Retrograde analysis
Encyclopedia
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 tablebase
s. 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" http://chessproblem.net/download/file.php?id=61.
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.
! 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.)
Note that in this example the actual next move is essentially irrelevant; Black has a choice of several relatively trivial ways of delivering instant checkmate
. (E.g. f3-d5#, d6-d5#, etc.).
One might ask: "If the white pawn was on g2 from the start of the game, how could the Black Queen come to be on f3, also a Black Bishop to be on h3? Is this problem valid?" The problem is indeed valid. The initial position has to be legal, but not particularly reasonable. That the Black Queen and Bishop were en prise in the initial position may be disappointing to some, it does not invalidate the problem.
. It is impossible to determine exactly what Black's last move actually was, so the solution has two lines:
Endgame tablebase
An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of a chess endgame position. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played.The tablebase...
s. In game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
at large, this method is called backward induction
Backward induction
Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions. It proceeds by first considering the last time a decision might be made and choosing what to do in any situation at that time. Using this...
. 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
Chess problem
A chess problem, also called a chess composition, is a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved. For instance, a position might be given with the instruction that White is to move first, and checkmate Black in two...
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" http://chessproblem.net/download/file.php?id=61.
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
Castling
Castling is a special move in the game of chess involving the king and either of the original rooks of the same color. It is the only move in chess in which a player moves two pieces at the same time. Castling consists of moving the king two squares towards a rook on the player's first rank, then...
is disallowed or an en passant
En passant
En passant is a move in the board game of chess . It is a special pawn capture which can occur immediately after a player moves a pawn two squares forward from its starting position, and an enemy pawn could have captured it had it moved only one square forward...
pawn
Pawn (chess)
The pawn is the most numerous and weakest piece in the game of chess, historically representing infantry, or more particularly armed peasants or pikemen. Each player begins the game with eight pawns, one on each square of the rank immediately in front of the other pieces...
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.
Example
An example of a retrograde analysis problem is shown at right. 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 passantEn passant
En passant is a move in the board game of chess . It is a special pawn capture which can occur immediately after a player moves a pawn two squares forward from its starting position, and an enemy pawn could have captured it had it moved only one square forward...
! 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.)
Note that in this example the actual next move is essentially irrelevant; Black has a choice of several relatively trivial ways of delivering instant checkmate
Checkmate
Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...
. (E.g. f3-d5#, d6-d5#, etc.).
One might ask: "If the white pawn was on g2 from the start of the game, how could the Black Queen come to be on f3, also a Black Bishop to be on h3? Is this problem valid?" The problem is indeed valid. The initial position has to be legal, but not particularly reasonable. That the Black Queen and Bishop were en prise in the initial position may be disappointing to some, it does not invalidate the problem.
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 left 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 passantEn passant
En passant is a move in the board game of chess . It is a special pawn capture which can occur immediately after a player moves a pawn two squares forward from its starting position, and an enemy pawn could have captured it had it moved only one square forward...
. It is impossible to determine exactly what Black's last move actually was, so the solution has two lines:
- 1.Ke6 and 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)
External links
- The Retrograde Analysis Corner at Janko.at