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 . Other cases that occur occasionally are (1) a rook and versus a rook and (2) 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 ("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 ; in other cases, the game is a draw (i.e. a book draw).
Terminology.
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 , resulting in a position that leads to an elementary checkmate.
Basic checkmates.
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.
A queen wins against a lone rook, unless there is an immediate draw by stalemate or due to perpetual check (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 .
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 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 . 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.
In this 2001 game between Boris Gelfand and Peter Svidler, 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 . 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.
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. 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 .
Queen versus two minor pieces.
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.)
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 .
 
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, so their colors will always be stated.
Queens and rooks with minor pieces.
In endgames with extra queens, tempo is often more important than material. Two queens can win against two queens and a knight about half the time, when they have the move.
Queens and minor pieces.
Examples from games.
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:
If 1...Kxh5 then 2.Qg6+ Kh4 3.Qh6+ skewers the black queen.
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 .
The second position is from a 1982 game between former world champion Boris Spassky and then world champion Anatoly Karpov. The position is a theoretical draw but Karpov later blundered in time trouble and resigned on move 84.
Example from a study.
In this 1967 study by Vitaly Halberstadt, White wins. The solution is: 
Not 2.Qxf7 stalemate.
Minor pieces only.
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.
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.
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 . 
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.
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:
In this position, if White could exchange bishops (or rooks) he would reach a drawn position. However, Black has a winning attack:
Speelman gave these conclusions:
Later tablebase analysis confirmed that rook and two minor pieces versus rook and one minor piece is a general win.
Summary.
Grandmaster Ian Rogers summarized several of these endgames .
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." Kenneth Harkness also stated this "rule" . 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." 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 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 .
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 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 .
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.
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 .
This table shows six-piece endgames .
This table shows seven-piece endgames (Lomonosov tablebases).