Chess endgame

This article uses algebraic notation to describe chess moves.

In chess and chess-like games, the endgame (or end game or ending) refers to the stage of the game when there are few pieces left on the board.

The line between middlegame and endgame is often not clear, and may occur gradually or with the quick exchange of a few pairs of pieces. The endgame, however, tends to have different characteristics from the middlegame, and the players have correspondingly different strategic concerns. In particular, pawns become more important; endgames often revolve around attempting to promote a pawn by advancing it to the eighth rank. The king, which has to be protected in the middlegame owing to the threat of checkmate, becomes a strong piece in the endgame. It can be brought to the center of the board and be a useful attacking piece.

Many people have composed endgame studies, endgame positions which are solved by finding a win for White when there is no obvious way of winning, or a draw when it seems White must lose.

Usually in the endgame, the stronger side should try to exchange pieces (knights, bishops, rooks, and queens), while avoiding the exchange of pawns. This generally makes it easier for him to convert his advantage into a won game. The defending side should strive for the opposite.

Endgames can be classified according to the type of pieces that remain. Some common types of endgames are discussed below.

Categories

Endgames can be divided into three categories:

1. Theoretical endgames – positions where the correct line of play is generally known and well-analyzed, so the solution is a matter of technique
2. Practical endgames – positions arising in actual games, where skillful play should transform it into a theoretical endgame position
3. artistic endgames (studies) – contrived positions which contain a theoretical endgame hidden by problematic complications (Portisch & Sárközy 1981:vii).

This article generally does not consider studies.

The start of the endgame

An endgame is when there are only a few pieces left. There is no strict criterion for when an endgame begins and different experts have different opinions. With the usual system for Chess piece relative value, Speelman considers that endgames are positions in which each player has thirteen or fewer points in material (not counting the king). Alternatively, an endgame is a position in which the king can be used actively, but there are some famous exceptions to that (Speelman 1981:7-8). Minev characterizes endgames as positions having four or fewer pieces other than kings and pawns (Minev 2004:5). Some authors consider endgames to be positions without queens while others consider a position to be an endgame when each player has less than a queen plus rook in material. Flear considers an endgame to be where each player has at most one piece (other than kings and pawns) and positions with more material where each player has at most two pieces to be "Not Quite an Endgame" (NQE), pronounced "nuckie" (Flear 2007:7-8).

Alburt and Krogius give three characteristics of an endgame: (Alburt & Krogius 2000:12)

1. Endgames favor an aggressive king
2. Passed pawns increase greatly in importance
3. Zugzwang is often a factor in endgames and rarely in other stages of the game.

Some problem composers consider that the endgame starts when the player who is about to move can force a win or a draw against any variation of moves (Portisch & Sárközy 1981:vii).

General considerations

In endgames with pieces and pawns, an extra pawn is a winning advantage in 50 to 60 percent of the cases. It becomes more decisive if the stronger side has a positional advantage (Euwe & Meiden 1966:xvi). In general, the player with a material advantage tries to exchange pieces and reach the endgame. In the endgame, the player with a material advantage should usually try to exchange pieces but avoid the exchange of pawns (Dvoretsky & Yusupov 2008:134). There are some exceptions to this: (1) endings in which both sides have two rooks plus pawns – the player with more pawns has better winning chances if a pair of rooks are not exchanged, and (2) bishops on opposite color with other pieces – the stronger side should avoid exchanging the other pieces. Also when all of the pawns are on the same side of the board, often the stronger side must exchange pawns to try to create a passed pawn.

In the endgame, it is better for the player with more pawns to avoid too many pawn exchanges, because they should be won for nothing. Also, endings with pawns on both sides of the board are much easier to win. A king and pawn endgame with an outside passed pawn should be a far easier win than a middlegame a rook ahead.

With the recent growth of computer chess, an interesting development has been the creation of endgame databases which are tables of stored positions calculated by retrograde analysis (such a database is called an endgame tablebase). A program which incorporates knowledge from such a database is able to play perfect chess on reaching any position in the database.

