Pawnless chess endgames

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Pawnless chess endgames

Pawnless chess endgames are chess endgames in which only a few pieces remain, and none of them are pawns. The basic checkmates are a type of pawnless endgame. Generally endgames without pawns do not occur very often in practice, except for the basic checkmates of king and queen versus king and king and rook versus king and queen versus rook harvcol|Hooper|1970|p=4. Others that do occur occasionally are a rook and minor piece versus a rook and a rook versus a minor piece, especially if the minor piece is a bishop harvcol|Nunn|2007|pp=156-65.

The study of some pawnless endgames goes back centuries, by players such as François-André Danican Philidor (1726-1795) and Domenico Lorenzo Ponziani (1719-1796). On the other hand, many of the details and recent results are due to the construction of endgame tablebases. Grandmaster John Nunn wrote a book summarizing the research of endgame tablebases.

The assessment of endgame positions assumes optimal play by both sides. In some cases, one side of these endgames can force a win; in other cases, the game is a draw (i.e. a book draw).

Queens and rooks are major pieces whereas knights and bishops are minor pieces.

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). See checkmate for more details.

Queen versus rook

Chess diagram|=
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Black is employing the third rank defense. White wins with correct play.
A queen wins against a lone rook, unless there is an immediate draw by stalemate or due to perpetual check. Normally the winning process involves the queen first winning the rook by a fork and then checkmating with the king and queen, but checkmates with the rook still on the board are possible in some positions or against incorrect defense.

The "third rank defense" by the rook is difficult for a human to crack. The "third rank defense" is when the rook is on the third rank or file from the edge of the board, his king is closer to the edge and the enemy king is on the other side (see the diagram). The winning move 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. And 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, with White heading for the Philidor position with a queen versus rook Harvcol|Müller|Lamprecht|2001|pp=331-33.

Queen versus two minor pieces

Chess diagram|=
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Ponziani 1782
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Artificial position where the attacking king is confined, draw.

* "Queen versus bishop and knight": A queen normally wins against a bishop and knight, but there is one drawing fortress position forming a barrier against the enemy king's approach Harvcol|Müller|Lamprecht|2001|pp=339-41. 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 harvcol|Hooper|Whyld|1992|p=46.

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

* "Queen versus two knights": Two knights can generally draw against a queen by setting up a fortress Harvcol|Müller|Lamprecht|2001|pp=339-41.

See fortress for more details about these endings.

Miscellaneous pawnless endings

Other types of pawnless endings have been studied Harvcol|Nunn|2002|. 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, and that is stated.

Queens only

Chess diagram small|=
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Comte vs. Le Roy, France, 1997
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Whoever moves first wins (Nunn)

* "Queen versus queen": usually a draw, but the side to move first wins in 41.75 percent of the positions Harvcol|Müller|Lamprecht|2001|p=400.

* "Two queens versus one queen": A win, see cross-check#Two queens versus one for an example Harvcol|Müller|Lamprecht|2001|p=400.

* "Two queens versus two queens": The first to move wins in 83 percent of the positions (see the diagram for an example). Wins require up to 44 moves Harvcol|Nunn|2002|pp=329,379, Harvcol|Schiller|1996|p=175.

Major pieces only

* "Queen versus two rooks": this is usually a draw, but either side may have winning chances Harvcol|Nunn|2002|p=311.

* "Queen and a rook versus a queen and a rook": Despite the equality of material, the player to move first wins in 83 percent of the positions Harvcol|Schiller|1996|p=175. ["The rule of thumb which governs endgames such as queen and rook versus queen and rook or two queens versus two queens is 'Whoever checks first wins'. In many cases it is a valid principle and certainly if the attacking force is well-coordinated, it can usually force mate or win material by a series of checks. However, there are many cases in which the win is not so easy... The sequence of checks must be quite precise..." harvcol|Nunn|2002|p=379. In a rook and pawn ending, if both sides queen a pawn, the side that gives check first frequently wins. harvcol|Müller|Pajeken|2008|p=223]

* "Queen and rook versus a queen": this is a win Harvcol|Nunn|2002|p=317.

* "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) Harvcol|Nunn|2002|p=320.

