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A pawnless chess endgame is a
chess endgame In chess and other similar 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 ...
in which only a few
pieces 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 * ...
remain, and no pawns. The basic
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 ...
s are types of pawnless endgames. Endgames without pawns do not occur very often in practice except for the basic checkmates of king and queen versus king, king and rook versus king, and queen versus rook. Other cases that occur occasionally are (1) a rook and versus a rook and (2) a rook versus a minor piece, especially if the minor piece is a
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 ca ...
. The study of some pawnless endgames goes back centuries by players such as François-André Danican Philidor (1726–1795) and
Domenico Lorenzo Ponziani Domenico Lorenzo Ponziani (9 November 1719 – 15 July 1796) was an Italian law professor, priest, chess player, composer and theoretician. He is best known today for his chess writing. Life Ponziani was born in Modena in 1719. In 1742 he grad ...
(1719–1796). On the other hand, many of the details and recent results are due to the construction of
endgame tablebase An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of chess endgame positions. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysin ...
s. Grandmaster
John Nunn John Denis Martin Nunn (born 25 April 1955) is an English chess grandmaster, a three-time world champion in chess problem solving, a chess writer and publisher, and a mathematician. He is one of England's strongest chess players and was former ...
wrote a book (''Secrets of Pawnless Endings'') summarizing the research of endgame tablebases for several types of pawnless endings. The assessment of endgame positions assumes
optimal play In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given (; ). The concept of a best response is central to John Nash's best-known contribu ...
by both sides. In some cases, one side of these endgames can ; in other cases, the game is a
draw Draw, drawing, draws, or drawn may refer to: Common uses * Draw (terrain), a terrain feature formed by two parallel ridges or spurs with low ground in between them * Drawing (manufacturing), a process where metal, glass, or plastic or anything ...
(i.e. a
book draw This glossary of chess explains commonly used terms in chess, in alphabetical order. Some of these terms have their own pages, like ''fork'' and ''pin''. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific ...
).


Terminology

* are queens and rooks. are
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 Christian denomination, church or the country, especially in a military capacity. Knighthood ...
and bishops. * A is a row of squares on the
chessboard A chessboard is a used to play chess. It consists of 64 squares, 8 rows by 8 columns, on which the chess pieces are placed. It is square in shape and uses two colours of squares, one light and one dark, in a chequered pattern. During play, the b ...
. A is a column of squares on the board. * If a player has two bishops, they are assumed to be on opposite colors unless stated otherwise. When the number of moves to win is specified,
optimal play In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given (; ). The concept of a best response is central to John Nash's best-known contribu ...
by both sides is assumed. The number of moves given to win is until either
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 ...
or the position is converted to a simpler position that is known to be a win. For example, with a queen versus a rook, that would be until either checkmate or the rook is , resulting in a position that leads to an elementary checkmate.


Basic checkmates

Checkmate can be forced against a lone king with a king plus (1) a queen, (2) a rook, (3) two bishops, or (4) a bishop and a knight (see
Bishop and knight checkmate The bishop and knight checkmate in chess is the checkmate of a lone king which can be by a king, a bishop, and a knight. With the stronger side to move and with perfect play, checkmate can be forced in at most thirty-three moves from any start ...
). See
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 ...
for more details. Checkmate is possible with two knights, but it cannot be forced. (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 ...
.)


