Retrograde analysis

Retrograde analysis is a technique employed by chess problem solvers 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.

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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.

Related Topics:
Castling - En passant - Pawn

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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 are proof game problems.

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An example of a retrograde analysis problem is shown above. The solver must deduce White's last move. At first blush, there seems to be no solution: on any square from which the white king could have moved, it would have been under a seemingly impossible double check. However, thinking more we can discover that if white king moved from f5, then the black move before that could be pawn f4xg3, taking the white pawn on g4 en passant! Thus before f4xg3, white must have played pawn g2-g4. But what did Black move before that? The white king on f5 was under check by the bishop on h3 and there was a white pawn on g2. The only possibility is that black moved knight g4-e5 with discovered check. Therefore White's last move was king f5 takes knight on e5. (The entire sequence of moves is thus 1...Ng4-e5 discovered check 2.g2-g4 f4xg3 double check 3.Kf5xe5.)

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