Queens and rooks with minor pieces

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White to move wins in 85 moves, discovered by computer analysis

* "Queen versus a rook and a minor piece": this is usually a draw Harvcol|Müller|Lamprecht|2001|p=402.

* "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 Harvcol|Müller|Lamprecht|2001|p=406.

* "Queen and a minor piece versus a rook and minor piece": this is normally a win for the queen Harvcol|Müller|Lamprecht|2001|pp=403-4.

* "Rook and two minor pieces versus a queen": draw Harvcol|Müller|Lamprecht|2001|p=405.

* "Queen and a minor piece versus two rooks": this is usually a draw for a knight; usually a win for a bishop, but it takes up to eighty-five moves. The 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. Accurate defense is required though. This defense can be broken down by a queen and bishop but not by a queen and knight. The case with a bishop is an unusual win with a small material advantage. It was thought to be a draw by human analysis, but computer analysis revealed a long forced win Harvcol|Müller|Lamprecht|2001|p=404, Harvcol|Nunn|2002|pp=328-29,367,372.

Queens and minor pieces

Chess diagram|=
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Kling and Horwitz, 1851
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Black is unable to prevent checkmate.

* "Queen versus three minor pieces": draw except for a queen versus three bishops all on the same color, which is a win for the queen Harvcol|Nunn|2002|p=328.

* "Four minor pieces versus a queen": a win for the pieces if they are the usual four minor pieces (see Kling and Horwitz) Harvcol|Fine|Benko|2003|p=583.

* "Queen and a minor piece versus a queen": this is usually a draw unless the stronger side can quickly win (see Nyazova vs Levant) harvcol|Speelman|1981|p=108.

* "Queen versus a minor piece": a win harvcol|Hooper|1970|p=4.

Example from game

Chess diagram|=
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Nyazova-Levant, USSR 1976
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White to move wins with 1. Qg8+ or 1. Qe6+
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+ Kh4:2. Qf6+ Kh3:3. Qc3+ Kg2:4. Qd2+ Kg1:5. Qe3+ Kf2:6. Nf4+ 1-0White could have won more quickly by 1. Qg8+ Kh4 2. Qg3+ Kxh5 3. Qg6+ Kh4 4. Qh6+ and White skewers the black queen harvcol|Speelman|1981|p=108.

Rooks and minor pieces

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J. Polgar-Kasparov, 1996
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Position before White's 70th move, a draw with correct play. Polgar blundered on move 79 and resigned after move 90.
Chess diagram|=
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Alekhine-Capablanca, 1927
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White to move, the game was drawn twelve moves later. The white king cannot be driven to the edge.

Chess diagram|=
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Karpov-Ftacnik, 1988
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Black to move, White wins because the black king and knight are far apart Harvcol|Müller|Pajeken|2008|p=237, Harvcol|Karolyi|Aplin|2007|pp=320-22, Harvcol|Nunn|2007|pp=158-59
Chess diagram|=
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Topalov-J. Polgar, 2008
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White to move, draw
clear
* "Rook and a knight versus a rook": this is a theoretical draw, but Judit Polgar lost a famous game to Garry Kasparov (see diagram) [http://www.chessgames.com/perl/chessgame?gid=1070866] when she blundered in a quickplay finish (a sudden death time control) harvcol|Nunn|2007|pp=159–61, 165. There are five cases that are wins when the defending king is restricted to the edge of the board harvcol|Grivas|2008|p=257.

* "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 defense is difficult. There are some winning positions such as the Philidor position, which occurs relatively often harvcol|Nunn|2007|pp=161–65. Also see the Cochrane Defense.

* "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 square as his bishop harvcol|Nunn|2002|p=31. See the game of Veselin Topalov versus Judit Polgar, where the draw clinched a win of their 2008 Dos Hermanas match. [ [http://chess.maribelajar.com/chesspublisher/viewgame.php?id=1208631002 Topalov-Polgar] ]

* "Rook versus a knight": this is usually a draw. There are two main exceptions: (1) the knight is separated from the king and may be trapped and won, (2) the king and knight are poorly placed harvcol|Nunn|2002|p=9.