Queen versus rook

A queen wins against a lone rook, unless there is an immediate
draw Draw, drawing, draws, or drawn may refer to: Common uses * Draw (terrain), a terrain feature formed by two parallel ridges or spurs with low ground in between them * Drawing (manufacturing), a process where metal, glass, or plastic or anything ...
by
stalemate Stalemate is a situation in the game of chess where the player whose turn it is to move is not in check and has no legal move. Stalemate results in a draw. During the endgame, stalemate is a resource that can enable the player with the inferi ...
or due to perpetual check (or if the rook or king can immediately capture the queen). In 1895, Edward Freeborough edited an entire 130-page book of analysis of this endgame, titled ''The Chess Ending, King & Queen against King & Rook''. Normally, the winning process involves first winning the rook with the queen via a fork and then checkmating with the king and queen, but forced checkmates with the rook still on the board are possible in some positions or against incorrect defense. With perfect play, in the worst winning position, the queen can win the rook or checkmate within 31 moves. The ''third-rank defense'' is when the rook is on the third rank or from the edge of the board, his king is closer to the edge and the enemy king is on the other side (see the diagram). This defense is difficult for a human to defeat. For example, the winning move in the position shown is the counterintuitive withdrawal of the queen from the seventh rank to a more central location, 1. Qf4, so the queen can make checking maneuvers to win the rook with a fork if it moves along the third rank. If the black king emerges from the back rank, 1... Kd7, then 2. Qa4+ Kc7; 3. Qa7+ forces Black into a second-rank defense (defending king on an edge of the board and the rook on the adjacent rank or file) after 3... Rb7. This position is a standard win, as White heads for the Philidor position with a queen versus rook (in the next section). A possible continuation: 4. Qc5+ Kb8 5. Kd6 Rg7 6. Qe5 Rc7 7. Qf4 Kc8 8. Qf5+ Kb8 9. Qe5 Rb7 10. Kc6+ Ka8 11. Qd5 Kb8 12. Qa5 hilidor—mate in 7''. The position also occurs in the game Enrico Vroombout vs Luuk Van Kooten in 2007, where Vroombout failed to win.


Philidor position

The Philidor position is a queen vs. rook position. If Black is to move in this position, he quickly loses his rook by a fork (or gets checkmated). For example, : 1... Rb1 : 2. Qd8+ Ka7 : 3. Qd4+ Ka8 : 4. Qh8+ Ka7 : 5. Qh7+ thus forking the rook on b1. If, on the other hand, White is to move in this position, he would like to be in this position except with Black to move. This can be accomplished by
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 ...
: : 1. Qe5+ Ka8 : 2. Qa1+ Kb8 : 3. Qa5 and now it is back to the same arrangement, but Black has to move and is in zugzwang. Nunn describes that with the pieces in the center of the board the queen ought to force the rook towards the ''Philidor position''. Nunn describes the various retreat positions for the rook, the "fourth, third, second" rank defenses, then the "Philidor position". It is usually easy for White to force Black into the Philidor position. When it is Black's turn to play in the Philidor position, the rook can be won in a few moves.


Example from game

In this 2001 game between
Boris Gelfand Boris Gelfand ( he, בוריס אברמוביץ' גלפנד; be, Барыс Абрамавіч Гельфанд, Barys Abramavich Hel'fand; russian: Борис Абрамович Гельфанд, Boris Abramovich Gel'fand; born 24 June 1968) ...
and Peter Svidler, the player with the queen should win, but the game was drawn because of the fifty-move rule after Black was unable to find the winning maneuvers to fork and capture the rook. The same position but with colors reversed occurred in a 2006 game between Alexander Morozevich and
Dmitry Jakovenko Dmitry Olegovich Jakovenko (russian: Дмитрий Олегович Яковенко; born 28 June 1983) is a Russian chess player. He was awarded the title Grandmaster by FIDE in 2001. Jakovenko was European champion in 2012. He was a member ...
– it was also drawn. At the end of that game, the rook became a
desperado Desperado may refer to: * Outlaw, particularly in the American Old West Books * ''Desperadoes'' (comics), a comic book series * ''Desperadoes'' (novel), a 1979 novel by Ron Hansen * Desperado Publishing, an American independent comic book publi ...
, and the game ended in
stalemate Stalemate is a situation in the game of chess where the player whose turn it is to move is not in check and has no legal move. Stalemate results in a draw. During the endgame, stalemate is a resource that can enable the player with the inferi ...
after the rook was captured (otherwise, the game would have eventually been a draw by
threefold repetition In chess, the threefold repetition rule states that a player may claim a draw if the same position occurs three times during the game. The rule is also known as repetition of position and, in the USCF rules, as triple occurrence of position.Articl ...
).


Browne versus Belle

The queen versus rook endgame was one of the first endgames completely solved by computers constructing an
endgame tablebase An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of chess endgame positions. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysin ...
. A challenge was issued to Grandmaster Walter Browne in 1978 where Browne would have the queen in a difficult position, defended by Belle using the queen versus rook tablebase. Browne could have won the rook or checkmated in 31 moves with perfect play. After 45 moves, Browne realized that he would not be able to win within 50 moves, according to the fifty-move rule. Browne studied the position and, later in the month, played another match from a different starting position. This time, he won by capturing the rook on the 50th move.


