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, except for the basic checkmates of king
versus king and king and rook
versus king and queen versus rook . Others that do occur occasionally are a rook and minor piece
versus a rook and a rook versus a minor piece, especially if the minor piece is a bishop
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 summarizing the research of endgame tablebases.
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).
Queens and rooks are major pieces whereas knights and bishops are minor pieces.
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.
Queen versus rook
A queen wins against a lone rook, unless there is an immediate draw
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 .
Queen versus two minor pieces
- 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 . 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 .
- Queen versus 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 .
- Queen versus two knights: Two knights can generally draw against a queen by setting up a fortress .
See fortress for more details about these endings.
Miscellaneous pawnless endings
Other types of pawnless endings have been studied . 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.
- Queen versus queen: usually a draw, but the side to move first wins in 41.75 percent of the positions .
- Two queens versus one queen: A win, see cross-check#Two queens versus one for an example .
- Two queens versus two queens: The first to move wins in 83 percent of the positions (see the diagram for an example). Wins require up to 44 moves , .
Major pieces only
- 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 first wins in 83 percent of the positions .
- Queen and rook versus a queen: this is a win .
- 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) .
Queens and rooks 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 normally a win for the queen .
- Rook and two minor pieces versus a queen: draw .
- 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. Accurate defense is required though. This defense can be broken down by a queen and bishop but not by a queen and knight. The case with a bishop is an unusual win with a small material advantage. It was thought to be a draw by human analysis, but computer analysis revealed a long forced win , .
Queens and minor pieces
- 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 if they are the usual four minor pieces (see Kling and Horwitz) .
- Queen and a minor piece versus a queen: this is usually a draw unless the stronger side can quickly win (see Nyazova vs Levant) .
- Queen versus a minor piece: a win .
Example from game
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+ Kf2
- 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 .
Rooks and minor pieces
- Rook and a knight versus a rook: this is a theoretical draw, but Judit Polgar lost a famous game to Garry Kasparov (see diagram) when she blundered in a quickplay finish (a sudden death time control) . There are five cases that are wins when the defending king is restricted to the edge of the board .
- 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. There are some winning positions such as the Philidor position, which occurs relatively often . Also see the 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 . See the game of Veselin Topalov versus Judit Polgar, where the draw clinched a win of their 2008 Dos Hermanas match.
- 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 .
- 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 . This was not known until computer analysis was done.
- Rook and a knight versus two knights: this is usually a draw but there are some wins that take 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 .
- Rook versus two minor pieces: normally a draw .
- Two rooks versus three minor pieces: normally a draw .
- Rook and two minor pieces versus a rook: a win .
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 .
- 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
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.
- 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 . White gets his knight to b7
with his king next to it to form a long-term fortress
- 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 , for example 86. Kd6 Bd1 87. Na1 Bd4 88. Kd5 Bxa1 .
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." This inaccurate statement was repeated in the 2003 edition revised by Grandmaster Pal Benko
. However, Fine recognized elsewhere in his book that a queen wins against a rook and that a queen normally beats a knight and a bishop (with the exception of one drawing fortress) . 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.
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 (on opposite colors) win against a knight, but it takes up to 66 moves if a bishop is initially trapped in a corner .
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) .
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.
- Pawnless endings are discussed on pages 87-96.