pawn In chess, a passed pawn is a pawn with no opposing pawns to prevent it from advancing to the eighth ; i.e. there are no opposing pawns in front of it on either the same or adjacent files. A passed pawn is sometimes colloquially called a ''pas ...
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 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 Opposition may refer to: Arts and media * ''Opposition'' (Altars EP), 2011 EP by Christian metalcore band Altars * The Opposition (band), a London post-punk band * '' The Opposition with Jordan Klepper'', a late-night television series on Com ...
is an important technique that is used to gain an advantage. When two kings are in opposition, they are on the same (or ) with one empty square separating them. The player having the move loses the opposition. That player must move the 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. The attacker should try to penetrate with or without the opposition. The tactics of
triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...
and
zugzwang Zugzwang (German for "compulsion to move", ) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal mov ...
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 Opposition may refer to: Arts and media * ''Opposition'' (Altars EP), 2011 EP by Christian metalcore band Altars * The Opposition (band), a London post-punk band * '' The Opposition with Jordan Klepper'', a late-night television series on Com ...
,
triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...
, and the Réti manoeuvre.


King and pawn versus king

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). 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 is an exception because the king may not be able to get out of the way of its pawn.


Knight and pawn endings

Knight A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the Christian denomination, church or the country, especially in a military capacity. Knighthood ...
and pawn endgames feature clever manoeuvring 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 In musical terminology, tempo ( Italian, 'time'; plural ''tempos'', or ''tempi'' from the Italian plural) is the speed or pace of a given piece. In classical music, tempo is typically indicated with an instruction at the start of a piece (ofte ...
, so knight and pawn endgames have much in common with king and pawn endgames. As a result,
Mikhail Botvinnik Mikhail Moiseyevich Botvinnik, ( – May 5, 1995) was a Soviet and Russian chess grandmaster. The sixth World Chess Champion, he also worked as an electrical engineer and computer scientist and was a pioneer in computer chess. Botvinnik ...
stated, “A knight ending is really a pawn ending.”


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 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 In musical terminology, tempo ( Italian, 'time'; plural ''tempos'', or ''tempi'' from the Italian plural) is the speed or pace of a given piece. In classical music, tempo is typically indicated with an instruction at the start of a piece (ofte ...
.


Bishop and pawn endings

Bishop A bishop is an ordained clergy member who is entrusted with a position of authority and oversight in a religious institution. In Christianity, bishops are normally responsible for the governance of dioceses. The role or office of bishop is ...
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 is one that is hemmed in by pawns of its own color, and has the burden of defending them. The adjacent diagram, from Molnar–Nagy, Hungary 1966, illustrates the concepts of good bishop versus bad bishop, opposition,
zugzwang Zugzwang (German for "compulsion to move", ) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal mov ...
, and outside passed pawn. White wins with 1. e6! (vacating e5 for his king) 1... Bxe6 2. Bc2! (threatening Bxg6) 2... Bf7 3. Be4! (threatening Bxc6) 3... Be8 4. Ke5! (seizing the opposition .e. the kings are two orthogonal squares apart, with the other player on moveand 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!


Bishop and pawn versus bishop on the same color

Two rules given by Luigi Centurini in the 19th century apply: * The game is a draw if the defending king can reach any square in front of the pawn that is opposite in color to the squares the bishops travel on. * If the defending king is behind the pawn and the attacking king is near the pawn, the defender can draw only if his king is attacking the pawn, he has the opposition, and his bishop can move on two diagonals that each have at least two squares available (other than the square it is on). This is the case for and the whose promotion square is not the same color as the bishop. The position in the second diagram shows a winning position for White, although it requires accurate play. A always wins if the defending bishop only has one long diagonal available. This position was reached in a game from the 1965
Candidates Tournament The Candidates Tournament (or in some periods Candidates Matches) is a chess tournament organized by FIDE, chess's international governing body, since 1950, as the final contest to determine the challenger for the World Chess Championship. The w ...
between
Lajos Portisch Lajos Portisch (born 4 April 1937) is a Hungarian chess Grandmaster, whose positional style earned him the nickname, the "Hungarian Botvinnik". One of the strongest non-Soviet players from the early 1960s into the late 1980s, he participated ...
and former
World Champion A world championship is generally an international competition open to elite competitors from around the world, representing their nations, and winning such an event will be considered the highest or near highest achievement in the sport, game, ...
Mikhail Tal Mikhail Nekhemyevich Tal; rus, Михаил Нехемьевич Таль, ''Mikhail Nekhem'yevich Tal' '', ; sometimes transliterated ''Mihails Tals'' or ''Mihail Tal'' (9 November 1936 – 28 June 1992) was a Soviet-Latvian chess player ...
. 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.