Queen versus two minor pieces

Defensive
fortresses 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'' ...
exist for any of the two minor pieces versus the queen. However, except in the case of two knights, the fortress usually cannot be reached against optimal play. (See
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'' ...
for more details about these endings.) * ''Queen versus bishop and knight'': A queen normally wins against a bishop and knight, but there is one 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 forming a barrier against the enemy king's approach. Another position given by Ponziani in 1782 is more artificial: the queen's king is confined in a corner by the bishop and knight which are protected by their king. * ''Queen versus two bishops'': A queen has a theoretical forced win against two bishops in most positions, but the win may require up to seventy-one moves (a draw can be claimed after fifty moves under the fifty-move rule); there is one drawing fortress position for the two bishops. * ''Queen versus two knights'': Two knights can generally draw against a queen if the king is near its knights and they are in a reasonable position by setting up a fortress.


Common pawnless endings (rook and minor pieces)

John Nunn John Denis Martin Nunn (born 25 April 1955) is an English chess grandmaster, a three-time world champion in chess problem solving, a chess writer and publisher, and a mathematician. He is one of England's strongest chess players and was former ...
lists these types of pawnless endgames as being common: (1) a rook versus a minor piece and (2) a rook and a minor piece versus a rook. * ''Rook versus a bishop'': this is usually a draw. The main exception is when the defending king is trapped in a corner that is of the same color square as his bishop (see Wrong bishop#Rook versus bishop). If the defending king is trapped in a corner that is the opposite color as his bishop, he draws (see Fortress (chess)#Fortress in a corner). See the game of Veselin Topalov versus Judit Polgar, where Topalov defended and drew the game to clinch a win of their 2008 Dos Hermanas match. * ''Rook versus a knight'': this is usually a draw. There are two main exceptions: the knight is separated from the king and may be trapped and won or the king and knight are poorly placed. Kamsky vs Bacrot, 2006 is an example of a rook vs knight ending which resulted in a win. In this game, Black underpromoted a pawn to a knight to avoid a checkmate and eventually lost the game after allowing his knight to be separated from the king. * ''Rook and a bishop versus a rook'': this is one of the most common pawnless endgames and is usually a theoretical draw. However, the rook and bishop have good winning chances in practice because the defence is difficult. There are some winning positions such as the Philidor position, which occurs relatively often. There are two main defensive methods: the
Cochrane Defense 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 ...
and the "second rank defense". Forced wins require up to 59 moves. As a result,
FIDE The International Chess Federation or World Chess Federation, commonly referred to by its French acronym FIDE ( Fédération Internationale des Échecs), is an international organization based in Switzerland that connects the various national c ...
extended the fifty-move rule to 100 moves and then to 75 moves for this endgame, before returning to fifty moves. 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 ...
for more information. * ''Rook and a knight versus a rook'': This is usually a simple draw with few winning positions. The winning positions require the defending king to be badly placed near a corner; this can not be forced in general. The Cochrane Defense can be used.


Miscellaneous pawnless endings

Other types of pawnless endings have been studied. Of course, there are positions that are exceptions to these general rules stated below. The fifty-move rule is not taken into account, and it would often be applicable in practice. When one side has two bishops, they are assumed to be on opposite colored squares, unless otherwise stated. When each side has one bishop, the result often depends on whether or not the bishops are on the same color, so their colors will always be stated.


Queens only

*''Queen versus queen:'' usually a draw, but the side to move first wins in 41.75% of the positions. There are some wins when one queen is in the corner, e.g. as a result of promoting a
rook pawn This glossary of chess explains commonly used terms in chess, in alphabetical order. Some of these terms have their own pages, like ''fork'' and ''pin''. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific ...
or
bishop pawn This glossary of chess explains commonly used terms in chess, in alphabetical order. Some of these terms have their own pages, like ''fork'' and ''pin''. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific ...
. *''Two queens versus one queen:'' Almost always a win. A
cross-check In chess, a cross-check is a tactic in which a check is played in response to a check, especially when the original check is blocked by a piece that itself either delivers check or reveals a discovered check from another piece. Sometimes the term ...
may be necessary, see cross-check#Two queens versus one for an example. A draw is possible in a few exceptional positions if the weaker side has an immediate perpetual check, e.g. with a white king on a1 and white queens on a2 and b1, the black king on e8, and the black queen giving check on d4. Black has as an unlimited supply of checks on d4, a4, and d1, and the white king cannot escape the corner. *''Two queens versus two queens:'' The first to move wins in 83% of the positions (see the Comte vs. Le Roy diagram for an example). Wins require up to 44 moves.


