In the game of

chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...

, an endgame study, or just study, is a composed position—that is, one that has been made up rather than played in an actual game—presented as a sort of puzzle, in which the aim of the solver is to find the essentially unique way for one side (usually White) to win or draw, as stipulated, against any moves the other side plays. If the study does not end in a mate or stalemate, it should be obvious that the game is either won or drawn, and White can have a selection of many different moves. There is no limit to the number of moves which are allowed to achieve the win; this distinguishes studies from the genre of direct mate problems (e.g. "mate in 2"). Such problems also differ qualitatively from the very common genre of tactical puzzles based around the middlegame, often based on an actual game, where a decisive tactic must be found.

Composed studies

Composed studies predate the modern form of chess.

Shatranj Shatranj ( ar, شطرنج; fa, شترنج; from Middle Persian ''chatrang'' ) is an old form of chess, as played in the Sasanian Empire. Its origins are in the Indian game of chaturaṅga. Modern chess gradually developed from this game, as ...

studies exist in manuscripts from the 9th century, and the earliest treatises on modern chess by the likes of

Luis Ramirez Lucena Luis is a given name. It is the Spanish form of the originally Germanic name or . Other Iberian Romance languages have comparable forms: (with an accent mark on the i) in Portuguese and Galician, in Aragonese and Catalan, while is archaic ...

and

Pedro Damiano Pedro Damiano ( pt, Pedro Damião; ''Damiano'' is the Italian form, much like the Latin ''Damianus''; 1480–1544) was a Portuguese chess player. A native of Odemira, he was a pharmacist by profession. He wrote ''Questo libro e da imparare gio ...

(late 15th and early 16th century) also include studies. However, these studies often include superfluous pieces, added to make the position look more "game-like", but which take no part in the actual solution (something that is never done in the modern study). Various names were given to these positions (Damiano, for example, called them "subtleties"); the first book which called them "studies" appears to be ''Chess Studies'', an 1851 publication by

Josef Kling Josef Kling (19 March 1811 – 1 December 1876), also found in English-language sources as Joseph Kling, was a German chess master and chess composer. He has been called "a pioneer of the modern style of chess." Although Kling was an expert on e ...

and

Bernhard Horwitz Bernhard Horwitz (1807 in Neustrelitz – 1885 in London) was a German and British chess master, chess writer and chess composer. Horwitz was born in Neustrelitz and went to school in Berlin, where he studied art. From 1837 to 1843, he was par ...

, which is sometimes also regarded as the starting point for the modern endgame study. The form is considered to have been raised to an art in the late 19th century, with

A. A. Troitsky Alexey Alexeyevich Troitsky (russian: Алексе́й Алексе́евич Тро́ицкий; March 14, 1866 – August 1942; also ''Alexei'', ''Troitzky'', ''Troitzki'') was a Russian chess theoretician. He is widely considered to have ...

and

Henri Rinck Henri Rinck (January 10, 1870 – February 17, 1952) was a French chess study composer, considered one of the most important early figures in the field. Biography Henri Rinck was born in Lyon (France) on January 10, 1870, where his family wer ...

particularly important in this respect. Most

composers A composer is a person who writes music. The term is especially used to indicate composers of Western classical music, or those who are composers by occupation. Many composers are, or were, also skilled performers of music. Etymology and Defi ...

, including Troitsky, Rinck, and other famous figures such as

Genrikh Kasparyan Genrikh Kasparyan ( hy, Հենրիկ Գասպարյան; 27 February 1910 in Tbilisi – 27 December 1995 in Yerevan) was a Soviet chess player. He is considered to have been one of the greatest composers of chess endgame studies. Outside Arme ...

, are known primarily for their studies, being little known as players. However, some famous players have also composed endgame studies, with

Emanuel Lasker Emanuel Lasker (; December 24, 1868 – January 11, 1941) was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years, from 1894 to 1921, the longest reign of any officially recognised World Chess Champ ...

Richard Réti Richard Selig Réti (28 May 1889 – 6 June 1929) was an Austro-Hungarian, later Czechoslovakian, chess player, chess author, and composer of endgame studies. He was one of the principal proponents of hypermodernism in chess. With the exce ...