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 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 on which his bishop operates. The weaker side should often try to make their bishop by placing their pawns on the same color of their bishop in order to defend their remaining pawns, thereby creating an impregnable
fortress A fortification is a military construction or building designed for the defense of territories in warfare, and is also used to establish rule in a region during peacetime. The term is derived from Latin ''fortis'' ("strong") and ''facere'' ...
.


Bishop versus knight endings (with pawns)

Current
theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may ...
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. Fine and Benko 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 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.


Knight and pawn versus bishop

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.


Rook and pawn endings

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). 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. When both sides have two rooks and pawns, the stronger side usually has more winning chances than if each had only one rook. Three rules of thumb regarding rooks are worth noting: # 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. # Rooks are very poor defenders relative to their attacking strength, so it is often good to sacrifice a pawn for activity. # 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 versus Tartakower, New York 1924 (se
annotated game without diagrams
o
Java board
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 and 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 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). The winning procedure can be very difficult and some positions require up to sixty moves to win. 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). The rook and pawn versus rook is the most common of the "piece and pawn versus piece" endgames. 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.)


Quotation

*"All rook and pawn endings are drawn." 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 Mark Izrailevich Dvoretsky (russian: Марк Изра́илевич Дворе́цкий; December 9, 1947 – September 26, 2016) was a Russian chess trainer, writer, and International Master. Biography Dvoretsky was born in Moscow in 1947. H ...
said that the statement is "semi-joking, semi-serious". This quotation has variously been attributed to Savielly Tartakower and to Siegbert Tarrasch. Writers Victor Korchnoi, John Emms, and
James Howell James Howell (c. 1594 – 1666) was a 17th-century Anglo-Welsh historian and writer who is in many ways a representative figure of his age. The son of a Welsh clergyman, he was for much of his life in the shadow of his elder brother Thomas Ho ...
, attribute the quote to Tartakower, whereas Dvoretsky,
Andrew Soltis Andrew Eden Soltis (born May 28, 1947) is an American chess grandmaster, author and columnist. He was inducted into the United States Chess Hall of Fame in September 2011. Chess career Soltis learned how the chess pieces moved at age 10 when he ...
, Karsten Müller, and Kaufeld & Kern attribute it to Tarrasch. John Watson attributed to Tarrasch "by legend" and says that statistics do not support the statement.
Benko Benko, Benkó (pron. '' enko') or Benkö, Benkő (pron. ') may refer to: Arts and entertainment * Filip Benko (born 1986), Swedish actor * Gregor Benko (born 1944), American writer, lecturer, record producer, and collector-historian * Gyula Benkő ...
wonders if it was due to Vasily Smyslov. 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.


Queen and pawn endings

In
queen Queen or QUEEN may refer to: Monarchy * Queen regnant, a female monarch of a Kingdom ** List of queens regnant * Queen consort, the wife of a reigning king * Queen dowager, the widow of a king * Queen mother, a queen dowager who is the mother ...
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 In the game of chess, perpetual check is a situation in which one player can a draw by an unending series of checks. This typically arises when the player who is checking cannot deliver checkmate, and failing to continue the series of checks give ...
. 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.


Queen and pawn versus queen

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 The rook and pawn versus rook endgame is a fundamentally important, widely studied chess endgame. Precise play is usually required in these positions. With optimal play, some complicated wins require sixty moves to either checkmate, capture the d ...
. It is very complicated and difficult to play. Human analysts were not able to make a complete analysis before the advent of endgame tablebases. This combination is a win less frequently than the equivalent ending with rooks.