* "Two rooks versus two minor pieces": this is normally a win Harvcol|Müller|Lamprecht|2001|p=405.

* "Two bishops and a knight versus a rook": this is usually a win but it takes up to sixty-eight moves Harvcol|Müller|Lamprecht|2001|p=404. Howard Staunton analyzed a position of this type in 1849.

Chess diagram|=
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Karpov-Kasparov, 1991.
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Position after 63. Kxh4. The game was drawn on move 115.

* "A bishop and two knights versus a rook": this is usually a draw, but there are some wins requiring up to forty-nine moves Harvcol|Müller|Lamprecht|2001|p=403. (See the position from Karpov versus Kasparov for a drawn position, and see fifty move rule for more discussion of this game.)

* "Rook and a bishop versus two knights": this is usually a win but it takes up to 223 moves Harvcol|Müller|Lamprecht|2001|p=404. This was not known until computer analysis was done.

* "Rook and a knight versus two knights": this is usually a draw but there are some wins that take up to 243 moves harvcol|Nunn|2002|p=330.

* "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 if the bishops are on opposite colors, but takes up to ninety-eight moves Harvcol|Müller|Lamprecht|2001|p=404.

* "Rook versus two minor pieces": normally a draw harvcol|Hooper|1970|p=4.

* "Two rooks versus three minor pieces": normally a draw harvcol|Hooper|1970|p=4.

* "Rook and two minor pieces versus a rook": a win harvcol|Hooper|1970|p=4.

Minor pieces only

Chess diagram|=
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Kling and Horowitz, 1851.
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This is a semi-fortress, but White wins in 45 moves.

* "Two bishops versus a knight": this is usually a win (assuming that the bishops are on opposite colors), but it takes up to sixty-six moves harvcol|Nunn|1995|p=265ff. See Effect of tablebases on endgame theory and see the example from a game below.

* "Two minor pieces versus one minor piece": except for two bishops (on opposite colors) versus one knight (above), this is normally a draw Harvcol|Müller|Lamprecht|2001|p=402, harvcol|Hooper|1970|p=4.

* "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 Harvcol|Müller|Lamprecht|2001|p=403,406.

* "Trivial cases": These are all trivial draws in general: bishop only, knight only, bishop versus knight, bishop versus bishop, knight versus knight.

Example from game

Chess diagram|=
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Botvinnik-Tal, 1961
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Position after 77. Kxa6.
An ending with two bishops versus a knight occurred in the seventeenth game of the 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. [ [http://www.chessgames.com/perl/chessgame?gid=1032550 Botvinnik–Tal, 1961 World Championship Game 17] game score at chessgames.com] : 77... Bf1+: 78. Kb6 Kd6: 79. Na5White to move may draw in this position: 1. Nb7+ Kd5 2. Kc7 Bd2 3. Kb6 Bf4 4. Nd8 Be3+ 5. Kc7 harvcol|Hooper|1970|p=5. White gets his knight to "b7" with his king next to it to form a long-term fortress. [At the time, it was known that this fortress could be broken down after many moves, but it was thought that the defender could then probably form the fortress in another corner. Computer analysis done later showed that the attacker can prevent the defender from re-forming the fortress, but the fifty move rule may be applicable in this case.] : 79.... Bc5+: 80. Kb7 Be2: 81. Nb3 Be3: 82. Na5 Kc5: 83. Kc7 Bf4+: 84. 0-1The game might continue 84. Kd7 Kb6 85. Nb3 Be3, followed by ...Bd1 and ...Bd4 harvcol|Speelman|1981|p=109-10, for example 86. Kd6 Bd1 87. Na1 Bd4 88. Kd5 Bxa1 harvcol|Hooper|1970|p=5.

Fine's rule

In his landmark 1941 book "Basic Chess Endings", 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 wins and that a Queen cannot successfully defend against four minor pieces." Harvcol|Fine|1941|p=572 This inaccurate statement was repeated in the 2003 edition revised by Grandmaster Pal Benko Harvcol|Fine|Benko|2003|p=585. However, Fine recognized elsewhere in his book that a queen wins against a rook Harvcol|Fine|1941|p=561 and that a queen normally beats a knight and a bishop (with the exception of one drawing fortress) Harvcol|Fine|1941|p=570-71. The advantage of a rook corresponds to a five-point material advantage using the traditional relative value of the pieces (pawn=1, knight=3, bishop=3, rook=5, queen=9). It turns out that there are several more exceptions, but they are endgames that rarely occur in actual games.

