Pawnless chess endgame

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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).


Terminology[edit]

  • major pieces are queens and rooks
  • minor pieces are knights and bishops
  • a rank is a row of squares on the chessboard
  • a file 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 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[edit]

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[edit]

a b c d e f g h
8
Chessboard480.svg
d8 black king
f7 white queen
b6 black rook
d5 white king
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. With perfect play, in the worst winning position, the queen can win the rook or checkmate within 31 moves (Müller & Lamprecht 2001:400).

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. A possible continuation: 4. Qc5+ Kb8 5. Kd6 Rg7 6. Qb6+ Kc8 7. Qc6+ Kb8 8. Qe8+ Kb7 9. Qe4+ Kb8 10. Kc6 Rb7 11. Qe8+ Ka7 12. Qd8

Example from game[edit]

Gelfand vs. Svidler, 2001
a b c d e f g h
8
Chessboard480.svg
e8 black queen
g7 white king
h7 white rook
g5 black king
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).

Browne versus BELLE[edit]

Browne vs. BELLE, game 1
a b c d e f g h
8
Chessboard480.svg
a8 white king
e8 black rook
f6 black king
a5 white queen
8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White can win but it ended in a draw
Browne vs. BELLE, game 2
a b c d e f g h
8
Chessboard480.svg
c8 white king
d8 white queen
c4 black rook
c3 black king
8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
White won

Queen versus rook was one of the first endgames completely solved by computers constructing an endgame tablebase. 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 position 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.[4] 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 (Nunn 2002:49).[5]

Queen versus two minor pieces[edit]

Ponziani 1782
a b c d e f g h
8
Chessboard480.svg
f7 white queen
b4 black king
a3 black bishop
c3 black knight
a1 white king
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[6]
a b c d e f g h
8
Chessboard480.svg
d7 black king
d4 white knight
e4 white king
e3 white bishop
a1 black queen
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.)

  • 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 (Müller & Lamprecht 2001:339–41). 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 (Hooper & Whyld 1992:46).
  • 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 rules of competition, see fifty-move rule); there is one drawing fortress position for the two bishops (Müller & Lamprecht 2001:339–41).
  • 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. (Müller & Lamprecht 2001:339–41).

Common pawnless endings (rook and minor pieces)[edit]

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
Chessboard480.svg
b8 white rook
a7 black knight
a5 black king
c5 white king
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
  • 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 (Nunn 2002a:9).[8]
  • 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 and the "second rank defense" (Nunn 2007:161–65). Forced wins require up to 59 moves. As a result, FIDE extended the fifty-move rule to 100 moves and then to 75 moves for this endgame, before returning to fifty moves (Speelman, Tisdall & Wade 1993:382). See rook and bishop versus rook endgame 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 (Nunn 2007:159–61). The Cochrane Defense can be used.[9]
Topalov vs. J. Polgar, 2008[10]
a b c d e f g h
8
Chessboard480.svg
h7 white bishop
e6 black rook
d4 black king
b3 white king
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
Chessboard480.svg
d8 black king
e7 black rook
d6 white king
d5 white bishop
f1 white rook
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[11]
a b c d e f g h
8
Chessboard480.svg
e6 black king
b5 white king
c5 white bishop
h4 black rook
g3 white rook
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[12]
a b c d e f g h
8
Chessboard480.svg
e8 white rook
h4 white king
f3 black king
e2 black knight
g1 black rook
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[13]
a b c d e f g h
8
Chessboard480.svg
a7 black rook
d7 black knight
d6 black king
d4 white king
b2 white rook
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[14]
a b c d e f g h
8
Chessboard480.svg
f7 white rook
b6 black knight
e6 white king
h3 black king
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[edit]

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[edit]

Comte vs. Le Roy, France, 1997
a b c d e f g h
8
Chessboard480.svg
h8 white queen
a7 black queen
b4 black king
e3 white queen
f2 white king
a1 black queen
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)
  • 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 (Nunn 2002a:329,379), (Stiller 1996:175).[15]

