We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 30 May 2025
Retrograde analysis has been applied to many problems. It enables to generate databases of positions or databases of patterns. For each possible position or pattern it enables to find the status of the position and other information such as the minimal number of moves required to win in the position. Once generated, databases enable to control, reduce or even replace search.
Retrograde analysis was first used to solve chess endgames [van den Herik and Herschberg 1985; Thompson 1986; Stiller 1996; Thompson 1996] containing up to six pieces. Chess endgame databases enable to play endgames perfectly and even discovered new chess knowledge about endgames [Nunn 1993].
Another successful application of retrograde analysis is the computation of Checkers endgames by Chinook [Lake et al. 1994; Schaeffer 1997] which is an important part of the program that solved Checkers [Schaeffer 2007]. Retrograde analysis has also been used in single player games such as the 16 puzzle. It consisted in computing an admissible heuristics involving only some of the pieces [Culberson and Schaeffer 1998]. Pattern database can also be combined and improve on single pattern databases [Korf and Felner 2002]. Another application of pattern databases is Rubik’s cube [Korf 1997] where separate databases for corner and side cubes can be computed and improve much the admissible heuristic. Pattern databases can also be used for the game of Go, computing for example databases on eyes or on life [Cazenave 1993; Cazenave 1996b; Cazenave 1996a]. Improvements include associating patterns to abstract conditions such as external liberties [Cazenave 2001] and reducing memory requirements using metarules [Cazenave 2003].
Some complex games such as Awari have been completely solved with retrograde analysis [Romein and Bal 2003].
In his thesis [Fraser 2002], Bill Fraser describes the BruteForce program that searches an endgame region in Go to calculate thermographs for every position. It enables his program to find means, temperatures, and orthodox lines of play. Our work is related since we use a brute force approach that takes ko into account, however we simply compute the values of positions and not the associated thermograph. Moreover we deal with long loops in the game graph, long loops only very rarely occur in Go positions.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
