Retrograde analysis is a technique employed by chess problem solvers to determine which moves were played leading up to a given position. In most problems, this technique is not required, but there is a whole genre of problems in which it is an important part; such problems are known as retros.
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 are proof game problems.
Above an example of retrograde analysis problem is shown. The problem asks to find out the last move white just made. At first glance it seems to be impossible to find a position from which white king could have been moved. In each position it would be under double check. However thinking more we can discover that if white king moved f5-e5, then black move before that could be pawn f4xg3, taking white pawn on g4 en passant! Thus before pawn f4xg4, white must have played pawn g2-g4. But how black moved before that? The white king on f5 was under check by 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 the last move by white was king f5xe5, capturing this black knight.
Partial retrograde analysis
Some problems use a method called "partial retrograde analysis" (PRA). In these, the history of a position cannot be determined with certainty, but each of the alternative histories demands a different solution. The problem to the right by W. Langstaff (from Chess Amateur 1922) is a relatively simple example; it is a mate in two. It is impossible to determine what move Black played last, but it is clear that he must have either moved the king or rook, or else played g7-g5 (g6-g5 is impossible, since the pawn would have been giving check). Therefore, either Black cannot castle, or White can capture on g6 en passant. It is impossible to determine exactly what Black´s last move actually was, so the solution has two lines:
- 1.Ke6 any 2.Rd8# (if Black moved the king or rook)
- 1.hxg6 e.p. (threat: 2.Rd8#) 1...O-O 2.h7# (if Black played g7-g5)
References
Raymond M. Smullyan wrote two well-received retrograde analysis riddle books:
- The Chess Mysteries of Sherlock Holmes, ISBN 0812923898
- The Chess Mysteries of the Arabian Knights, ISBN 0-394-74869-7
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