Major pieces only[edit]

Centurini 1885 (Fine & Benko diagram 1096)
a b c d e f g h
8
Chessboard480.svg
g8 black rook
h8 black king
g7 black rook
a1 white queen
h1 white king
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.
  • Queen versus two rooks: this is usually a draw, but either side may have a win (Nunn 2002a:311).
  • Queen and a rook versus a queen and a rook: Despite the equality of material, the player to move first wins in 83% of the positions (Stiller 1996:175).[16]
  • Queen and rook versus a queen: this is a win (Nunn 2002a: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) (Nunn 2002a:320).

A curious ending of two rooks against three rooks occurred in a game between Paul Lamford and Gile Andruet from a match Wales versus France in 1980. This proved an easy win for the three rooks. Andruet had earlier been forced to underpromote to a rook to avoid a stalemating defence for Lamford.

  • 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 (Levenfish & Smyslov 1971:13).

Queens and rooks with minor pieces[edit]

a b c d e f g h
8
Chessboard480.svg
c5 white queen
b4 black bishop
g4 black rook
h3 black king
d1 white king
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
  • Queen versus a rook and a minor piece: this is usually a draw (Müller & Lamprecht 2001:402). 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 (Mednis 1996:120–29).
  • 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 (Müller & Lamprecht 2001:406).
  • Queen and a minor piece versus a rook and minor piece: this is normally a win for the queen (Müller & Lamprecht 2001:403–4).
a b c d e f g h
8
Chessboard480.svg
c7 white king
d7 black rook
f6 black king
f3 white bishop
g2 white queen
d1 black rook
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
  • 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. This case with a bishop and queen versus rooks is unusual in that such a small material advantage forces a win. It was thought to be a draw by human analysis, but computer analysis revealed a long forced win (Müller & Lamprecht 2001:404), (Nunn 2002a:328–29,367,372).

Queens and minor pieces[edit]

Kling & Horowitz, 1851
a b c d e f g h
8
Chessboard480.svg
f8 white bishop
h8 black king
f7 white bishop
f6 white king
e5 white knight
f5 white knight
f1 black queen
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
  • Queen versus one minor piece: a win for the queen (Hooper 1970:4).
  • 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 (Nunn 2002a:328).
  • 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) (Speelman 1981:108). 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 (Nunn 2002a:70–122).

Examples from games[edit]

Nyazova vs. Levant, USSR 1976
a b c d e f g h
8
Chessboard480.svg
e8 white queen
f7 white king
h5 white knight
g4 black king
h1 black queen
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
Chessboard480.svg
b6 black king
b4 black queen
b3 white knight
d3 white king
b2 white queen
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 then world champion Anatoly Karpov.[17] The position is a theoretical draw but Karpov later blundered in time trouble and resigned on move 84.

Example from a study[edit]

V. Halberstadt, 1967
a b c d e f g h
8
Chessboard480.svg
b8 black king
f7 black queen
f6 white bishop
e3 white king
f1 white queen
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! (not 2. Qxf7?? stalemate.) 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[edit]

