Retrograde Analysis

In chess, retrograde analysis is a computational method used to solve game positions for optimal play by working backward from known outcomes (e.g. checkmate), such as the construction of endgame tablebases. In game theory at large, this method is called backward induction. For most games, retrograde analysis is only feasible in late game situations of reduced complexity, such as a chess position where few pieces remain in play.

Among chess problem solvers, retrograde analysis is a technique employed to determine which moves were played leading up to a given position. While this technique is rarely needed for solving ordinary chess problems, there is a whole sub-genre of chess problems in which it is an important part; such problems are known as retros. An example with full analysis is available in Thomas Volet's "An Introduction to Retroanalytic Inference" .

Retros may ask, for example, for a mate in two, but the main puzzle (at least in modern retros) is in explaining the history of the position. This may be important to determine, for example, if castling is disallowed or an en passant pawn capture is possible. Other problems may ask specific questions relating to the history of the position such as "is the bishop on c1 promoted?". This is essentially a matter of logical reasoning, with high appeal for puzzle enthusiasts.

Sometimes it is necessary to determine if a particular position is legal, with "legal" meaning that it could be reached by a series of legal moves, no matter how bad. Another important branch of retrograde analysis problems is proof game problems.