Pawnless chess endgame

A pawnless chess endgame is a chess endgame in which only a few pieces remain and none of them is a pawn. 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 and queen versus king, king and rook versus king, and queen versus rook (Hooper 1970:4). Other cases that occur occasionally are (1) a rook and minor piece versus a rook and (2) a rook versus a minor piece, especially if the minor piece is a bishop (Nunn 2007:156–65).

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 (Secrets of Pawnless Endings) summarizing the research of endgame tablebases for several types of pawnless endings.

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).

Contents
This article uses algebraic notation to describe chess moves.

Terminology

When the number of moves to win is specified, optimal play by both sides is assumed. The number of moves given to win is until either checkmate 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 captured, resulting in a position that leads to an elementary checkmate.

Basic checkmates

Main article: checkmate

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. Checkmate is possible with two knights, but it cannot be forced. (See Two knights endgame.)

Queen versus rook

a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
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 (Nunn 2002:49) (or if rook can immediately capture the queen). Normally the winning process involves the queen first winning the rook by 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.

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). 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, with White heading for the Philidor position with a queen versus rook (Müller & Lamprecht 2001:331–33). In 1895 Edward Freeborough edited an entire 130-page book of analysis of this endgame, The Chess Ending, King & Queen against King & Rook.

Example from game

Gelfand vs. Svidler, 2001
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black to move should win

In this 2001 game[1] between Boris Gelfand and Peter Svidler,[2] Black should win but the game was a draw because of the fifty-move rule. Black can win in several ways, for instance:

1... Qc8
2. Kf7 Qd8
3. Rg7+ Kf5
4. Rh7 Qd7+
5. Kg8 Qe8+
6. Kg7 Kg5, and wins.

The same position but with colors reversed occurred in a 2006 game between Alexander Morozevich and Dmitry Jakovenko – it was also drawn (Makarov 2007:170).[3] At the end of that game the rook became a desperado and the game ended in stalemate after the rook was captured (otherwise the game would have eventually been a draw because of perpetual check, i.e. threefold repetition).

Queen versus two minor pieces

Ponziani 1782
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Artificial position where the attacking king is confined, draw.
Pachman vs. Guimard, 1955[4]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Position after 68. Nd4, Black wins

Defensive fortresses 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 for more details about these endings.)

Common pawnless endings (rook and minor pieces)

John Nunn 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 (Nunn 2007:156–65).

de La Bourdonnais vs. McDonnell, 1834 match
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Position after 92...Ka5, draw
Topalov vs. J. Polgar, 2008[6]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move, draw
Philidor, 1749
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move wins, Black to move draws (Nunn 2002a:178)
Timman vs. Lutz, 1995[7]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black to move, drawn 52 moves later (Lutz 1999:129–31)
J. Polgar vs. Kasparov, 1996[8]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Position before White's 70th move, a draw with correct play. Polgar blundered on move 79 and resigned after move 90.
Alekhine vs. Capablanca, 1927[9]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move, the game was drawn twelve moves later. The white king cannot be driven to the edge.
Karpov vs. Ftáčnik, 1988[10]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black to move. This combination is usually a draw but here White wins because the black king and knight are far apart (Müller & Pajeken 2008:237), (Károlyi & Aplin 2007:320–22), (Nunn 2007:158–59).

Miscellaneous pawnless endings

Other types of pawnless endings have been studied (Nunn 2002a). 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

Comte vs. Le Roy, France, 1997
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Whoever moves first wins (Nunn)

Major pieces only

Centurini 1885 (Fine & Benko diagram 1096)
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black to move draws. Black would win with the king on h7 instead.

Queens and rooks with minor pieces

a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move wins
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move wins in 85 moves, discovered by computer analysis

Queens and minor pieces

Kling & Horowitz, 1851
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black is unable to prevent checkmate

Examples from games

Nyazova vs. Levant, USSR 1976
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
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+ Kg2
6. Nf4+ 1-0

White could have won more quickly by 1. Qg8+ Kh4 2. Qg3+ Kxh5 3. Qg6+ Kh4 4. Qh6+ and White skewers the black queen (Speelman 1981:108).

Spassky vs. Karpov, 1982
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Position after 68. Nxb3, a theoretical draw

The second position is from a 1982 game between former world champion Boris Spassky and world champion Anatoly Karpov.[13] The position is a theoretical draw but Karpov later blundered in time trouble and resigned on move 84.

Example from a study

V. Halberstadt, 1967
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move and win

In this 1967 study by Vitaly Halberstadt, White wins. The solution is 1. Be5+ Ka8 2. Qb5! 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# (Nunn 2002b:48,232).

Rooks and minor pieces

Horwitz & Kling, 1851
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White to move wins
Karpov vs. Kasparov, Tilburg, 1991[14]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Position after 63. Kxh4. The game was drawn on move 115.