Rook versus a minor piece

The difference in between a rook and a is about two points or a little less, the equivalent of two pawns. * A rook and a pawn versus a minor piece: normally a win for the rook but there are some draws. In particular, if the pawn is on its sixth rank and is a or , and the bishop does not control the pawn's promotion square, the position is a draw. See Wrong bishop. * A rook versus a minor piece: normally a draw but in some cases the rook wins, see
pawnless chess endgame A pawnless chess endgame is a chess endgame in which only a few pieces remain, and no pawns. The basic checkmates are types of pawnless endgames. Endgames without pawns do not occur very often in practice except for the basic checkmates of king a ...
. * A rook versus a minor piece and one pawn: usually a draw but the rook may win. * A rook versus a minor piece and two pawns: usually a draw but the minor piece may win. * A rook versus a minor piece and three pawns: a win for the minor piece. If both sides have pawns, the result essentially depends on how many pawns the minor piece has for the exchange: * No pawns for the exchange (i.e. same number of pawns on each side): the rook usually wins. * One pawn for the exchange (i.e. minor piece has one more pawn): the rook usually wins, but it is technically difficult. If all of the pawns are on one side of the board it is usually a draw. * Two pawns for the exchange: this is normally a draw. With a bishop either side may have winning chances. With a knight, the rook may have winning chances and the defense is difficult for the knight if the pawns are scattered. * Three pawns for the exchange: this is normally a win for the minor piece.


Two minor pieces versus a rook

In an endgame, two 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 In political science, an initiative (also known as a popular initiative or citizens' initiative) is a means by which a petition signed by a certain number of registered voters can force a government to choose either to enact a law or hold a ...
is more important in this endgame than any other. The general outcome can be broken down by the number of pawns. * The two pieces have one or more extra pawns: always a win for the pieces. * Same number of pawns: usually a draw but the two pieces win more often than the rook. * The rook has one extra pawn: usually a draw but either side may have winning chances, depending on positional factors. * The rook has two additional pawns: normally a win for the rook.


Queen versus two rooks

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. While playing for a draw, the defender (the side with fewer pawns) should try to avoid situations in which the queen and rooks are forcibly traded into a losing king and pawn endgame.


Queen versus rook and minor piece

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.


Queen versus rook

* Without pawns, the queen normally wins but it can be difficult and there are some drawn positions (see Philidor position#Queen versus rook). * If the rook has one pawn drawing positions are possible, depending on the pawn and the proximity of the rook and king. See fortress (chess)#Rook and pawn versus queen. Otherwise the queen wins. * If the rook has two
connected pawns In chess, connected pawns are two or more pawns of the same color on adjacent , as distinct from isolated pawns. These pawns are instrumental in creating pawn structure because, when diagonally adjacent, like the two rightmost white pawns, they ...
the position is usually a draw. For any other two pawns, the queen wins except in the positions where a fortress with one pawn can be reached. * If the rook has three or more pawns the position is usually a draw but there are cases in which the queen wins and some in which the rook wins. * If the queen also has a pawn or pawns it wins except in unusual positions.


Piece versus pawns

There are many cases for a lone piece versus pawns. The position of the pawns is critical. * Minor piece versus pawns: A minor piece versus one or two pawns is normally a draw, unless the pawns are advanced. Three pawns either draw or win, depending on how advanced they are. Three connected pawns win against a bishop if they all get past their fourth rank. A knight can draw against three connected pawns if none are beyond their fourth rank. * Rook versus pawns: If the rook's king is not near, one pawn draws and two pawns win. If the rook's king is near, the rook wins over one or two pawns and draws against three. Four pawns usually win but the rook may be able to draw, depending on their position. More than four pawns win against the rook. * Queen versus pawns: A queen can win against any number of pawns, depending on how advanced they are. The queen would win against eight pawns on the second rank but one pawn on the seventh rank may draw (see Queen versus pawn endgame) and two advanced pawns may win.


Positions with a material imbalance

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 (bishop or knight) and a pawn (see
Chess piece relative value In chess, a relative value (or point value) is a standard value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to assessing a position. Valuation systems almost always assign ...
). 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.