A four-point material advantage is often enough to win in some endings without pawns. For example, a queen wins versus a rook (as mentioned above, but 31 moves may be required); as well as when there is matching additional material on both sides, i.e.: a queen and any minor piece versus a rook and any minor piece; a queen and a rook versus two rooks; and two queens versus a queen and a rook. Another type of win with a four-point material advantage is the double exchange – two rooks versus any two minor pieces. There are some other endgames with four-point material differences that are generally long theoretical wins. 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 (on opposite colors) win against a knight, but it takes up to 66 moves if a bishop is initially trapped in a corner harvcol|Nunn|1995|pp=265ff.

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) Harvcol|Müller|Lamprecht|2001|pp=400-6 Harvcol|Nunn|2002|pp=325-29.

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.)

General remarks on these endings

Many of these endings are listed as a win in a certain number of moves. That assumes perfect play by both sides, which is rarely achieved if the number of moves is large. Also, finding the right moves may be exceedingly difficult for one or both sides. When a forced win is more than 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.

ee also

* Chess endgame
* Checkmate
* Chess endgame literature
* Chess piece point value

Notes

References

*Citation
year=1941
title=Basic Chess Endings
edition=1st
publisher=McKay
ID=ISBN 0-679-14002-6

*Citation
last1=Fine|first1=Reuben
year=2003
title=Basic Chess Endings
edition=2nd
publisher=McKay
ID=ISBN 0-8129-3493-8

*Citation
year=2008
title=Practical Endgame Play - mastering the basics
publisher=Everyman Chess
ID=ISBN 978-1-85744-556-5

* Citation
title=A Pocket Guide to Chess Endgames
year=1970
publisher=Bell & Hyman
ID=ISBN 0-7135-1761-1

*citation
last1=Hooper | first1=David
last2=Whyld | first2=Kenneth | authorlink2=Kenneth Whyld
year=1992
title=The Oxford Companion to Chess
edition=2nd
publisher=Oxford University Press
ID=ISBN 0-19-280049-3

* Citation
last1=Karolyi|first1=Tibor
last2=Aplin|first2=Nick
title=Endgame Virtuoso Anatoly Karpov
year=2007
publisher=New In Chess
ID=ISBN 978-90-5691-202-4

*Citation
year=2001
title=Fundamental Chess Endings
publisher=Gambit Publications
ID=ISBN 1-901983-53-6

*Citation
last1=Müller|first1=Karsten
last2=Pajeken|first2=Wolfgang
year=2008
title=How to Play Chess Endings
publisher=Gambit Publications
ID=ISBN 978-1-904600-86-2

*Citation
year=1995
title=Secrets of Minor-Piece Endings
publisher=Batsford
ID=ISBN 0-8050-4228-8

*Citation
last=Nunn|first=John
year=2002
title=Secrets of Pawnless Endings
edition = 2nd
publisher=Gambit Publications
ID=ISBN 1-901983-65-X

* Citation
last=Nunn|first1=John
title=Secrets of Practical Chess
year=2007
edition = 2nd
publisher=Gambit Publications
ID=ISBN 978-1-904600-70-1

*citation
year=1981
title=Endgame Preparation
publisher=Batsford
id=ISBN 0-7134-4000-7

*Citation
last=Stiller|first=Lewis
editor-last=Nowakowski|editor-first=Richard
year=1996
title=Multilinear Algebra and Chess Endgames
chapter=On Numbers and Endgames: Combinatorial Game Theory in Chess Endgames
publisher = Cambridge University Press
ID=ISBN 0-521-57411-0

*Citation
year=1996
title=Endgame Play
publisher=Batsford
ID=ISBN 0-7134-7920-5
Pawnless endings are discussed on pages 87-96.

* [http://www.cs.unimaas.nl/icga/journal/contents/content25-2.htm#SECRETS Book review]

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