Major pieces only

* ''Queen versus rook'': see above. * ''Queen versus two rooks'': this is usually a draw, but either side may have a win. * ''Queen versus three rooks'': this is nearly always a win for the rooks. This is rare in serious play, and occurs when promoting to a queen would give stalemate, but three rooks versus a queen is usually a straightforward win, especially when the defending king must be quite well confined for stalemate to be an issue for QRR v Q. * ''Queen and a rook versus a queen and a rook'': Despite the equality of , the player to move first wins in 83% of the positions. In a rook and pawn ending, if both sides queen a pawn, the side that gives check first frequently wins. * ''Queen and rook versus a queen'': this is a win. * ''Two rooks versus a rook'': this is usually a win because the attacking king can usually escape checks by the opposing rook (which is hard to judge in advance). * ''Rook versus rook'': this is normally a draw, but a win is possible in some positions where one of the kings is in the corner or on the edge of the board and threatened with checkmate. See for example the
Saavedra position The Saavedra position is one of the best-known chess endgame studies. It is named after the Spanish priest Fernando Saavedra (1849–1922), who lived in Glasgow during the late 19th century. Though not a strong player, he spotted a win involving ...
.


Queens and rooks with minor pieces

* ''Queen versus a rook and a '': this is usually a draw. The queen has good winning chances if the king and rook are near one edge and the minor piece is near the opposite edge. In the case of the knight, the queen can trap it on the edge; then the king assists in winning it. Against the bishop, the queen makes moves eventually forcing the bishop onto a square where it can be won. * ''Two rooks and a minor piece versus a queen'': this is usually a win for the three pieces, but it can take more than fifty moves. * ''Queen and a minor piece versus a rook and minor piece'': this is normally a win for the queen. * ''Rook and two minor pieces versus a queen'': draw. * ''Queen and a minor piece versus two rooks'': this is usually a draw for a knight and a win for a bishop, although the win takes up to eighty-five moves. The best method of defense is to double the rooks on the third rank with the opposing king on the other side and keep the king behind the rooks, though this does not always guarantee the draw. This case with a bishop and queen versus rooks is unusual in that such a small advantage forces a win. It was thought to be a draw by human analysis, but computer analysis revealed a long forced win. * ''Queen and a minor piece versus a rook and two minor pieces'': In a typical stable position, queen and knight win against rook, bishop, and knight, but mating requires up to 545 moves. Other piece combinations are a draw, except that a queen and a minor piece win against a rook and a same colored bishop pair. The KQN v KRBN win is surprising since the difference in material is only one point (other pawnless combinations up to seven pieces require greater difference to win), and a queen and a minor piece draw against a queen. However, compared to KQ, KRBN is vulnerable to fork and capture by the opposing queen, and KRBN is slowly outmaneuvered by KQN, until KQN wins a piece or a rook–knight exchange. Also, while in most open endgames, a knight is weaker than a bishop, a queen and a knight make a strong attacking combination. Also, two knights make a strong defense if the superior side does not have an extra piece that can be exchanged for the two knights, and we have KQ v KNN draw (and thus KQN v KRNN draw) despite KRB v KNN win. * ''Queen, rook, and minor piece versus queen and rook'': as of 2006, had not been analysed, but was thought to be too volatile to draw general conclusions. In endgames with queens, a minor piece advantage is not often decisive. Tempo is often more important than material in these situations. Two queens can win against two queens and a knight about half the time, when they have the move.


