Retrograde analysis in chess

Retrograde analysis is the art of reasoning backwards in chess. Instead of asking “what is the best move?”, you look at a position and work out what must already have happened: which moves were played, what was captured, and in what order.

What is retrograde analysis?

Every chess position is the end of a story. Pieces cannot jump over each other (except the knight), pawns never move backwards, and a captured piece never returns. Because the rules are so strict, a position often holds enough evidence to rebuild part of the game that produced it. Reconstructing that history is called retrograde analysis, usually shortened to retro analysis or just retro.

In over-the-board play it hardly matters how a position arose. In chess problems it is the whole point. Retro problems are a long-standing branch of chess composition, and they reached a wide audience through the logician Raymond Smullyan, whose books The Chess Mysteries of Sherlock Holmes and The Chess Mysteries of the Arabian Knights turn retro puzzles into detective stories.

The clues retro solvers use

• Material. Count the pieces. Every missing piece was captured, and every capture was made by a piece of the other colour. Sixteen pieces per side at the start means the count is always exact.
• Pawn files. A pawn can only change file by capturing. A pawn on a different file from where it started, or two pawns on the same file, proves that captures happened, and tells you how many.
• Bishops and square colours. A bishop stays on its colour forever. A light-squared bishop on a dark square must be a promoted piece.
• Pieces that cannot have left. A bishop behind its own unmoved pawns has never moved. A rook boxed in by its own king and pawns has not moved either.
• Kings. A king away from its home square walked there one square per move, and never through a square that was attacked at the time.
• Checks. Only one side can be in check, and the check must come from the last move. A double check can only arise in certain ways, which often pins down the last move exactly.
• Tempo. If a side needed fewer moves than it actually played, the spare moves went somewhere. A piece that went out and came back is the classic answer.

Worked example: the queen that came home

From the starting position, White and Black have each played exactly three moves, and this is the result:

Read the evidence. White is missing the e-pawn and has a knight on c3. Black is missing the d-pawn, and at first sight nothing else of Black’s has moved.

Count the captures. Both sides lost a pawn, so there were two captures: one by White, one by Black.

Find the capturers. The only white piece that can capture a pawn without leaving a trace is the e-pawn itself: it took on d5. Then a black piece captured that pawn on d5, and it must be a piece that is now back home, because Black has nothing standing on d5. The queen is the only black piece that can reach d5 and return to d8 in time.

1. e4 d5 2. exd5 Qxd5 3. Nc3 Qd8

The queen on d8 looks as if it never moved, but it went out, captured and returned. That is the essential retro trick: the position hides moves that left no visible mark.

Tempo: the moves you cannot see

Here is a puzzle with no diagram, because the answer is the starting position itself. After two moves by each side the board looks exactly like the start. What was played? Both sides had to spend two moves without changing anything, so each side moved a knight out and back:

1. Nf3 Nf6 2. Ng1 Ng8

(Other knight moves work too, which is why a good retro problem must be built so that only one sequence fits.) Tempo reasoning, asking “where did the spare moves go?”, solves a large share of retro problems.

Types of retro problems

• Proof games. Find a game that reaches a given position in a given number of moves. When the number is the smallest possible, it is a shortest proof game. Read more in What is a proof game?
• Last-move problems. “What was the last move?” The position allows exactly one legal last move, and you have to prove which.
• Legality problems. Is this position reachable at all? Or which piece, added to the board, would make it legal?
• Castling and en passant problems. Can White still castle? Is an en passant capture possible right now? Both depend on history, not on the position alone.
• Retractors. You take moves back instead of playing them forward, then usually deliver mate.

Conventions: castling and en passant

Because the right to castle and the right to capture en passant depend on the past, retro composers follow agreed conventions. Castling is assumed to be allowed unless it can be proved that the king or rook has moved. An en passant capture is allowed only if it can be proved that the last move was the two-square pawn advance. Many of the most elegant retro problems turn on exactly these two rules.

Retrograde analysis in computer chess

The same name is used for a different technique in chess programming. Endgame tablebases, which know the perfect result of every position with a few pieces, are built by retrograde analysis: the program starts from every checkmate and works backwards, move by move, to label every position as a win, draw or loss. The idea is the same, reasoning from the end back to the beginning, but here a computer does it for every position at once.

A step-by-step method

1. Compare the position with the starting position and list everything that changed.
2. Count the missing pieces on both sides: that is the number of captures.
3. For each capture, find which enemy piece could have made it, and when.
4. Count how many moves the visible changes need, and compare with the moves available. Spare moves are hidden somewhere.
5. Use checks and pins to fix the order.

A longer version with common traps is in How to solve retro chess puzzles.

Practise every day

Three Moves Ago is a free daily retrograde analysis puzzle: you get a target position and have to find the three moves each side played to reach it. Browse all past cases, or start with today’s.

Frequently asked questions