Vasily Smyslov Vasily Vasilyevich Smyslov ( rus, Васи́лий Васи́льевич Смысло́в, Vasíliy Vasíl'yevich Smyslóv; 24 March 1921 – 27 March 2010) was a Soviet and Russian chess grandmaster, who was World Chess Champion from 1957 to ...

, and

Jan Timman Jan Timman (born 14 December 1951) is a Dutch chess grandmaster who was one of the world's leading chess players from the late 1970s to the early 1990s. At the peak of his career, he was considered to be the best non-Soviet player and was known a ...

being perhaps the most notable ones.

Examples

's study is one of the most famous of all time. It is White to play and draw. At first sight, this seems an impossible task: if White tries to chase after Black's pawn he can never catch it (1.Kh7 h4 2.Kh6 h3 etc. is clearly hopeless), while it is clear that Black will simply take White's pawn if he tries to promote it. White can draw, however, by taking advantage of the fact that the king can move towards both pawns at once. The solution is 1. Kg7 h4 (1...Kb6 2. Kf6! h4 3.Ke5! transposes) 2. Kf6! Kb6 (if 2...h3, then 3.Ke6 h2 4.c7 Kb7 5.Kd7 allows white to promote his pawn) 3. Ke5! Now, if 3...Kxc6, then 4.Kf4 stops Black's pawn after all, while if 3...h3 4.Kd6 allows White to promote his pawn. Either way, the result is a draw. (Also see

King and pawn versus king endgame The chess endgame with a king and a pawn versus a king is one of the most important and fundamental endgames, other than the basic checkmates. It is an important endgame for chess players to master, since most other endgames have the potential of ...

, the section Rule of the square.) Not all studies are as simple as the above Réti example. This study (first diagram) is by

(first published in ''Magyar Sakkélet'', 1962). White is to play and draw. The main line of the solution is 1. Ra1 a2 2. Ke6 Ba3 3. Bf4 Bb2 4. Be5 a3 5. Kd5 Bg6 6. Bd4 Bf7+ 7. Ke4 Bc4 8. Rg1, but there are various alternatives for both sides. For example, White could try 1.Bf4 on his first move, with the idea 1...Bxa2 2.Bxd6 and 3.Bxa3 is a draw, but Black can defeat this idea with 1...Bxf4 2.Rxa3 Bc2, which wins. To understand why one move works and another one does not, requires quite advanced chess knowledge. Indeed, it will not be obvious to many players that the position at the end of the given line (second diagram) is a draw at all. One of the most notable studies is

Leopold Mitrofanov Leopold Adamovich Mitrofanov (July 2, 1932November 26, 1992) was a Russian chess composer, an International Judge of Chess Composition (awarded 1971) and an International Master of Chess Composition (awarded 1980). He was born in Leningrad (now St. ...

's 1967 first-prize winner. Unfortunately, Mitrofanov's original study was subsequently found to have a , a miraculous defense that enabled Black either to obtain

perpetual check In the game of chess, perpetual check is a situation in which one player can a draw by an unending series of checks. This typically arises when the player who is checking cannot deliver checkmate, and failing to continue the series of checks giv ...

or reach a

drawn Draw, drawing, draws, or drawn may refer to: Common uses * Draw (terrain), a terrain feature formed by two parallel ridges or spurs with low ground in between them * Drawing (manufacturing), a process where metal, glass, or plastic or anything ...

ending End, END, Ending, or variation, may refer to: End *In mathematics: **End (category theory) **End (topology) **End (graph theory) ** End (group theory) (a subcase of the previous) **End (endomorphism) *In sports and games **End (gridiron football) ...

. Solution: 1. b6+ Ka8 2. Re1! Nxe1 3. g7 h1=Q (if 3...Nc4+ then 4.Kb5 h1=Q 5.g8=Q+ Bb8 6.a7 Na3+ 7.Kc6 Qh2 8.axb8=Q+ Qxb8 9.b7+ Ka7 10.Qg1+ Ka6 11.Qb6 mate) 4. g8=Q+ Bb8 5. a7 Nc6+ 6. dxc6 Qxh5+ 7. Qg5 (not 7.Ka6 Qe2+ or 7.Kb4? Qh4+ with perpetual check) Qxg5+ 8. Ka6 (the queen is deflected from the white diagonal where she could give check) 8... Bxa7 (or 8...Qb5+ 9.Kxb5 Nc2 10.c7 and wins) 9. c7! (a silent move; the double threat c8=Q+ and b7 mate forces Black to sacrifice the queen) 9... Qa5+ 10. Kxa5 Kb7 11. bxa7 and White wins.