Queens and minor pieces

* ''Queen versus one minor piece'': a win for the queen. * ''Queen versus two minor pieces'': see above. * ''Queen versus three minor pieces'': draw except for a queen versus three bishops all on the same color, which in many positions is a win for the queen. * ''Four minor pieces versus a queen'': a win for the pieces if they are the usual four minor pieces (see the position from
Kling Kling is a surname. Geographical distribution As of 2014, 40.2% of all known bearers of the surname ''Kling'' were residents of Germany (frequency 1:6,549), 33.3% of the United States (1:35,616), 7.4% of Sweden (1:4,371), 4.0% of France (1:54,920 ...
and Horowitz).
Alexey Troitsky Alexey Alexeyevich Troitsky (russian: Алексе́й Алексе́евич Тро́ицкий; March 14, 1866 – August 1942; also ''Alexei'', ''Troitzky'', ''Troitzki'') was a Russian chess theoretician. He is widely considered to have ...
showed that four knights win against a queen. * ''Queen and a minor piece versus a queen'': this is usually a draw unless the stronger side can quickly win (see Nyazova vs. Levant and Spassky vs. Karpov). With a knight, however, the stronger side has good winning chances in practice because the knight can create non-linear threats to fork the opponent's pieces and very accurate play is required from the defender to hold the position. There are 38 positions of reciprocal zugzwang and the longest win takes 35 moves until the knight forks the queen and king. * ''Queen and two minor pieces versus queen and one minor piece'': generally a draw except in the case QBB vs QN (won for the bishops). Many combinations involve extremely long winning lines.


Examples from games

An endgame with queen and knight versus queen is usually drawn, but there are some exceptions where one side can quickly win material. In the game between Nyazova and Levant, White won: :1. Qe6+ Kh4 If 1...Kxh5 then 2.Qg6+ Kh4 3.Qh6+ skewers the black queen. :2. Qf6+ Kh3 :3. Qc3+ Kg2 :4. Qd2+ Kg1 :5. Qe3+ Kg2 :6. Nf4+ If 6...Kf1 then 7.Qe2+ Kg1 8.Qe1+ Kh2 9.Qf2+ Qg2 10.Qxg2#. White could have won more quickly by 1.Qg8+ Kh4 2.Qg3+ Kxh5 3.Qg6+ Kh4 4.Qh6+ and White skewers the black queen.
The second position is from a 1982 game between 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, ...
Boris Spassky Boris Vasilievich Spassky ( rus, Бори́с Васи́льевич Спа́сский, Borís Vasíl'yevich Spásskiy; born January 30, 1937) is a Russian chess grandmaster who was the tenth World Chess Champion, holding the title from 1969 ...
and then world champion
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 Ches ...
. The position is a theoretical draw but Karpov later blundered in time trouble and
resigned Resignation is the formal act of leaving or quitting one's office or position. A resignation can occur when a person holding a position gained by election or appointment steps down, but leaving a position upon the expiration of a term, or choos ...
on move 84.


Example from a study

In this 1967 study by Vitaly Halberstadt, White wins. The solution is: :1. Be5+ Ka8 :2. Qb5 Not 2.Qxf7 stalemate. :2... Qa7+! 3. Ke2! Qb6! 4. Qd5+ Qb7 5. Qa5+ Qa7 6. Qb4! Qa6+ 7. Kd2! Qc8 8. Qa5+ Kb7 9. Qb5+ Ka8 10. Bd6! Qb7 11. Qe8+ Ka7 12. Bc5+ Ka6 13. Qa4#.