Effect of tablebases on endgame theory

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 The fifty-move rule in chess states that a player can claim a draw if no has been made and no pawn has been moved in the last fifty moves (for this purpose a "move" consists of a player completing a turn followed by the opponent completing a tur ...
is not taken into account in these studies.) Major changes to endgame theory as a result of tablebases include the following: * Queen versus rook (see Philidor position#Queen versus rook). There are two changes here enabling the rook to put up a better defense, but the queen still wins. (a) People usually opt for a second-rank defense with the rook on the second rank and the king behind it (or symmetrical positions on the other edges of the board). Tablebases show that a third-rank defense takes a while to breach, which is difficult for a human to do. (b) People had assumed that the rook needs to stay as close to the king for as long as possible, but tablebases show that it is best to move the rook away from the king at some earlier point. * Queen and pawn versus queen. Tablebases have shown that this can be won in many more positions than was thought, but the logic of the moves is presently beyond human understanding. * Queen versus two bishops. This was thought to be a draw due to the existence of a drawing
fortress A fortification is a military construction or building designed for the defense of territories in warfare, and is also used to establish rule in a region during peacetime. The term is derived from Latin ''fortis'' ("strong") and ''facere'' ...
position, but the queen can win most of the time by preventing the bishops from getting to the fortress. However, it can take up to 71 moves to force a win. * Queen versus two knights. This was thought to be a draw, but the queen has more winning positions than was previously thought. Also, many analysts gave a position (see diagram) that they thought was a draw but it is actually a win for the queen. In the diagram, White checkmates in 43 moves, starting with 1. Qc7 (the only winning move). Note that Nunn says "The general result is undoubtedly a draw, but there are many losing positions, some of them very lengthy." On the other hand, 73.44% of positions are won by the queen, almost all of the remainder being positions where the side with two knights can immediately capture the queen – 97.59% of positions with the side with the queen to move are won by that side. + However, these percentages can be misleading, and most "general results" are based on the analysis of grandmasters using the tablebase data. For instance, although nearly 90 percent of all of these positions are wins for the queen, it is generally a draw if the king is not separated from the knights and they are on reasonable squares. * Two bishops versus a knight. This was thought to be a draw but the bishops generally win. However, it takes up to 66 moves. The position in the diagram was thought to be a draw for over one hundred years, but tablebases show that White wins in 57 moves. All of the long wins go through this type of semi-fortress position. It takes several moves to force Black out of the temporary fortress in the corner; then precise play with the bishops prevents Black from forming the temporary fortress in another corner. Before computer analysis, Speelman listed this position as unresolved, but "probably a draw". * Queen and bishop versus two rooks. This was thought to be a draw but the queen and bishop usually win. It takes up to 84 moves. * Rook and bishop versus bishop and knight, bishops on opposite colors. This was thought to be a draw but the rook and bishop generally win. It takes up to 98 moves.
Magnus Carlsen Sven Magnus Øen Carlsen (born 30 November 1990) is a Norwegian chess grandmaster who is the reigning five-time World Chess Champion. He is also a three-time World Rapid Chess Champion and five-time World Blitz Chess Champion. Carlsen has h ...
successfully converted this configuration within the 50-move limit against Francisco Vallejo Pons in 2019. Even with best play from the starting RB v BN position, the stronger side would have won a piece well within 50 moves. * Rook and bishop versus rook. The second-rank defense was discovered using tablebases.


Longest forced win

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 that position was 545 (see the first 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 the pawn to a Knight (leading to a position similar to the first diagram), after which it takes another 543 moves to win the game. The
fifty-move rule The fifty-move rule in chess states that a player can claim a draw if no has been made and no pawn has been moved in the last fifty moves (for this purpose a "move" consists of a player completing a turn followed by the opponent completing a tur ...
was ignored in the calculation of these results and lengths, and as of 2014, these games could never occur, because of the seventy-five move rule.


Endgame classification

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: *a = number of White light-squared bishops *b = number of White dark-squared bishops *c = number of Black light-squared bishops *d = number of Black dark-squared bishops 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.


Frequency table

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).


Quotations

* " order to improve your game, you must study the endgame before anything else; for, whereas the endings can be studied and mastered by themselves, the middlegame and the opening must be studied in relation to the endgame." (Emphasis in original.) * "... the endgame is as important as the opening and middlegame ... three of the five losses sustained by
Bronstein Bronstein is the surname of: * Lev Davidovich Bronstein, birth name of Leon Trotsky (1879–1940), Russian Marxist revolutionary and politician * David Bronstein (1924–2006), Soviet chess Grandmaster * Hila Bronstein (born 1983), German singer, ...
in his drawn ... match with Botvinnik in 1951 were caused by weak endgame play." * "Studying the opening is just memorizing moves and hoping for traps, but studying the endgame is chess." –
Joshua Waitzkin Joshua Waitzkin (born December 4, 1976) is an American former chess player, martial arts competitor, and author. As a child, he was recognized as a prodigy, and won the U.S. Junior Chess championship in 1993 and 1994. The film '' Searching for ...
* "If you want to win at chess, begin with the ending." –
Irving Chernev Irving Chernev (January 29, 1900 – September 29, 1981) was a chess player and prolific Russian-American chess author. He was born in Pryluky in the Russian Empire (now in Ukraine) and emigrated to the United States in 1905. Chernev was a na ...
''
Chess Life The monthly ''Chess Life'' and bi-monthly ''Chess Life Kids'' (formerly ''School Mates'' and ''Chess Life for Kids'') are the official magazines published by the United States Chess Federation (US Chess). ''Chess Life'' is advertised as the "mos ...
'', Sept. 1961, p. 253
* "Repeating moves in an ending can be very useful. Apart from the obvious gain of time on the clock one notices that the side with the advantage gains psychological benefit." –
Sergey Belavenets Sergey Vsevolodovich Belavenets (russian: Серге́й Всеволодович Белавенец; 18 July 19106 March 1942) was a Soviet chess master, theoretician, and chess journalist. Early life Belavenets was born in Smolensk to a n ...
* "It cannot be too greatly emphasized that the most important role in pawn endings is played by the king." – Siegbert Tarrasch * "After a bad opening, there is hope for the middle game. After a bad middle game, there is hope for the endgame. But once you are in the endgame, the moment of truth has arrived." – Edmar Mednis * "Patience is the most valuable trait of the endgame player." – Pal Benko