Minor pieces only

Kling & Horowitz, 1851
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
This is a semi-fortress, but White wins in 45 moves.
ECE #1907, Belle
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
1. Ba4+ wins in 66 moves (the only winning move), (Matanović 1993:512–13)

Example from game

Botvinnik vs. Tal, 1961[15]
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Position after 77. Kxa6, Black wins

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.[16]

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 (Hooper 1970:5). White gets his knight to b7 with his king next to it to form a long-term fortress.[17]

79.... Bc5+
80. Kb7 Be2
81. Nb3 Be3
82. Na5 Kc5
83. Kc7 Bf4+
84. 0-1

The game might continue 84. Kd7 Kb6 85. Nb3 Be3, followed by ...Bd1 and ...Bd4 (Speelman 1981:109–10), for example 86. Kd6 Bd1 87. Na1 Bd4 88. Kd5 Bxa1 (Hooper 1970:5).

Examples with an extra minor piece

An extra minor piece on one side with a queen versus queen 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.

R. Blau vs. Unzicker, 1949
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black to move, wins

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 (Speelman 1981:108–9).
Vladimorov vs. Palatnik, 1977
a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Black to move, wins

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 Be4
8. Rf2 Rc1
9. resigns, (Speelman 1981:109).

Speelman gave these conclusions:

Summary

Grandmaster Ian Rogers summarized several of these endgames (Rogers 2010:37–39).

Recap of some pawnless endgames
Attacker Defender Status Assessment
Win Easy[18]
Draw Easy, if defender goes to the right corner
Draw Easy
Draw Easy, if the Cochrane Defense is used[19]
Draw Easy
Draw Easy, but use care[20]
Win Easy
Draw Easy for the defender
Draw Difficult for the defender
Draw Easy

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." (Fine 1941:572) Kenneth Harkness also stated this "rule" (Harkness 1967:49). 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." (Fine 1941:553) This inaccurate statement was repeated in the 2003 edition revised by Grandmaster Pal Benko (Fine & Benko 2003:585). However, Fine recognized elsewhere in his book that a queen wins against a rook (Fine 1941:561) and that a queen normally beats a knight and a bishop (with the exception of one drawing fortress) (Fine 1941:570–71). 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. Fine's statement has been superseded by computer analysis (Howell 1997:136).

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 win against a knight, but it takes up to 66 moves if a bishop is initially trapped in a corner (Nunn 1995:265ff).

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) (Müller & Lamprecht 2001:400–6) (Nunn 2002a: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.

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, pin, 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 (Speelman, Tisdall & Wade 1993:7–8).

Common pawnless endgames
Attacking pieces Defending pieces Longest win Winning %
10 100
16 100
10 42
31 99
18 35
27 48
19 99.97
33 99.5
30 94
67 92.1
33 53.4
41 48.4
71 92.1
42 93.1
63 89.7
59 40.1
33 35.9
66 91.8

This table shows six-piece endgames with some positions requiring more than 100 moves to win (Stiller 1996).

Endgames requiring more than 100 moves to win
Attacking pieces Defending pieces Longest win Winning %
243[21] 78
223 96
190 72
153 86
140 77
101 94

See also

Notes

  1. ^ Gelfand vs. Svidler
  2. ^ ChessBase and ChessGames.com give Gelfand as White but Makarov gives Svidler as White. Makarov also makes a White/Black error in discussing the game.
  3. ^ Morozevich vs. Jakovenko
  4. ^ Pachman vs. Guimard
  5. ^ Topalov vs. Polgar
  6. ^ Topalov vs. J. Polgar, 2008
  7. ^ Timman vs. Lutz, 1995
  8. ^ J. Polgar vs. Kasparov, 1996
  9. ^ Alekhine vs. Capablanca, 1927
  10. ^ Karpov vs. Ftáčnik 1988
  11. ^ "In a battle where both sides have two queens and nothing else, the player who begins with check can win because the queens are of overpowering strength against a naked king." (Benko 2007:70)
  12. ^ "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..." (Nunn 2002a:379). In a rook and pawn ending, if both sides queen a pawn, the side that gives check first frequently wins. (Müller & Pajeken 2008:223)
  13. ^ Spassky vs. Karpov, 1982
  14. ^ Karpov vs. Kasparov, 1991
  15. ^ Botvinnik vs. Tal, 1961
  16. ^ Botvinnik vs. Tal, 1961 World Championship Game 17 game score at chessgames.com
  17. ^ 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 again 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.
  18. ^ Rogers says that this endgame has an undeserved reputation for being difficult, but that it is hard to go wrong with the queen. Nunn notes that it is difficult for a human to play either side perfectly.
  19. ^ Nunn says that this endgame is tricky to defend and there are many marginal positions that require very precise defense to draw.
  20. ^ Nunn points out that there is only one drawing fortress, but the win for the queen is long and difficult (it often requires more than fifty moves).
  21. ^ Stiller and Nunn both say 243, but Müller & Lamprecht say 242

References

Further reading

External links