Rooks and minor pieces

* ''Two rooks versus two minor pieces'': this is normally a win for the rooks.
Henri Rinck Henri Rinck (January 10, 1870 – February 17, 1952) was a French chess study composer, considered one of the most important early figures in the field. Biography Henri Rinck was born in Lyon (France) on January 10, 1870, where his family we ...
discovered more than 100 positions that are exceptions. * ''Two bishops and a knight versus a rook'': this is usually a win for the three pieces but it takes up to sixty-eight moves. Howard Staunton analyzed a position of this type in 1847, and correctly concluded that the normal result of this ending is a win for the three minor pieces. * ''A bishop and two knights versus a rook'': this is usually a draw, but there are some wins for the three pieces requiring up to forty-nine moves. Staunton in 1847 correctly concluded that the normal result of this endgame is a draw.
Bernhard Horwitz Bernhard Horwitz (1807 in Neustrelitz – 1885 in London) was a German and British chess master, chess writer and chess composer. Horwitz was born in Neustrelitz and went to school in Berlin, where he studied art. From 1837 to 1843, he was part ...
and
Josef Kling Josef Kling (19 March 1811 – 1 December 1876), also found in English-language sources as Joseph Kling, was a German chess master and chess composer. He has been called "a pioneer of the modern style of chess." Although Kling was an expert on e ...
gave the same appraisal in 1851. During
adjournment In parliamentary procedure, an adjournment ends a meeting. It could be done using a motion to adjourn. A time for another meeting could be set using the motion to fix the time to which to adjourn. This motion establishes an adjourned meeting. ...
of the Karpov versus Kasparov game, Kasparov (initially unsure if it is a draw) analyzed that a successful defense is having the king near a corner that the bishop does not control, keeping the rook far away to prevent
forks In cutlery or kitchenware, a fork (from la, furca 'pitchfork') is a utensil, now usually made of metal, whose long handle terminates in a head that branches into several narrow and often slightly curved tines with which one can spear foods eit ...
, and threatening to sacrifice it (for stalemate or for the bishop, which results in a draw, 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 ...
). Tablebases show that it is usually a draw, no matter which corner the defending king is in. (See the position from the Karpov versus Kasparov game for a drawn position, and see Fifty-move rule#Karpov vs. Kasparov, 1991 for more discussion of this game.) Curiously, Grandmaster
James Plaskett Harold James Plaskett (born 18 March 1960) is a British chess grandmaster and writer. Biography Early life and personal life Plaskett was born in Dhekelia, Cyprus, on 18 March 1960 and was educated at Bedford Modern School, England. In the ...
also had an adjournment of a London league game at the same time, versus David Okike; the last week of October 1991. After resumption it quickly resolved itself into the same pawnless ending. That game, too, was drawn. * ''Rook and a bishop versus two knights'': this is usually a win for the rook and bishop but it takes up to 223 moves. The result of this endgame was unknown until computer analysis proved the forced win. * ''Rook and a knight versus two knights'': this is usually a draw, but there are some wins for the rook and knight that take up to 243 moves. * ''Rook and a knight versus a bishop and knight'': this is usually a draw, but there are some wins for the rook and knight that take up to 190 moves. * ''Rook and a bishop versus a bishop and knight'': this is usually a draw if the bishops are on the same color. It is usually a win for the rook and bishop if the bishops are on opposite colors, but wins take up to ninety-eight 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 he ...
successfully converted this configuration with opposite-coloured bishops 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 a bishop versus two bishops'': this is usually a draw, but there are some long wins if the defending bishops are on the same color. * ''Rook and a knight versus two bishops'': this is usually a draw if the defending bishops are on opposite colors. It is a win if the defending bishops are on the same color, but it can take up to 140 moves. * ''Rook versus two minor pieces'': this is normally a draw. * ''Two rooks versus three minor pieces'': this is normally a draw. * ''Rook and two minor pieces versus a rook'': a win for the three pieces. With two knights, White must not exchange rooks and avoid losing a knight, but the three pieces have great checkmating power. * ''Rook and two minor pieces versus rook and one minor piece'': a win for the three pieces, see § Examples with an extra minor piece below. * ''Two rooks and a minor piece versus two rooks'': a win if the minor piece is a bishop. Normally a draw if the minor piece is a knight, but some very long wins exist. That being said, with so many major pieces on the board most positions are not tactically quiet, so general conclusions are difficult to draw. * ''Two rooks versus four bishops'': normally a draw (if the bishops come in two pairs).


