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

[edit] Basic checkmates

Main article: checkmate

Checkmates 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

Image:chess_zhor_26.png
Image:chess_zver_26.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
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Third rank defense, White wins with correct play

A queen wins against a lone rook, unless there is an immediate draw by stalemate or 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 counter-intuitive 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. (Another position is more artificial: the queen's king is on a1 confined by Ba3 and Nc3 protected by their king.)
  • 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.
  • 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.

  • Rook versus a minor piece (bishop or knight): this is usually a draw.
  • Queen and a minor piece versus a queen: this is usually a draw.
  • Queen versus a rook and a minor piece: this is usually a draw.
  • Queen versus two rooks: this is usually a draw, but either side may have winning chances.
  • 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).
  • 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.
  • Rook and a bishop versus two knights: this is usually a win but it takes up to 223 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 and a minor piece versus a queen: this is usually a win but it can take more than fifty moves.
  • Queen and a minor piece versus a rook and minor piece: this is usually a win.
  • 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.

[edit] Fine's rule

In his landmark 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 50 moves are required: 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.

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 2001:400-406) (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.

[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. Therefore a chess player should concentrate on endings with pawns after learning the basic checkmates.

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

[edit] References

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