Pawnless chess endgames

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This article uses algebraic notation to describe chess moves.

Pawnless chess endgames are chess endgames in which only a few pieces remain, and none of them are pawns. The basic checkmates are a type of pawnless endgame. Generally endgames without pawns do not occur very often in practice, but some of the more common ones follow.

Contents 1 Basic checkmates 2 Queen versus rook 3 Queen versus two minor pieces 4 Miscellaneous pawnless endings 4.1 Queen and rook, without minor pieces 4.2 Queen and rook, with minor pieces 4.3 Queen and minor pieces, without rooks 4.4 Rook, without queens, usually with minor pieces 4.5 Minor pieces only 4.5.1 Example from game 5 Fine's rule 6 General remarks on these endings 7 See also 8 Notes 9 References 10 Further reading

[edit] 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.

[edit] Queen versus rook

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

The "third rank defense" by the rook is difficult for a human to crack. The "third rank defense" is when the rook is on the third rank or file from the edge of the board, his king is closer to the edge and the enemy king is on the other side (see the diagram). The winning move is the counterintuitive withdrawal of the queen from the seventh rank to a more central location, 1. Qf4, so the queen can make checking maneuvers to win the rook with a fork if it moves along the third rank. And if the black king emerges from the back rank, 1... Kd7, then 2. Qa4+ Kc7; 3. Qa7+ forces Black into a second-rank defense (defending king on an edge of the board and the rook on the adjacent rank or file) after 3... Rb7. This position is a standard win, with White heading for the Philidor position with a queen versus rook (Müller & Lamprecht 2001:331-33).

[edit] Queen versus two minor pieces

• 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).

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

• Two knights: Two knights can generally draw against a queen by setting up a fortress (Müller & Lamprecht 2001:339-41).

See fortress for more details about these endings.

[edit] Miscellaneous pawnless endings

Other types of pawnless endings have been studied (Nunn 2002). Of course, there are positions that are exceptions to these general rules stated below.

The fifty move rule is not taken into account, and it would often be applicable in practice. When one side has two bishops, they are assumed to be on opposite colored squares, unless otherwise stated. When each side has one bishop, the result often depends on whether or not the bishops are on the same color, and that is stated.

[edit] Queen and rook, without minor pieces

• Queen versus two rooks: this is usually a draw, but either side may have winning chances.

• Queen and a rook versus a queen and a rook: Despite the equality of material, the player to move wins in 67.74 percent of positions.

• Queen and rook versus a queen: this is a win.

• Two queens versus one queen: A win, see cross-check#Two queens versus one for an example.

[edit] Queen and rook, with minor pieces

• Queen versus a rook and a minor piece: this is usually a draw.

• Two rooks and a minor piece versus a queen: this is usually a win for the three pieces, but it can take more than fifty moves.

• Queen and a minor piece versus a rook and minor piece: this is usually a win for the queen.

• Queen and a minor piece versus two rooks: this is usually a draw for a knight; usually a win for a bishop, but it takes up to eighty-five moves. The defense is to double the rooks on the third rank with the opposing king on the other side, and keep the king behind the rooks. This defense can be broken down by a queen and bishop but not by a queen and knight. Accurate defense is required though. The case with a bishop is an unusual win with a small material advantage.

• Rook and two minor pieces versus a queen: draw.

[edit] Queen and minor pieces, without rooks

• Queen and a minor piece versus a queen: this is usually a draw.

• 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.

• Four minor pieces versus a queen: a win for the pieces (Fine & Benko 2003:583).

[edit] Rook, without queens, usually with minor pieces

• Rook and a knight piece versus a rook: this is a theoretical draw, but Judit Polgar lost a famous game to Garry Kasparov (see diagram) [1] when she blundered in a quickplay finish (a sudden death time control) (Nunn 2007:159-61, 165). There are five cases that are wins when the defending king is restricted to the edge of the board (Grivas 2008:257).

• Rook and a bishop versus a rook: this is one of the most common pawnless endgames and is usually a theoretical draw. However, the rook and bishop have good winning chances in practice because the defense is difficult (Nunn 2007:161ff). There are some winning positions. See Philidor position#Rook and bishop versus rook and Cochrane Defense.

• Rook versus a bishop: this is usually a draw. The main exception is when the defending king is trapped in a corner that is of the same square as his bishop (Nunn 2002:31). See the game of Veselin Topalov versus Judit Polgar, where the draw clinched a win of their 2008 Dos Hermanas match.^[1]

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

• Two rooks versus two minor pieces: this is normally a win.