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: *''
Basic Chess Endings ''Basic Chess Endings'' (abbreviated BCE) is a book on chess endgames which was written by Grandmaster Reuben Fine and originally published on October 27, 1941. It is considered the first systematic book in English on the endgame phase of the g ...
'', by Reuben Fine and Pal Benko, 1941, 2003, McKay. . The 1941 edition by Fine was the first of the modern endgame books in English. It was recently revised by Benko. *''Dvoretsky's Endgame Manual, second edition'', by
Mark Dvoretsky Mark Izrailevich Dvoretsky (russian: Марк Изра́илевич Дворе́цкий; December 9, 1947 – September 26, 2016) was a Russian chess trainer, writer, and International Master. Biography Dvoretsky was born in Moscow in 1947. H ...
, 2006, Russel Enterprises. . A modern manual book by a noted chess teacher. *''Encyclopedia of Chess Endings III – Rook Endings 2'', Andras Adorjan, Alexander Beliavsky, Svetozar Gligorić, Robert Hübner,
Anatoly Karpov Anatoly Yevgenyevich Karpov ( rus, links=no, Анато́лий Евге́ньевич Ка́рпов, p=ɐnɐˈtolʲɪj jɪvˈɡʲenʲjɪvʲɪtɕ ˈkarpəf; born May 23, 1951) is a Russian and former Soviet chess grandmaster, former World Che ...
,
Garry Kasparov Garry Kimovich Kasparov (born 13 April 1963) is a Russian chess grandmaster, former World Chess Champion, writer, political activist and commentator. His peak rating of 2851, achieved in 1999, was the highest recorded until being surpassed by ...
, Viktor Kortchnoi, Anthony Miles,
Nikolay Minev Nikolay (or Nikolai) Nikolaev Minev ( bg, Николай Николаев Минев, 8 November 1931 – 10 March 2017) was a Bulgarian chess International Master (IM) and noted chess author. Minev was born on 8 November 1931, in Rousse, Bulgari ...
, John Nunn and Jan Timman., 1986, Chess Informant, . Comprehensive book with 1746 endings divided in groups according to ECE classification. Annotated in System of chess signs . *''Essential Chess Endings: the Tournament Player's Guide'', by James Howell, 1997,
Batsford Batsford is a village and civil parish in the Cotswold district of Gloucestershire, England. The village is about 1½ miles north-west of Moreton-in-Marsh. There is a falconry centre close to the village and Batsford Arboretum is nearb ...
. . A small but comprehensive book. *''Fundamental Chess Endings'', by Karsten Müller and Frank Lamprecht, 2001, Gambit Publications. . Highly regarded – comprehensive and modern. *''Grandmaster Secrets: Endings'', by
Andrew Soltis Andrew Eden Soltis (born May 28, 1947) is an American chess grandmaster, author and columnist. He was inducted into the United States Chess Hall of Fame in September 2011. Chess career Soltis learned how the chess pieces moved at age 10 when he ...
, 1997, 2003, Thinker's Press, . An elementary book. *''Just the Facts!: Winning Endgame Knowledge in One Volume'', Lev Alburt and
Nikolai Krogius Nikolai Vladimirovich Krogius (; 22 July 1930 – 14 July 2022) was a Russian chess Grandmaster, International Arbiter (1985), psychologist, chess coach, chess administrator, and author. He won several tournament titles at Sochi and in East ...
, 2000, Newmarket Press. . A good introductory book. *''Pandolfini's Endgame Course'', by Bruce Pandolfini, 1988, Fireside, . Many short elementary endgame lessons. *''Silman's Complete Endgame Course: From Beginner To Master'',
Jeremy Silman Jeremy Silman (born August 28, 1954) is an American International Master (IM) of chess and writer. Silman was born in Del Rio, Texas. He began playing chess at the age of 12. He has won the American Open, the National Open, and the U.S. Open, an ...
, 2007, Siles Press, . Has a unique approach, it presents material in order of difficulty and the need to know of various classes of players. It starts with material for the absolute beginner and progresses up to master level material. *''Winning Chess Endings'', by Yasser Seirawan, 2003, Everyman Chess. . A good introductory book. *''One Pawn Saves the Day: A World Champion's Favorite Studies'', by Sergei Tkachenko, 2017, Limited Liability Company Elk and Ruby Publishing House . 100 studies whose common theme is that white ends up with just one pawn in the finale, yet manages to win or draw. *''One Knight Saves the Day: A World Champion's Favorite Studies'', by Sergei Tkachenko, 2017, Limited Liability Company Elk and Ruby Publishing House . 100 studies whose common theme is that white ends up with just one knight in the finale, yet manages to win or draw. *''One Bishop Saves the Day: A World Champion's Favorite Studies'', by Sergei Tkachenko, 2017, Limited Liability Company Elk and Ruby Publishing House . 100 studies whose common theme is that white ends up with just one bishop in the finale, yet manages to win or draw. *''One Rook Saves the Day: A World Champion's Favorite Studies'', by Sergei Tkachenko, 2017, Limited Liability Company Elk and Ruby Publishing House . 100 studies whose common theme is that white ends up with just one rook in the finale, yet manages to win or draw.


