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).

Terminology
  • 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
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
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Black is employing the third rank defense. White can win this position in as few as 19 moves with correct play.

A queen wins against a lone rook, unless there is an immediate draw by stalemate or due to perpetual check (Nunn 2002a:49) (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, The Chess Ending, King & Queen against King & Rook. Normally the winning process involves first winning the rook by the queen with 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, as White heads for the Philidor position with a queen versus rook (Müller & Lamprecht 2001:331–33). 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 [Philidor—mate in 7].

Example from game
Gelfand vs. Svidler, 2001
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Black can win this position in as few as 13 moves with optimal play from both sides.

In this 2001 game[1] between Boris Gelfand and Peter Svidler,[2] the player with the queen should win, but the game was drawn because of the fifty-move rule after he 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 – 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
Browne vs. BELLE, game 1
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White can win but it ended in a draw
Browne vs. BELLE, game 2
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White won

The queen versus rook endgame 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 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.[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 2002a:49).[5]

Queen versus two minor pieces
Ponziani 1782
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Artificial position where the attacking king is confined, draw
Pachman vs. Guimard, 1955[6]
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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)

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).

  • 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 (Nunn 2002a:31) (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.[7]
  • 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] 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.[9]
  • 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.[10]
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Position after 92...Ka5, draw
Topalov vs. J. Polgar, 2008[11]
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White to move, draw
Philidor, 1749
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White to move wins, Black to move draws (Nunn 2002a:178)
Timman vs. Lutz, 1995[12]
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Black to move, drawn 52 moves later (Lutz 1999:129–31)
J. Polgar vs. Kasparov, 1996[13]
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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.
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White to move, the game was drawn twelve moves later. The white king cannot be driven to the edge.
Karpov vs. Ftáčnik, 1988[15]
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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
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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% of the positions (Müller & Lamprecht 2001:400). There are some wins when one queen is in the corner, e.g. as a result of promoting a rook pawn or bishop pawn (Hooper 1970:17–19).
  • Two queens versus one queen: Almost always a win. A cross-check may be necessary, see cross-check#Two queens versus one for an example (Müller & Lamprecht 2001:400). 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 (Nunn 2002a:329,379), (Stiller 1996:175).[16]

Major pieces only
Centurini 1885
(Fine & Benko diagram 1096)
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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 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.[17]
  • 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).[18]
  • 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).
  • 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
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White's knight is trapped by the Black queen, but the White rook cannot be driven from its defense. This position is a draw.
  • 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).
  • Rook and two minor pieces versus a queen: draw (Müller & Lamprecht 2001:405).
  • 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).
  • 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.[19] 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.

Queens and minor pieces
Kling & Horowitz, 1851
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Black is unable to prevent checkmate

Examples from games
Nyazova vs. 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

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+ 1–0

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 (Speelman 1981:108).

Spassky vs. Karpov, 1982
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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.[20] 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
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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.

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# (Nunn 2002b:48,232).

Rooks and minor pieces
Horwitz & Kling, 1851
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White to move wins
  • Two rooks versus two minor pieces: this is normally a win for the rooks (Müller & Lamprecht 2001:405). Henri Rinck discovered more than 100 positions that are exceptions (Roycroft 1972:203).
  • 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[21]
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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 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; 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 (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 knight versus a bishop and knight: this is normally a draw.
  • 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). Magnus Carlsen 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.[22]
  • 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).
  • Rook and two minor pieces versus rook and one minor piece: see § Examples with an extra minor piece below.
  • Two rooks and a minor piece versus two rooks: this is normally a draw, but some very long wins exist.[23]

Minor pieces only
Kling & Horowitz, 1851
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ECE #1907, Belle
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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). Three knights win against one knight (Dvoretsky 2011:283).
  • Three minor pieces versus two minor pieces: if neither player has a pair of same-colored bishops, this is a draw except in the cases of two bishops and a knight versus two knights, and two bishops and a knight versus bishop and knight, which are wins. (In other words, if there are no same-colored bishop pairs, this is a won endgame exactly when the stronger side has the bishop pair and the weaker side lacks it.) There are also wins in some unusual situations where underpromotion has resulted in one player having two bishops travelling on the same colors.[24]
  • Two minor pieces:
  • 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
Botvinnik vs. Tal, 1961[25]
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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.[26]