Horwitz & Kling, 1851
a b c d e f g h
8
Chessboard480.svg
f7 black king
g6 black bishop
e5 black bishop
d2 white rook
c1 white king
d1 white rook
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
  • 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 (Müller & Lamprecht 2001:404). 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 (Staunton 1848:439–40).
Karpov vs. Kasparov, Tilburg, 1991[18]
a b c d e f g h
8
Chessboard480.svg
d8 black rook
c6 white bishop
f6 black king
f4 white knight
h4 white king
d3 white knight
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.
  • 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 (Müller & Lamprecht 2001:403). Staunton in 1847 correctly concluded that the normal result of this endgame is a draw (Staunton 1848:439). Bernhard Horwitz and Josef Kling gave the same appraisal in 1851 (Horwitz & Kling 1986:142). During adjournment 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, and threatening to sacrifice it (for stalemate or for the bishop, which results in a draw, see two knights endgame). Tablebases show that it is usually a draw, no matter which corner the defending king is in (Kasparov 2010:303). (See the position from the Karpov versus Kasparov game for a drawn position, and see fifty-move rule for more discussion of this game.) Curiously, Grandmaster James Plaskett also had an adjournment of a London league game at the same time, versus David Okike which, after resumption, 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 (Müller & Lamprecht 2001:404). 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 (Nunn 2002a: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 (for the rook and bishop) if the bishops are on opposite colors, but takes up to ninety-eight moves (Müller & Lamprecht 2001:404).
  • 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 (Müller & Lamprecht 2001:404).
  • Rook versus two minor pieces: this is normally a draw (Hooper 1970:4).
  • Two rooks versus three minor pieces: this is normally a draw (Hooper 1970:4).
  • Rook and two minor pieces versus a rook: a win for the three pieces (Hooper 1970:4). With two knights, White must not exchange rooks and avoid losing a knight, but the three pieces have great checkmating power (Roycroft 1972:195,203).

Minor pieces only[edit]

Kling & Horowitz, 1851
a b c d e f g h
8
Chessboard480.svg
f8 white bishop
b7 black knight
b6 black king
d5 white king
a4 white bishop
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
Chessboard480.svg
b5 white bishop
e2 black knight
b1 white king
c1 white bishop
d1 black king
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 (the only winning move). White wins the knight on move 66, converting the position to a basic checkmate (Matanović 1993:512–13).
  • 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. (Nunn 1995:267). See Effect of tablebases on endgame theory, fortress (chess)#A semi-fortress and see the example from the Botvinnik versus Tal game below.
    • other cases: this is normally a draw in all other cases (Müller & Lamprecht 2001:402), (Hooper 1970:4). Edmar Mednis considered the difficulty of defending these positions:
      • Two bishops versus one bishop: The easiest for the defender to draw, unless the 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 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 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 knight can be lost if it is separated from its king (Mednis 1996:36–40).
  • Three knights and a king can force checkmate against a lone king within 20 moves (unless the defending king can win one of the knights), but this can only happen if the attacking side has underpromoted a pawn to a knight. (Fine 1941:5–6).
  • 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 (Müller & Lamprecht 2001:403,406).
  • 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[edit]

Botvinnik vs. Tal, 1961[19]
a b c d e f g h
8
Chessboard480.svg
a6 white king
e6 black king
b4 black bishop
b3 white knight
g2 black bishop
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.[20]

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.[21]

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[edit]

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
Chessboard480.svg
e6 black king
d5 black knight
e5 white bishop
g5 white rook
c4 black bishop
h3 black rook
b2 white king
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
Chessboard480.svg
e8 white rook
b7 black bishop
e7 black bishop
e6 black king
b4 black rook
f4 white bishop
g3 white king
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:

  • 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 (Speelman 1981:170).

Summary[edit]

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

Recap of some pawnless endgames
Attacker Defender Status Assessment
Chess qlt45.svg Chess rdt45.svg Win Difficult[22]
Chess rlt45.svg Chess bdt45.svg Draw Easy, if defender goes to the right corner
Chess rlt45.svg Chess ndt45.svg Draw Easy
Chess rlt45.svg Chess blt45.svg Chess rdt45.svg Draw Easy, if the Cochrane Defense is used[23]
Chess rlt45.svg Chess nlt45.svg Chess rdt45.svg Draw Easy
Chess qlt45.svg Chess bdt45.svg Chess bdt45.svg Draw Easy, but use care[24]
Chess qlt45.svg Chess bdt45.svg Chess ndt45.svg Win Easy
Chess qlt45.svg Chess ndt45.svg Chess ndt45.svg Draw Easy for the defender
Chess qlt45.svg Chess nlt45.svg Chess qdt45.svg Draw Difficult for the defender
Chess qlt45.svg Chess blt45.svg Chess qdt45.svg Draw Easy

Fine's rule[edit]

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[edit]

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[edit]