Minor pieces only

* Trivial cases: These are all trivial draws in general: bishop only, knight only, bishop versus knight, bishop versus bishop, knight versus knight. * Two minor pieces: ** Two bishops is a basic
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 ...
(if the bishops are on opposite colors) ** A bishop and knight is a basic checkmate, see
bishop and knight checkmate The bishop and knight checkmate in chess is the checkmate of a lone king which can be by a king, a bishop, and a knight. With the stronger side to move and with perfect play, checkmate can be forced in at most thirty-three moves from any start ...
** Two knights cannot force checkmate, 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 ...
* Two minor pieces versus one minor piece: ** Two bishops versus a knight: this is a win (except for a few trivial positions where Black can immediately force a draw), but it can take up to 66 moves. See Effect of tablebases on endgame theory, Fortress (chess)#Semi-fortress in two bishops vs. knight and see the example from the Botvinnik versus Tal game below. Also see the tournament game of Manotas vs van Riemsdijk, where Black (the side with the bishops) broke the Kling and Horwitz semi-fortress and won the knight. ** Other cases: this is normally a draw in all other cases.
Edmar Mednis Edmar John Mednis ( lv, Edmārs Džons Mednis; March 22, 1937 – February 13, 2002) was a Latvian-American chess player and writer of Latvian people, Latvian origin. He was awarded the title of Grandmaster (chess), Grandmaster by FIDE in 198 ...
considered the difficulty of defending these positions: *** ''Two bishops versus one bishop'': The easiest for the defender to draw, unless the defending king is caught in a corner. *** ''Two knights versus one bishop'': any normal position is an easy draw. *** ''Two knights versus one knight'': an easy draw if the defending king is not trapped on the edge. However, if the king is trapped on the edge, there may be a win similar to the two knights versus a pawn endgame. *** ''Bishop and knight versus a bishop on the same color'': may be lost if the defending king is on the edge; otherwise an easy draw. *** ''Bishop and knight versus a bishop on the opposite color'': normally a draw but the defense may be difficult if the defending king is confined near a corner that the attacking bishop controls. *** ''Bishop and knight versus a knight'': best winning chances (other than two bishops versus knight). The difficulty of defense is not clear and the defending knight can be lost if it is separated from its king. * Three minor pieces versus one minor piece: a win except in some unusual situations involving an underpromotion to a bishop on the same color as a player's existing bishop. More than fifty moves may be required to win. Three knights win against one knight. * Three minor pieces versus two minor pieces: if neither player has a pair of same-colored bishops, this is a won endgame exactly when the stronger side has the bishop pair and the weaker side lacks it (i.e. BBN vs BN or BBN vs NN). Otherwise, it is a draw. Unusual situations where underpromotion has resulted in one player's having two bishops travelling on the same colors are more complicated: for example, BBN (different colors) vs BB (same colors) is not a general win, but contains some very long winning lines.Post_by_Marc_Bourzutschky,_specialist_in_endgame_tablebase
s.html" ;"title="endgame tablebase">Post by Marc Bourzutschky, specialist in endgame tablebase
s">endgame tablebase">Post by Marc Bourzutschky, specialist in endgame tablebase
s RybkaForum, 31 July 2012
*Three knights can force checkmate against a lone king within 20 moves (unless the defending king can win one of the knights), but this combination of pieces can only happen if the attacking side has underpromoted a pawn to a knight.


Example from game

An ending with two bishops versus a knight occurred in the seventeenth game of the World Chess Championship 1961, 1961 World Chess Championship match between Mikhail Botvinnik and Mikhail Tal. The position occurred after White captured a pawn on a6 on his 77th move, and White resigned on move 84. :77... Bf1+ :78. Kb6 Kd6 :79. Na5 White to move may draw in this position: 1.Nb7+ Kd5 2.Kc7 Bd2 3.Kb6 Bf4 4.Nd8 Be3+ 5.Kc7. White gets his knight to b7 with his king next to it to form a long-term
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'' ...
. :79... Bc5+ :80. Kb7 Be2 :81. Nb3 Be3 :82. Na5 Kc5 :83. Kc7 Bf4+ The game might continue 84.Kd7 Kb6 85.Nb3 Be3, followed by ...Bd1 and ...Bd4, for example 86.Kd6 Bd1 87.Na1 Bd4 88.Kd5 Bxa1.


Examples with an extra minor piece

An extra minor piece on one side with a queen versus queen endgame or rook versus rook endgame is normally a theoretical draw. An endgame with two minor pieces versus one is also drawn, except in the case of two bishops versus a knight. But a rook and two minor pieces versus a rook and one minor piece is different. In these two examples from games, the extra minor piece is enough to win. In this position, if the bishops were on the same color, White might have a chance to exchange bishops and reach an easily drawn position. (Exchanging rooks would also result in a draw.) Black wins: :1... Re3 :2. Bd4 Re2+ :3. Kc1 Nb4 :4. Bg7 Rc2+ :5. Kd1 Be2+ :6. resigns, because 6. Ke1 Nd3 is checkmate. In this position, if White could exchange bishops (or rooks) he would reach a drawn position. However, Black has a winning attack: :1... Rb3+ :2. Kh2 Bc6 :3. Rb8 Rc3 :4. Rb2 Kf5 :5. Bg3 Be4 :6. Re2 Bg5 :7. Rb2 Kg4 :8. Rf2 Rc1 :9. resigns Speelman gave these conclusions in 1981: * Rook and two bishops versus rook and bishop – thought to be a win * Rook, bishop, and knight versus rook and bishop – good winning chances, probably a win if the bishops are on opposite colors * Rook, bishop, and knight versus rook and knight – thought to be a win. Later tablebase analysis confirmed that rook and two minor pieces versus rook and one minor piece is a general win.