Max Euwe and Walter Meiden give these five generalizations:

1. In king and pawn endings, an extra pawn is decisive in more than 90 percent of the cases
2. In endgames with pieces and pawns, an extra pawn is a winning advantage in 50 to 60 percent of the cases. It becomes more decisive if the stronger side has a positional advantage
3. The king plays an important role in the endgame
4. Initiative is more important in the endgame than in other phases of the game. In rook endgames the initiative is usually worth at least a pawn
5. Two connected passed pawns are very strong. If they reach their sixth rank they are generally as powerful as a rook (Euwe & Meiden 1966:xvi-xvii).

Common types of endgames

Basic checkmates

Checkmate with the rook

These are positions in which one side has only a king and the other side has one or two pieces and can checkmate the opposing king, with the pieces working together with their king. In conjunction with its king, a queen or a rook can easily checkmate a lone king, but a single minor piece (a bishop or knight) can not. See Wikibooks - Chess/The Endgame for a demonstration of these two checkmates. Two bishops (plus their king) can easily checkmate a lone king, provided that the bishops move on opposite color squares. (Two or more bishops on the same color can not checkmate.) A bishop and knight (plus their king) can also checkmate a lone king, although the checkmate procedure is long (up to 33 moves with correct play) and is difficult for a player who does not know the correct technique.

Two knights cannot force checkmate against a lone king (see Two knights endgame), but if the weaker side also has a pawn, checkmate is sometimes possible, because positions which would be stalemate without the pawn are not stalemate with the additional pawn. If the pawn is blocked by a knight on or behind the Troitzky line, the knights have a long theoretical win. There are some other positions when the pawn is past the Troitzky line in which the knights can force checkmate, but the procedure is long and difficult. In either case, in competition the fifty-move rule will often result in the game being drawn first. (While there is a board position that allows two knights to checkmate a lone king, such requires a careless move by the weaker side to execute; he cannot be driven into the corner.)

King and pawn endings

King and pawn endgames involve only kings and pawns on one or both sides. International Master Cecil Purdy said "Pawn endings are to chess as putting is to golf."

In king and pawn endings, an extra pawn is decisive in more than 90 percent of the cases (Euwe & Meiden 1966:xvi). Getting a passed pawn is crucial (a passed pawn is one which does not have an opposing pawn on its file or on adjacent files on its way to promotion). Nimzovich once said that a passed pawn has a "lust to expand". An outside passed pawn is particularly deadly. The point of this is a decoy – while the defending king is preventing it from queening, the attacking king wins pawns on the other side.

Opposition is an important technique that is used to gain an advantage. When two kings are in opposition, they are on the same file (or rank) with an empty square separating them. The player having the move loses the opposition. He must move his king and allow the opponent's king to advance. Note however that the opposition is a means to an end, which is penetration into the enemy position. If the attacker can penetrate without the opposition, he should do so. The tactics of triangulation and zugzwang as well as the theory of corresponding squares are often decisive.

King and pawn versus king

Müller & Lamprecht, diagram 2.11

White to move wins with 1. Kb6. Black to move draws with 1... Kc5.

This is one of the most basic endgames. A draw results if the defending king can reach the square in front of the pawn or the square in front of that (or capture the pawn). If the attacking king can prevent that, the king will assist the pawn in being promoted to a queen or rook, and checkmate can be achieved. A rook pawn is an exception because the king may not be able to get out of the way of its pawn.

Unlike most positions, king and pawn endgames can usually be analyzed to a definite conclusion, given enough skill and time. An error in a king and pawn endgame almost always turns a win into a draw or a draw into a loss – there is little chance for recovery. Accuracy is most important in these endgames. There are three fundamental ideas in these endgames: opposition, triangulation, and the Réti manoeuvre (Nunn 2007:113ff).

Knight and pawn endings

Knight and pawn endgames feature clever maneuvering by the knights to capture opponent pawns. While a knight is poor at chasing a passed pawn, it is the ideal piece to block a passed pawn. Knights cannot lose a tempo, so knight and pawn endgames have much in common with king and pawn endgames. As a result, Mikhail Botvinnik stated that “a knight ending is really a pawn ending.” (Beliavsky & Mikhalchishin 2003:139)

An outside passed pawn can outweigh a protected passed central pawn, unlike king and pawn endgames. A knight blockading a protected passed pawn attacks the protector, while the knight blockading an outside passed pawn is somewhat out of action.