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.[27]

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

R. Blau vs. Unzicker, 1949
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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
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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 Kg4
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

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

Recap of some pawnless endgames
AttackerDefenderStatusAssessment
WinDifficult[28]
DrawEasy, if defender goes to the correct corner
DrawEasy
DrawEasy, if the Cochrane Defense is used[29]
DrawEasy
DrawEasy, but use care[30]
WinEasy
DrawEasy for the defender
DrawDifficult for the defender
DrawEasy

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 piecesDefending piecesLongest winWinning %
—10100
—16100
1042
3199
1835
2748
—1999.97
—3399.5
3094
6792.1
3353.4
4148.4
7192.1
4293.1
6389.7
5940.1
3335.9
6691.8

This table shows six-piece endgames (Stiller 1996).

Six-piece endgames
Attacking piecesDefending piecesLongest winWinning %
243[31]78
22396
19072
15386
14077
10194
9969
9887
9286
9283
8694
8592
8296
7572
7387
7381
7294
7190
6980
6895
6598
6385
5473
5265
5182
4953
4892
4666
4483
4475
3863
3794
3668
3575
3262
3261
3199
2963
2757
1867
1262

This table shows seven-piece endgames (Lomonosov tablebases).

  • Many of the combinations listed involve single piece capture and transposition into six-piece territory almost immediately from the starting position.
Seven-piece endgames
Attacking piecesDefending piecesLongest win (distance to mate)Winning %
54562.79 (85.6 with White to move, 39.98 with Black to move)
304?
262?
262?
246?
246?
238?
232?
229?
212?
210?
197?
195?
192?
182?
176?
176?
169?
154?
152?
150?
149?
140?
136?
134?
122?
120?
117?
115?
112?
106?
105?
102?
98?
88?
86?
77?
70?

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. Browne vs BELLE, game 1
  5. Browne vs BELLE, game 2
  6. Pachman vs. Guimard
  7. Topalov vs. Polgar
  8. This ending was the subject of the oldest documented endgame study, by al-Aldi in the 9th century AD. 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. http://www.chessgames.com/perl/chessgame?gid=1411263
  10. 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".
  11. Topalov vs. J. Polgar, 2008
  12. Timman vs. Lutz, 1995
  13. J. Polgar vs. Kasparov, 1996
  14. Alekhine vs. Capablanca, 1927
  15. Karpov vs. Ftáčnik 1988
  16. "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)
  17. Such an underpromotion occurred in Dinara Dordzhieva vs Alexandra Kosteniuk, Russian Team Championship (Women) R6, (7 May 2018), Sochi. This was not strictly a pawnless endgame, because there were two blocked pawns on the a-file, but they did not change the principle involved.
  18. "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)
  19. However, most positions in this endgame have immediate threats, and in a large fraction of random positions, KRBN can draw by trapping/capturing/exchanging the opposing knight, or using this and other threats to force move repetition; there is also a drawing fortress position (with Na2 Bc3 Rd4).
  20. Spassky vs. Karpov, 1982
  21. Karpov vs. Kasparov, 1991
  22. Francisco Vallejo Pons vs Magnus Carlsen, GRENKE Chess Classic, Karlsruhe GER, rd 2, 21 April 2019.
  23. Open chess diary by Tim Krabbé, entry 298
  24. http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=25373 (post by Marc Bourzutschky, specialist in endgame tablebases)
  25. Botvinnik vs. Tal, 1961
  26. Botvinnik vs. Tal, 1961 World Championship Game 17 game score at chessgames.com
  27. 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.
  28. 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).
  29. Nunn says that this endgame is tricky to defend and there are many marginal positions that require very precise defense to draw.
  30. 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).
  31. Stiller and Nunn both say 243, but Müller & Lamprecht say 242

References

Further reading
  • Ward, Chris (1996), Endgame Play, Batsford, ISBN 0-7134-7920-5 Pawnless endings are discussed on pages 87–96.
  • Pachman, Luděk (1983), Chess Endings for the Practical Player, Routledge & Kegan Paul, ISBN 0-7100-9266-0 Pawnless endings are discussed on pages 9–22.
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