See also

* Outline of chess: Endgame topics *
Checkmate Checkmate (often shortened to mate) is any game position in chess and other chess-like games in which a player's king is in check (threatened with ) and there is no possible escape. Checkmating the opponent wins the game. In chess, the king is ...
* Chess middlegame *
Chess opening A chess opening or simply an opening is the initial stage of a chess game. It usually consists of established theory; the other phases are the middlegame and the endgame. Many opening sequences have standard names such as the "Sicilian Defen ...
* Chess terminology Endgame topics * Chess endgame literature * Corresponding squares * Endgame study * Endgame tablebase * Endgame theory *
Fortress A fortification is a military construction or building designed for the defense of territories in warfare, and is also used to establish rule in a region during peacetime. The term is derived from Latin ''fortis'' ("strong") and ''facere'' ...
*
Opposition Opposition may refer to: Arts and media * ''Opposition'' (Altars EP), 2011 EP by Christian metalcore band Altars * The Opposition (band), a London post-punk band * '' The Opposition with Jordan Klepper'', a late-night television series on Com ...
*
Pawnless chess endgame A pawnless chess endgame is a chess endgame in which only a few pieces remain, and no pawns. The basic checkmates are types of pawnless endgames. Endgames without pawns do not occur very often in practice except for the basic checkmates of king a ...
* Prokeš maneuver * Tarrasch rule *
Triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...
* Wrong bishop * Wrong rook pawn *
Zugzwang Zugzwang (German for "compulsion to move", ) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal mov ...
Specific endgames * Bishop and knight checkmate * King and pawn versus king endgame * Lucena position * Opposite-colored bishops endgame * Philidor position * Queen and pawn versus queen endgame * Queen versus pawn endgame * Réti endgame study *
Rook and bishop versus rook endgame The rook and bishop versus rook endgame is a chess endgame where one player has just a king, a rook, and a bishop, and the other player has just a king and a rook. This combination of is one of the most common pawnless chess endgames. It is gene ...
* Rook and pawn versus rook endgame * Saavedra position *
Two knights endgame The two knights endgame is a chess endgame with a king and two knights versus a king. In contrast to a king and two bishops (on opposite-colored squares), or a bishop and a knight, a king and two knights cannot checkmate against a lone king (howe ...


References

Bibliography * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * The last part (pages 197–257) is a supplement containing Troitzky's analysis of two knights versus pawns. * *


Further reading

* * * *


External links


Interactive Endgames Simulator





Basic chess endgames practice
{{DEFAULTSORT:Chess Endgame Chess terminology Chess theory