Knight and pawn versus knight

Fine and Benko, diagram 228

White to play wins; Black to play draws

This is generally a draw since the knight can be sacrificed for the pawn, however the king and knight must be covering squares in the pawn's path. If the pawn reaches the seventh rank and is supported by its king and knight, it usually promotes and wins (Fine & Benko 2003:113).

Bishop and pawn endings

Molnar-Nagy, 1966

Bishop and pawns endgame. White to move. White has a good bishop, black a bad one.

Bishop and pawn endgames come in two distinctly different variants. If the opposing bishops go on the same color of square, the mobility of the bishops is a crucial factor. A bad bishop is one that is hemmed in by pawns of its own color, and has the burden of defending them.

The diagram on the right, from Molnar-Nagy, Hungary 1966, illustrates the concepts of good bishop versus bad bishop, opposition, zugzwang, and outside passed pawn. White wins with 1.e6! (vacating e5 for his king) Bxe6 2.Bc2! Bf7 3.Be4! Be8 4.Ke5! Seizing the opposition (i.e. the kings are two orthogonal squares apart, with the other player on move) and placing Black in zugzwang—he must either move his king, allowing White's king to penetrate, or his bishop, allowing a decisive incursion by White's bishop. 4...Bd7 5.Bxg6!

Bishop and pawn versus bishop on the same color

Centurini

Draw

Centurini, 1847

White to move wins

Two rules given by Luigi Centurini in the 19th century apply:

• The game is a draw if the defending king can reach any square in front of the pawn that is opposite in color to the squares the bishops travel on.
• If the defending king is behind the pawn and the attacking king is near the pawn, the defender can draw only if his king is attacking the pawn, he has the opposition, and his bishop can move on two diagonals that each have at least two squares available (other than the square it is on (Fine & Benko 2003:152). This is the case for central pawns and the bishop pawn whose promotion square is not the same color as the bishop (Fine & Benko 2003:154).

The position in the second diagram shows a winning position for White, although it requires accurate play. A knight pawn always wins if the defending bishop only has one long diagonal available (Fine & Benko 2003:155-56).

Portisch vs. Tal, 1965

Position before 67. Bd5!

This position was reached in a game from the 1965 Candidates Tournament between Lajos Portisch and former World Champion Mikhail Tal.^[1] White must defend accurately and utilize reciprocal zugzwang. Often he has only one or two moves that avoid a losing position. Black was unable to make any progress and the game was drawn on move 83 (Nunn 1995:169).

Bishops on opposite colors

White to play, a draw. White wins if the pawn is on f5 instead of e5 (Fine & Benko 2003:184-92).

Endings with bishops of opposite color, meaning that one bishop works on the light squares, the other one working on dark squares, are notorious for their drawish character. Many players in a poor position have saved themselves from a loss by trading down to such an endgame. They are often drawn even when one side has a two pawn advantage since the weaker side can create a blockade on the squares which his bishop operates on. Interestingly, the weaker side should often try to make his bishop bad by placing his pawns on the same color of his bishop in order to defend his remaining pawns, thereby creating an impregnable fortress.

Bishop versus knight endings (with pawns)

Current theory is that bishops are better than knights about 60 percent of the time, in the middlegame and endgame. The more symmetrical the pawns are (i.e. Black's pawns are on the same files as White's pawns), the better it is for the knight. The knight is best suited at an outpost in the center whereas the bishop is strongest when it can attack targets on both sides of the board or a series of squares of the same color (Beliavsky & Mikhalchishin 1995:122).

Fine and Benko (Fine & Benko 2003:205) give four conclusions:

1. In general the bishop is better than the knight.
2. When there is a material advantage, the difference between the bishop and knight is not very important. However, the bishop usually wins more easily than the knight.
3. If the material is even, the position should be drawn. However, the bishop can exploit positional advantages more efficiently.
4. When most of the pawns are on the same color as the bishop (i.e. a bad bishop), the knight is better.

Bishop and pawn versus knight

Müller & Lamprecht, diagram 5.02

White to move wins; Black to move draws

This is a draw if the defending king is in front of the pawn or sufficiently close. The defending king can occupy a square in front of the pawn of the opposite color as the bishop and cannot be driven away. Otherwise the attacker can win (Fine & Benko 2003:206).