Early example

Most old

shatranj Shatranj ( ar, شطرنج; fa, شترنج; from Middle Persian ''chatrang'' ) is an old form of chess, as played in the Sasanian Empire. Its origins are in the Indian game of chaturaṅga. Modern chess gradually developed from this game, as ...

studies are not valid in modern chess because of changed rules. However, the moves of the king, rook, and knight are unchanged. In this Arabic study White wins because the black knight is poorly placed. With White to move the best move is 1. Rd1, but it is not the only winning move. If Black is to move, 1... Kb8! 2. Kc6! Na5+! 3. Kb6! Nc4+ 4. Kb5! Ne5 5. Re1! Nd7 6. Kc6! wins.

Studies and special moves

The special moves or rules of chess, such as castling, underpromotion, double-square pawn advance, and ''

en passant ''En passant'' (, "in passing") is a method of capturing in chess that occurs when a pawn captures a horizontally adjacent enemy pawn that has just made an initial two-square advance. The capturing pawn moves to the square that the enemy pa ...

'' are commonly a key feature of studies, as are

sacrifices Sacrifice is the offering of material possessions or the lives of animals or humans to a deity as an act of propitiation or worship. Evidence of ritual animal sacrifice has been seen at least since ancient Hebrews and Greeks, and possibly exi ...

Castling

Castling in the

endgame Endgame, Endgames, End Game, End Games, or similar variations may refer to: Film * ''The End of the Game'' (1919 film) * ''The End of the Game'' (1975 film), short documentary U.S. film * ''Endgame'' (1983 film), 1983 Italian post-apocalyptic f ...

occurs seldom and is more often seen in studies. Here is one example where White wins by privilege of castling rights. : 1.0-0-0? Ra2! 2.d7 Ra1+ 3.Kc2 Rxd1 4.Kxd1 Kc7 drawn. White needs: 1. d7! Kc7 2. d8=Q+! Kxd8 3. 0-0-0+ simultaneously attacking the

king King is the title given to a male monarch in a variety of contexts. The female equivalent is queen, which title is also given to the consort of a king. *In the context of prehistory, antiquity and contemporary indigenous peoples, the ...

and

rook Rook (''Corvus frugilegus'') is a bird of the corvid family. Rook or rooks may also refer to: Games *Rook (chess), a piece in chess * Rook (card game), a trick-taking card game Military * Sukhoi Su-25 or Rook, a close air support aircraft * US ...

that is captured next move.

Study engineering

With the creation and popularization of chess-playing computer software programs, a number of which have achieved

Elo ratings The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor. The Elo system was invented as an improved ch ...

higher than top human players, many composers collaborate with them both in composing and solving compositions. Though proven to be helpful, positions have been found which cause even the strongest engines to incorrectly evaluate the outcome. Chess master

Frédéric Lazard Frédéric Lazard (20 February 1883, in Marseille – 18 November 1948, in Le Vésinet) was a French chess master, problemist and journalist. He lived in Paris, where he played in many local tournaments. He took twice 4th place in 1905, shared 3r ...

's 1946 composition is White to play and draw. As of early 2021, top chess engines such as

Stockfish Stockfish is unsalted fish, especially cod, dried by cold air and wind on wooden racks (which are called "hjell" in Norway) on the foreshore. The drying of food is the world's oldest known preservation method, and dried fish has a storage l ...

evaluate the position as clearly won for Black. Solution: 1. Ne4+ Kh4 (1...dxe4 2.Be1#) 2. Ng3! Qf8 (2...fxg3 3.Bb6) 3. Be1 fxg3 4. Bf2! d4 (4...Qxf2 stalemate, 4...gxf2 5.g3+ Kh3 stalemate) 5. Bxd4 c5 6. Bxc5 Qf1+ 7. Bg1 Qf2 8. Bxf2 gxf2 9. g3+ Kxg3 drawn.

References

External links

ARVES biographical data on composers

Handbook of Chess Composition
{{Chess, state=collapsed Chess endgames Chess problems