Summary

Grandmaster Ian Rogers summarized several of these endgames. ; General result John Nunn also covers many pawnless chess endings in his book. He gives a "general result", which he describes as: "derived ... not by looking at statistics for winning percentages, which can be very misleading, but by personally examining the endings concerned."


Fine's rule

In his landmark 1941 book ''
Basic Chess Endings ''Basic Chess Endings'' (abbreviated BCE) is a book on chess chess endgame, endgames which was written by Grandmaster (chess), Grandmaster Reuben Fine and originally published on October 27, 1941. It is considered the first systematic book in Engl ...
'', Reuben Fine inaccurately stated, "Without pawns one must be at least a Rook ahead in order to be able to mate. The only exceptions to this that hold in all cases are that the double
exchange Exchange may refer to: Physics *Gas exchange is the movement of oxygen and carbon dioxide molecules from a region of higher concentration to a region of lower concentration. Places United States * Exchange, Indiana, an unincorporated community * ...
wins and that a Queen cannot successfully defend against four minor pieces." Kenneth Harkness also stated this "rule". Fine also stated "There is a basic rule that in endings without pawns one must be at least a rook ahead to be able to win in general." This inaccurate statement was repeated in the 2003 edition revised by Grandmaster
Pal Benko Pál C. Benkő ( hu, Benkő Pál; July 15, 1928 – August 26, 2019) was a Hungarian-American chess player, author, and composer of endgame studies and chess problems. Early life Benko was born on July 15, 1928 in Amiens, France, where his ...
. However, Fine recognized elsewhere in his book that a queen wins against a rook and that a queen normally beats a knight and a bishop (with the exception of one drawing fortress). The advantage of a rook corresponds to a five-point advantage using the traditional relative value of the pieces (pawn = 1, knight = 3, bishop = 3, rook = 5, queen = 9). It turns out that there are several more exceptions, but they are endgames that rarely occur in actual games. Fine's statement has been superseded by computer analysis. 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 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. In practice, the fifty-move rule comes into play because more than fifty moves are often required to either checkmate or reduce the endgame to a simpler case: two bishops and a knight versus a rook (requires up to 68 moves); and two rooks and a minor piece versus a queen (requires up to 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. Two bishops win against a knight, but it takes up to 66 moves if a bishop is initially trapped in a corner. 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). 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 proved by computer in 2005 and was the first ending with seven pieces that was completely solved. (See
endgame tablebase An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of chess endgame positions. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysin ...
.)


General remarks on these endings

Many of these endings are listed as a win in a certain number of moves. That assumes
perfect play A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full inform ...
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 fifty moves long, some positions can be won within the fifty move limit (for a draw claim) and others cannot. 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.


Tables

This a table listing several pawnless endings, the number of moves in the longest win, and the winning percentage for the first player. The winning percentage can be misleading – it is the percentage of wins out of all possible positions, even if a piece can immediately be captured or won by a
skewer A skewer is a thin metal or wood stick used to hold pieces of food together. The word may sometimes be used as a metonym, to refer to the entire food item served on a skewer, as in "chicken skewers". Skewers are used while grilling or roasting ...
,
pin A pin is a device used for fastening objects or material together. Pin or PIN may also refer to: Computers and technology * Personal identification number (PIN), to access a secured system ** PIN pad, a PIN entry device * PIN, a former Dutch ...
, or fork. The largest number of moves to a win is the number of moves until either checkmate or transformation to a simpler position due to winning a piece. Also, the fifty-move rule is not taken into account. * Many of the combinations listed involve single piece capture and transposition into six-piece territory almost immediately from the starting position.


References

Bibliography * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


Further reading

* Pawnless endings are discussed on pages 87–96. * Pawnless endings are discussed on pages 9–22. * Pawnless endings are discussed on pages 259–288.


External links


Book review

Interactive Chess Endgames vs Chess Computer

Sergienko vs. Vescovi Moscow 2010, R+3N vs. R+B+N

Volkov vs. Minasian Moscow 2009, Q+R+N vs. 2Q
{{Chess Chess endgames he:סיום (שחמט)#סיום ללא רגלים