• Two bishops and a knight versus a rook: this is usually a win but it takes up to sixty-eight moves. Howard Staunton analyzed a position of this type in 1849.

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

• Rook and a bishop versus two knights: this is usually a win but it takes up to 223 moves.

• Rook and a knight versus two knights: this is usually a win but it takes up to 243 moves.

• Rook and a bishop versus a bishop and knight: this is usually a draw if the bishops are on the same color. It is usually a win if the bishops are on opposite colors, but takes up to ninety-eight moves.

• 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).

[edit] Minor pieces only

• Two bishops versus a knight: this is usually a win (assuming that the bishops are on opposite colors), but it takes up to sixty-six moves. See Effect of tablebases on endgame theory and see the example from a game below.

• Two minor pieces versus one minor piece: except for two bishops (on opposite colors) versus one knight (above), this is normally a draw.

• 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 (allowing the opponent to claim a draw under FIDE rules).

[edit] Example from game

An ending with two bishops versus a knight occurred in the seventeenth game of the World Chess Championship 1961 match between Mikhail Botvinnik and Mikhail Tal. The position occurred after White captured a pawn on his 77th move, and White resigned on move 84. ^[2]

• 77... Bf1+
• 78. Kb6 Kd6
• 79. Na5 Bc5+
• 80. Kb7 Be2
• 81. Nb3 Be3
• 82. Na5 Kc5
• 83. Kc7 Bf4+
• 84. 0-1

[edit] Fine's rule

In his landmark 1941 book Basic Chess Endings, Reuben Fine inaccurately stated that in endgames without pawns, at least the advantage of a rook (or equivalent material) is required to win, with two exceptions in which less of an advantage is sufficient (chapter IX of the first edition). 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). The two exceptions noted by Fine are (1) the double exchange – two rooks versus any two minor pieces, and (2) four minor pieces versus a queen. (Fine & Benko 2003:585). It turns out that there are several exceptions, but they are endgames that rarely occur in actual games (except for perhaps a queen versus a rook).

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, but the fifty move rule comes into play in competition because in general more than fifty moves are required to either checkmate or reduce the endgame to a simplier case: two bishops and a knight versus a rook (68 moves); and two rooks and a minor piece versus a queen (82 moves for the bishop, 101 moves for the knight).

A three-point material advantage can also result in a forced win, in some cases. For instance, some of the cases of a queen versus two minor piece are such positions (as mentioned above). In addition, the four minor pieces win against a queen. Two bishops (on opposite colors) win against a knight, but it takes up to 66 moves if a bishop is initially trapped in a corner (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 2002:325-29).

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.)

[edit] General remarks on these endings

Other than the basic checkmates with a queen and with a rook, the endgames without pawns occur rarely in actual games.

Note: 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 can't. 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.

[edit] See also

• Chess endgame
• Checkmate

[edit] Notes

[edit] References

• Fine, Reuben & Benko, Pal (2003), Basic Chess Endings (second ed.), McKay, ISBN 0-8129-3493-8 
• Grivas, Efstratios (2008), Practical Endgame Play - mastering the basics, Everyman Chess, ISBN 978-1-85744-556-5 
• Hooper, David & Whyld, Kenneth (1992), The Oxford Companion to Chess (second ed.), Oxford University Press, ISBN 0-19-280049-3 
• Karolyi, Tibor & Aplin, Nick (2007), Endgame Virtuoso Anatoly Karpov, New In Chess, ISBN 978-90-5691-202-4 
• Müller, Karsten & Lamprecht, Frank (2001), Fundamental Chess Endings, Gambit Publications, ISBN 1-901983-53-6 
• Müller, Karsten & Pajeken, Wolfgang (2008), How to Play Chess Endings, Gambit Publications, ISBN 978-1-904600-86-2 
• Nunn, John (1995), Secrets of Minor-Piece Endings, Batsford, ISBN 0-8050-4228-8 
• Nunn, John (2002), Secrets of Pawnless Endings (second ed.), Gambit Publications, ISBN 1-901983-65-X 
• Nunn, John (2007), Secrets of Practical Chess (second ed.), Gambit Publications, ISBN 978-1-904600-70-1 

[edit] Further reading

• Ward, Chris (1996), Endgame Play, Batsford, ISBN 0-7134-7920-5  Pawnless endings are discussed on pages 87-96.