Knight and pawn versus bishop

Muller & Lamprecht, diagram 5.23, from Fine, 1941

White to move wins; Black to move draws

This is a draw if the defending king is in front of the pawn or sufficiently near. The bishop is kept on a diagonal that the pawn must cross and the knight cannot both block the bishop and drive the defending king away. Otherwise the attacker can win (Fine & Benko 2003:209).

Rook and pawn endings

Rook and pawn endgames are often drawn in spite of one side having an extra pawn. (In some cases, two extra pawns are not enough to win.) An extra pawn is harder to convert to a win in a rook and pawn endgame than any other type of endgame except a bishop endgame with bishops on opposite colors. Rook endings are probably the deepest and most well studied endgames. They are a common type of endgame in practice, occurring in about 10 percent of all games (including ones that do not reach an endgame) (Emms 2008:7). These endgames occur frequently because rooks are often the last pieces to be exchanged. The ability to play these endgames well is a major factor distinguishing masters from amateurs (Nunn 2007:125). When both sides have two rooks and pawns, the stronger side usually has more winning chances than if each had only one rook (Emms 2008:141).

Three rules of thumb regarding rooks are worth noting:

1. Rooks should almost always be placed behind passed pawns, whether one's own or the opponent's (the Tarrasch rule). A notable exception is in the ending of a rook and pawn versus a rook, if the pawn is not too far advanced. In that case, the best place for the opposing rook is in front of the pawn.
2. Rooks are very poor defenders relative to their attacking strength. So it is often good to sacrifice a pawn for activity.
3. A rook on the seventh rank can wreak mayhem among the opponent's pawns. The power of a rook on the seventh rank is not confined to the endgame. The classic example is Capablanca–Tartakower, New York 1924 (see annotated game without diagrams or Java board)

An important winning position in the rook and pawn versus rook endgame is the so-called Lucena position. If the side with the pawn can reach the Lucena position, he wins. However, there are several important drawing techniques such as the Philidor position, the back rank defense (rook on the first rank, for rook pawns and knight pawns only), the frontal defense, and the short side defense. A general rule is that if the weaker side's king can get to the queening square of the pawn, the game is a draw and otherwise it is a win, but there are many exceptions.

Rook and pawn versus rook

Fine & Benko, diagram 646

White to play wins because of the Lucena position. Black to play draws with 1... Ra8+, either because of perpetual check or winning the pawn.

Generally (but not always), if the defending king can reach the queening square of the pawn the game is a draw (see Philidor position), otherwise the attacker usually wins (if it is not a rook pawn) (see Lucena position) (Fine & Benko 2003:294). The winning procedure can be very difficult and some positions require up to sixty moves to win (Speelman, Tisdall & Wade 1993:7). If the attacking rook is two files from the pawn and the defending king is cut off on the other side, the attacker normally wins (with a few exceptions) (Fine & Benko 2003:294). The rook and pawn versus rook is the most common of the "piece and pawn versus piece" endgames (Nunn 2007:148).

The most difficult case of a rook and pawn versus a rook is when the attacking rook is one file over from the pawn and the defending king is cut off on the other side. Siegbert Tarrasch gave the following rules for this case: "For a player defending against a pawn on the fifth or even sixth ranks to obtain a draw, even after his king has been forced off the queening square, the following conditions must obtain: The file on which the pawn stands divides the board into two unequal parts. The defending rook must stand in the longer part and give checks from the flank at the greatest possible distance from the attacking king. Nothing less than a distance of three files makes it possible for the rook to keep on giving check. Otherwise it would ultimately be attacked by the king. The defending king must stand on the smaller part of the board." See the short side defense at Rook and pawn versus rook endgame.

Quotation

• "All rook and pawn endings are drawn."

