In the game of chess, 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 to win or draw, as stipulated, against any moves the other side plays. 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. 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 studies exist in manuscripts from the 9th century, and the earliest treatises on modern chess by the likes of Luis Ramirez Lucena and Pedro Damiano 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. Various names were given to these positions ; the first book which called them "studies" appears to be Chess Studies, an 1851 publication by Josef Kling and Bernhard Horwitz, 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 and Henri Rinck particularly important in this respect. Most composers, including Troitsky, Rinck, and other famous figures such as Genrikh Kasparyan, are known primarily for their studies, being little known as players. However, some famous players have also composed endgame studies, with Emanuel Lasker, Richard Réti, Vasily Smyslov, and Jan Timman 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, 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 in two directions at once: towards Black's pawn and towards White's own. The solution is 1. Kg7 h42. Kf6! Kb63. 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. Not all studies are as simple as the above Réti example. This study is by Genrikh Kasparyan. 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 is a draw at all. One of the most notable studies is Leopold Mitrofanov'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 or reach a drawnending. Solution: 1. b6+ Ka8 2. Re1! Nxe1 3. g7 h1=Q4. g8=Q+ Bb8 5. a7 Nc6+ 6. dxc6 Qxh5+8... Bxa79. c7!9... Qa5+ 10. Kxa5 Kb7 11. bxa7 and White wins.
Early example
Most old shatranj 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 are commonly a key feature of studies, as are sacrifices.
Castling
Castling in the endgame occurs seldom and is more often seen in studies. Here is one example where White wins by privilege of castling rights. White needs: 1. d7! Kc7 2. d8=Q! Kxd8 3. 0-0-0+ simultaneously attacking the king and rook 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 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's 1946 composition is White to play and draw. Top chess engines, such as Stockfish, evaluate the position as clearly won for Black. Solution: 1. Ne4+ Kh42. Ng3! Qf83. Be1 fxg3 4. Bf2! d45. Bxd4 c5 6. Bxc5 Qf1+ 7. Bg1 Qf2 8. Bxf2 gxf2 9. g3+ Kxg3 drawn.