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 %
Chess qlt45.svg Chess kdt45.svg 10 100
Chess rlt45.svg Chess kdt45.svg 16 100
Chess qlt45.svg Chess qdt45.svg 10 42
Chess qlt45.svg Chess rdt45.svg 31 99
Chess rlt45.svg Chess bdt45.svg 18 35
Chess rlt45.svg Chess ndt45.svg 27 48
Chess blt45.svgChess blt45.svg Chess kdt45.svg 19 99.97
Chess blt45.svgChess nlt45.svg Chess kdt45.svg 33 99.5
Chess qlt45.svgChess qlt45.svg Chess qdt45.svg 30 94
Chess qlt45.svgChess rlt45.svg Chess qdt45.svg 67 92.1
Chess qlt45.svgChess blt45.svg Chess qdt45.svg 33 53.4
Chess qlt45.svgChess nlt45.svg Chess qdt45.svg 41 48.4
Chess qlt45.svg Chess bdt45.svgChess bdt45.svg 71 92.1
Chess qlt45.svg Chess bdt45.svgChess ndt45.svg 42 93.1
Chess qlt45.svg Chess ndt45.svgChess ndt45.svg 63 89.7
Chess rlt45.svgChess blt45.svg Chess rdt45.svg 59 40.1
Chess rlt45.svgChess nlt45.svg Chess rdt45.svg 33 35.9
Chess blt45.svgChess blt45.svg Chess ndt45.svg 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 %
Chess rlt45.svgChess nlt45.svg Chess ndt45.svgChess ndt45.svg 243[25] 78
Chess rlt45.svgChess blt45.svg Chess ndt45.svgChess ndt45.svg 223 96
Chess rlt45.svgChess nlt45.svg Chess bdt45.svgChess ndt45.svg 190 72
Chess qlt45.svgChess nlt45.svg Chess rdt45.svgChess rdt45.svg 153 86
Chess rlt45.svgChess nlt45.svg Chess bdt45.svgChess bdt45.svg 140 77
Chess rlt45.svgChess rlt45.svgChess nlt45.svg Chess qdt45.svg 101 94

See also[edit]

Notes[edit]

  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. ^ Browne vs BELLE, game 1
  5. ^ Browne vs BELLE, game 2
  6. ^ Pachman vs. Guimard
  7. ^ Topalov vs. Polgar
  8. ^ This endgame was studied as early as the 12th century, and the studies are still valid. Studies from this period involving other pieces are no longer valid because the rules have changed. Hawkins, Jonathan, Amateur to IM, 2012, p. 179, ISBN 978-1-936277-40-7
  9. ^ Incidentally, the longest decisive game (210 moves) between masters under standard time controls ended with this material, see Neverov vs. Bogdanovich. Andy Soltis, "Chess to Enjoy", Chess Life, p. 12, Dec. 2013, and chessbase article: "210-move drama in Kiev".
  10. ^ Topalov vs. J. Polgar, 2008
  11. ^ Timman vs. Lutz, 1995
  12. ^ J. Polgar vs. Kasparov, 1996
  13. ^ Alekhine vs. Capablanca, 1927
  14. ^ Karpov vs. Ftáčnik 1988
  15. ^ "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)
  16. ^ "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)
  17. ^ Spassky vs. Karpov, 1982
  18. ^ Karpov vs. Kasparov, 1991
  19. ^ Botvinnik vs. Tal, 1961
  20. ^ Botvinnik vs. Tal, 1961 World Championship Game 17 game score at chessgames.com
  21. ^ 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.
  22. ^ 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. Capablanca says this is a very difficult position to win with queen; when the defense is skillful only a very good player can win. Pandolfini says that it is not easy (Pandolfini 2009:67).
  23. ^ Nunn says that this endgame is tricky to defend and there are many marginal positions that require very precise defense to draw.
  24. ^ 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).
  25. ^ Stiller and Nunn both say 243, but Müller & Lamprecht say 242

References[edit]

Further reading[edit]

External links[edit]