The context of this quote shows it is a comment on the fact that a small advantage in a rook and pawn endgame is less likely to be converted into a win. Mark Dvoretsky said that the statement is "semi-joking, semi-serious" (Dvoretsky & Yusupov 2008:159). This quotation has variously been attributed to Savielly Tartakower and to Siegbert Tarrasch. Writers Victor Korchnoi (Korchnoi 2002:29), John Emms (Emms 2008:41), and James Howell (Howell 1997:36) attribute the quote to Tartakower, whereas Dvoretsky (Dvoretsky 2006:158), Andy Soltis (Soltis 2003:52), and Karsten Müller^[2] attribute it to Tarrasch. John Watson attributed to Tarrasch "by legend" and says that statistics do not support the statement (Watson 1998:81-82). Benko wonders if it was due to Vasily Smyslov (Benko 2007:186). Attributing the quote to Tarrasch may be a result of confusion between this quote and the Tarrasch rule concerning rooks. The source of the quote is currently unresolved.^[3] Benko noted that although the saying is usually said with tongue in cheek, it is truer in practice than one might think (Benko 2007:189).

Queen and pawn endings

In Queen and pawn endings, passed pawns have paramount importance, because the queen can escort it to the queening square alone. The advancement of the passed pawn outweighs the number of pawns. The defender must resort to perpetual check. These endings are frequently extremely long affairs. For an example of a Queen and pawn endgame see Kasparov versus The World – Kasparov won although he had fewer pawns because his was more advanced. For the ending with a queen versus a pawn, see Queen versus pawn endgame.

Queen and pawn versus queen

Müller & Lamprecht, diagram 9.12A

White to play wins; Black to play draws

The queen and pawn versus queen endgame is the second most common of the "piece and pawn versus piece" endgames, after rook and pawn versus rook. It is very complicated and difficult to play. Human analysts were not able to make a complete analysis before the advent of endgame tablebases (Nunn 2007:148). This combination is a win less frequently than the equivalent ending with rooks.

According to Fine and Benko, this ending is a draw unless the pawn is a bishop pawn or a central pawn (i.e. king pawn or queen pawn) and the pawn is in the seventh rank and is supported by its king. If the defending king can get in front of the pawn, the game is a draw; otherwise it is best for the defender to keep his king far away from the pawn. The defender should keep checking until he runs out of check, and then pin the pawn (Fine & Benko 2003:538). Based on computer analysis, Müller and Lamprecht give a different description. According to them, normally the defending king needs to be in front of the pawn. A rook pawn or knight pawn is a theoretical draw if the defending king is in front or near the pawn or if the king is in the opposite corner. A knight pawn has more practical winning chances than a rook pawn. A bishop pawn or central pawn is a win if the defending king is not in front of the pawn. A bishop pawn has better winning chances than a central pawn (Müller & Lamprecht 2001:316). John Nunn states that analysis since Fine's initial work (in 1941) has shown that there are many more winning positions than were known at that time (ignoring the fifty-move rule in some cases) (Nunn 2007:148-53,248-49). Wins by the side with the pawn take up to 59 moves (Speelman, Tisdall & Wade 1993:7). A cross-check may be necessary to win, see cross-check#Botvinnik vs. Minev game for an example.

Edmar Mednis gives this breakdown when the defending king is not able to help: (Mednis 1987:126–27,134)

• A bishop pawn is the best pawn to have. It is relatively easy to advance and is a win once it reaches the seventh rank.
• A central pawn wins if it reaches the seventh rank, but it is difficult to get it there. Even if the pawn reaches the sixth rank, the position is usually a draw.
• A knight pawn is relatively easy to get to the seventh rank, but the position may be a theoretical draw.
• Positions with rook pawns are theoretical draws, but in practice it may be difficult to draw.

Rook versus a minor piece

Chéron, 1926

White to play draws; Black to play wins (Müller & lamprecht 2001:273)

The difference in material between a rook and a minor piece is about two points or a little less, the equivalent of two pawns.

• A rook and a pawn versus a minor piece: normally a win for the rook but there are some draws. In particular, if the pawn is on its sixth rank and is a bishop pawn or rook pawn, and the bishop does not control the pawn's promotion square, the position is a draw (de la Villa 2008:221). See wrong bishop.
• A rook versus a minor piece: normally a draw but in some cases the rook wins, see pawnless chess endgame.
• A rook versus a minor piece and one pawn: usually a draw but the rook may win.
• A rook versus a minor piece and two pawns: usually a draw but the minor piece may win.
• A rook versus a minor piece and three pawns: a win for the minor piece.

