In chess, 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 quite different characteristics from the middlegame, and the players have quite different strategical 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 centre 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.

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

Contents 1 Common types of endgames 1.1 Basic checkmates 1.2 King and pawn 1.3 Knight and pawn 1.4 Bishop and pawn 1.5 Rook and pawn 1.6 Queen and pawn 1.7 Asymmetric positions 1.8 Endings with no pawns 1.8.1 Fine's rule 1.8.2 General remarks on these endings 2 Longest forced win 3 General 4 Books on endgames 5 See also 6 External links

Common types of endgames

Basic checkmates

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. A queen or a rook can easily checkmate a lone king. See Wikibooks - Chess/The Endgame for a demonstration of these two mates. Two bishops can easily checkmate a lone king (provided the bishops move on opposite colour squares). A bishop and knight 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, 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 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 usually result in the game being drawn first.

King and pawn

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

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.

See King and pawn versus king for the important ending of a king and pawn versus a king.

Knight and pawn

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 can't lose a tempo, so knight and pawn endgames have much in common with king and pawn endgames. An outside passed pawn can outweigh a central protected passed 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.

Bishop and pawn

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.

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.

The diagram on the right, from Molnar-Nagy, Hungary 1966, illustrates the concepts of good bishop vs. bad bishop, opposition, zugzwang, and outside passed pawn. White wins with 1. e6! Bxe6 2. Bc2 Bf7 3. Be4 Be8 4. Ke5 Bd7 5. Bxg6! (See algebraic chess notation.)

Rook and pawn

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. The great master Tartakower once jocularly said "All rook and pawn endings are drawn". Rook endings are probably the deepest and most well studied endgames. They are the second most common type of endgame in practice, behind rook and minor piece versus rook and minor piece (with pawns).

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).
2. Rooks are very poor defenders relative to their attacking strength. So it is often good to sacrifice a pawn for activity. This is especially so in the following case
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 script board)

An important winning position in the endgame of a rook and pawn versus a rook 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.

Queen and pawn

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.

Asymmetric positions

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. 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.

Endings with no pawns

Besides the basic checkmates, there are other endings with no pawns. Some of the more common ones follow.

A queen wins against a rook, but the third rank defense by the rook(see the diagram) is difficult for a person to crack, unless he knows how. (In the third rank defense, 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.)

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 (see diagram). Another position is more artificial: the queen's king is on a1 confined by Ba3 and Nc3 protected by their king.

A queen generally has a theoretical win against two bishops, but many ordinary positions require up to 71 moves (a draw can be claimed after 50 moved under the rules of competition, see fifty move rule); and there is one drawing fortress position for the two bishops.

Two knights can generally draw against a queen by setting up a fortress (see the diagram).

A rook versus a minor piece (bishop or knight) is generally a draw. A rook plus a minor piece versus a rook is usually a draw; as is a queen and a minor piece versus a queen. A queen versus a rook and a minor piece is generally a draw. Of course, there are positions that are exceptions to these general rules.

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. 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. In 2005, a computer was used to prove that four knights win against a queen (number of moves?). This was the first ending with seven pieces that was completely solved.

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!). The number of moves given are the number of moves to convert the endgame to a simpler endgame (or checkmate), and are from Fundamental Chess Endings, by Müller and Lamprecht; and Secrets of Pawnless Endings, by John Nunn. Rook and two bishops v rook and one bishop is winning more frequently than most books think, because the attacker's king can advance on the opposite colored square from the defender's bishop.

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.

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. The only one of them that occurs with any frequency is the queen versus a rook. Therefore a person studying endgames should concentrate more on endings with pawns (after learning the basic checkmates with a queen and with a rook).

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 50 moves long, some positions can be won within the 50 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 on-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.

Longest forced win

In October 2005, Marc Bourzutschky and Yakov Konoval announced that a position in the ending of a king, two rooks and a knight versus a king and two rooks requires 290 moves to convert to a winning endgame (and six more moves to checkmate). This type of ending is thought to be a draw in general. The old record was 243 moves from a position in a rook and knight versus two knights endgame, discovered by Lewis Stiller in 1991. (Endings of a rook and knight versus two knights are generally draws.) The fifty move rule is ignored in these endgames.

General

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 sould usually try to exchange pieces but avoid the exchange of pawns. 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.

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 a tablebase). A program which incorporates knowledge from such a database is able to play perfect chess on reaching any position in the database.

Pieces	Percentage
Rook & minor piece vs. rook & minor piece	15.13
Rook versus rook