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 (usually White) to win or draw, as stipulated, against any moves the other side plays.
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.
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 (late 15th and early 16th century) also include studies.
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.
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.
White can draw, however, by taking advantage of the fact that the king can move towards both pawns at once.
This study (first diagram) is by Genrikh Kasparyan (first published in Magyar Sakkélet, 1962).
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.
[1] Unfortunately, Mitrofanov's original study was subsequently found to have a cook, a miraculous defense that enabled Black either to obtain perpetual check or reach a drawn ending.
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.
Most old shatranj studies are not valid in modern chess because of changed rules.
In this Arabic study White wins because the black knight is poorly placed.
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.
With the creation and popularization of chess-playing computer software programs, many of which have achieved Elo ratings significantly 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.
and black cannot advance his pawns as the bishop will take them; if he recaptures it is stalemate.