If both sides have pawns, the result essentially depends on how many pawns the minor piece has for the exchange:

• No pawns for the exchange (i.e. same number of pawns on each side): the rook usually wins.
• One pawn for the exchange (i.e. minor piece has one more pawn): the rook usually wins, but it is technically difficult. If all of the pawns are on one side of the board it is usually a draw.
• Two pawns for the exchange: this is normally a draw. With a bishop either side may have winning chances. With a knight, the rook may have winning chances and the defense is difficult for the knight if the pawns are scattered.
• Three pawns for the exchange: this is normally a win for the minor piece (Fine & Benko 2003:459ff).

Two minor pieces versus a rook

Capablanca-Lasker, 1914^[4]

Black to play draws (Muller & lamprecht 2001:23)

In an endgame, two minor pieces are approximately equivalent to a rook plus one pawn. The pawn structure is important. The two pieces have the advantage if the opponent's pawns are weak. Initiative is more important in this endgame than any other. The general outcome can be broken down by the number of pawns.

• The two pieces have one or more extra pawns: always a win for the pieces.
• Same number of pawns: usually a draw but the two pieces win more often than the rook.
• The rook has one extra pawn: usually a draw but either side may have winning chances, depending on positional factors.
• The rook has two additional pawns: normally a win for the rook (Fine & Benko 2003:449-58).

Queen versus two rooks

Leko-Kramnik, World championship, 2004^[5]

Black to move won

Without pawns this is normally drawn but either side wins in some positions. A queen and pawn are normally equivalent to two rooks, which is usually a draw if both sides have an equal number of additional pawns. Two rooks plus one pawn versus a queen is also generally drawn. Otherwise, if either side has an additional pawn, that side normally wins (Fine & Benko 2003:566-67).

Queen versus rook and minor piece

van Wely-Yusupov, 2000^[6]

Black to move won

If there are no pawns, the position is usually drawn, but either side wins in some positions. A queen is equivalent to a rook and bishop plus one pawn. If the queen has an additional pawn it wins, but with difficulty. A rook and bishop plus two pawns win over a queen (Fine & Benko 2003:563).

Queen versus rook

Philidor, 1777

White wins with either side to move

• Without pawns, the queen normally wins but it can be difficult and there are some drawn positions (see Philidor position#Queen versus rook).
• If the rook has one pawn drawing positions are possible, depending on the pawn and the proximity of the rook and king. See fortress (chess)#Rook and pawn versus queen. Otherwise the queen wins.
• If the rook has two connected pawns the position is usually a draw. For any other two pawns, the queen wins except in the positions where a fortress with one pawn can be reached.
• If the rook has three or more pawns the position is usually a draw but there are cases in which the queen wins and some in which the rook wins.
• If the queen also has a pawn or pawns it wins except in unusual positions (Fine & Benko 2003:570-79).

Piece versus pawns

Johann Berger 1914 (Fine & Benko diagram 1053)

White to play wins. Black wins if his pieces are one rank more advanced (pawns on f3, g3, and h2, king on h3).

There are many cases for a lone piece versus pawns. The position of the pawns is critical.

• Minor piece versus pawns: A minor piece versus one or two pawns is normally a draw, unless the pawns are advanced. Three pawns either draw or win, depending on how advanced they are. Three connected pawns win against a bishop if they all get past their fourth rank (Fine & Benko 2003:93ff,129-30). A knight can draw against three connected pawns if none are beyond their fourth rank (Müller & Lamprecht 2001:62).
• Rook versus pawns: If the rook's king is not near, one pawn draws and two pawns win. If the rook's king is near, the rook wins over one or two pawns and draws against three. Four pawns usually win but the rook may be able to draw, depending on their position. More than four pawns win against the rook (Fine & Benko 2003:275,292-93).
• Queen versus pawns: A queen can win against any number of pawns, depending on how advanced they are. The queen would win against eight pawns on the second rank but a pawn on the seventh rank may draw (see Queen versus pawn endgame) and two advanced pawns may win (Fine & Benko 2003:526ff).

Endings with no pawns

Fine & Benko, diagram 967

White to play wins; Black to play draws

Besides the basic checkmates, there are other endings with no pawns. They do not occur very often in practice. Two of the most common pawnless endgames (when the defense has a piece in addition to the king) are (1) a queen versus a rook and (2) a rook and bishop versus a rook. A queen wins against a rook, see pawnless chess endgame#Queen versus rook. A rook and bishop versus a rook is generally a theoretical draw (see Cochrane Defense), but the defense is difficult and there are winning positions (see Philidor position#Rook and bishop versus bishop).

