Proof Game

A proof game is a type of retrograde analysis chess problem. The solver must construct a game starting from the initial chess position, which ends with a given position (thus proving that that position is reachable) after a specified number of moves. A proof game is called a shortest proof game if no shorter solution exists. In this case the task is simply to construct the shortest possible game ending with the given position.

When published, shortest proof games will normally present the solver with a diagram - which is the final position to be reached - and a caption such as "SPG in 9.0". "SPG" here is short for "shortest proof game" and the "9.0" indicates how many moves must be played to reach the position; 9.0 means the position is reached after black's ninth move, 7.5 would mean the position is reached after seven and a half moves (that is, after white's eighth move) and so on. Sometimes the caption may be more verbose, for example "Position after white's seventh move. How did the game go?".

Most published SPGs will have only one solution: not only must the moves in the solution be unique, their order must also be unique. They can present quite a strong challenge to the solver, especially as assumptions which might be made from a glance at the initial position often turn out to be incorrect. For example, a piece apparently standing on its initial square may turn out to actually be a promoted pawn (this is known as the Pronkin theme). There are some proofgames which have more than one solution, and the number of solutions is then given in the stipulation. The majority of SPGs have a solution from about six to about thirty moves, although examples with unique solutions more than fifty moves long have been devised.

A number of chess problem composers have specialised in SPGs, with one of the most notable examples being Michel Caillaud who did much to popularise the genre in the 1970s and 1980s.