Positions with a material imbalance

A rook is worth roughly two pawns plus a bishop or a knight. A bishop and knight are worth roughly a rook and a pawn, and a queen is worth a rook, a minor piece (bishop or knight) and a pawn (see chess piece relative value). Three pawns are often enough to win against a minor piece, but two pawns rarely are.

However, with rooks on the board, the bishop often outweighs the pawns. This is because the bishop defends against enemy rook attacks, while the bishop's own rook attacks enemy pawns and reduces the enemy rook to passivity. This relates to Rule 2 with rooks (above).

A bishop is usually worth more than a knight. A bishop is especially valuable when there are pawns on both wings of the board, since it can intercept them quickly.

Effect of tablebases on endgame theory

Endgame tablebases have made some minor corrections to historical endgame analysis, but they have made some more significant changes to endgame theory too. (The fifty-move rule is not taken into account in these studies.) Major changes to endgame theory as a result of tablebases include (Müller & Lamprecht 2001:8,400-406):

• Queen versus rook (see Philidor position#Queen versus rook). There are two changes here enabling the rook to put up a better defense, but the queen still wins. (a) People usually opt for a second-rank defense with the rook on the second rank and the king behind it (or symmetrical positions on the other edges of the board). Tablebases show that a third-rank defense takes a while to breach, which is difficult for a human to do. (b) People had assumed that the rook needs to stay as close to the king for as long as possible, but tablebases show that it is best to move the rook away from the king at some earlier point (Nunn 2002:49ff).
• Queen and pawn versus queen. Tablebases have shown that this can be won in many more positions than was thought, but the logic of the moves is presently beyond human understanding (Nunn 1995:265).
• Queen versus two bishops. This was thought to be a draw due to the existence of a drawing fortress position, but the queen can win most of the time by preventing the bishops from getting to the fortress. However, it can take up to 71 moves to force a win (Nunn 2002:290ff).

This position was thought to be drawn, but White to move wins in this position. Some similar positions are actually drawn (e.g. with the queen on e2).

• Queen versus two knights. This was thought to be a draw and generally it is, but the queen has more winning positions than was previously thought. Also, many analysts gave a position (see diagram) that they thought was a draw but it is actually a win for the queen (Nunn 2002:300ff). In the diagram, White checkmates in 43 moves, starting with 1. Qc7 (the only winning move). Note that Nunn says "The general result is undoubtedly a draw, but there are many losing positions, some of them very lengthy." On the other hand, Batsford Chess Endings states that 89.7 percent of the starting positions are wins for the queen (Speelman, Tisdall & Wade 1993:7). However, these percentages can be misleading, and most "general results" are based on the analysis of grandmasters using the tablebase data (Müller & Lamprecht 2001:406), (Nunn 2002:324). For instance, although nearly 90 percent of all of these positions are wins for the queen, it is generally a draw if the king is not separated from the knights and they are on reasonable squares (Müller & Lamprecht 2001:339).

This position was thought to be drawn (Kling and Horwitz, 1851), but White wins.

• Two bishops versus a knight. This was thought to be a draw but the bishops generally win. However, it takes up to 66 moves. The position in the diagram was thought to be a draw for over one hundred years, but tablebases show that White wins in 45 moves. All of the long wins go through this type of semi-fortress position. It takes several moves to force Black out of the temporary fortress in the corner; then precise play with the bishops prevents Black from forming the temporary fortress in another corner (Nunn 1995:265ff).
• Queen and bishop versus two rooks. This was thought to be a draw but the queen and bishop usually win. It takes up to 84 moves (Nunn 2002:367ff).
• Rook and bishop versus bishop and knight, bishops on opposite colors. This was thought to be a draw but the rook and bishop generally win. It takes up to 98 moves (Nunn 2002:342ff).

Longest forced win

White to move has a forced win, starting with 1. Rg1+ (the only winning move). White wins a rook on move 290. Sixty-eight of the moves are the only move which preserves the win.