Checkers Is Solved

Abstract

The game of checkers has roughly 500 billion billion possible positions (5 x 10(20)). The task of solving the game, determining the final result in a game with no mistakes made by either player, is daunting. Since 1989, almost continuously, dozens of computers have been working on solving checkers, applying state-of-the-art artificial intelligence techniques to the proving process. This paper announces that checkers is now solved: Perfect play by both sides leads to a draw. This is the most challenging popular game to be solved to date, roughly one million times as complex as Connect Four. Artificial intelligence technology has been used to generate strong heuristic-based game-playing programs, such as Deep Blue for chess. Solving a game takes this to the next level by replacing the heuristics with perfection.

Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents

“…Despite multiple successes of search algorithms in artificial intelligence (e.g., Campbell, Hoane, & Hsu, 2002;Schaeffer et al, 2007;Silver et al, 2016), planning in the Arcade Learning Environment remains rare compared to methods that learn policies or value functions (but see the papers by Bellemare, Naddaf, et al, 2013;Guo, Singh, Lee, Lewis, & Wang, 2014;Jinnai & Fukunaga, 2017;Lipovetzky et al, 2015;Shleyfman, Tuisov, & Domshlak, 2016, for published planning results in the ALE). Developing heuristics that are general enough to be successfully applied to dozens of different games is a challenging problem.…”

The Singularity May Be Near

“…Intelligence is not measured as a standalone value, but with respect to the problems it allows to solve. For many problems such as playing checkers [17], it is possible to completely solve the problem (provide an optimal solution after considering all possible options) after which no additional performance improvement would be possible [18]. "…”

Game-Tree Search Using Proof Numbers: The First Twenty Years

“…Examples include earlier detection of terminal positions and reuse of proofs and disproofs for different positions. For example, the standard technique of retrograde analysis can be combined with PNS variants for detecting terminal positions earlier (Schaeffer et al, 2007;Schadd et al, 2008). Müller (2003, 2005b) propose a number of game-specific techniques to statically detect winning and losing shapes in the one-eye and life and death problems in Go.…”

“…To address these shortcomings, many variations of the algorithm have been developed (cf. van den Herik and Winands, 2008), and these variants have been successfully applied to a large number of domains including chess (Breuker, 1998), Othello (Nagai, 2002), shogi (Seo, Iida, and Uiterwijk, 2001;Nagai, 2002), Lines of Action (LOA) (Winands, Uiterwijk, and van den Herik, 2004), Go (Kishimoto and Müller, 2005b), checkers (Schaeffer et al, 2007), Connect6 (Xu et al, 2009;Wu et al, 2011), the multi-player game Rolit , and even chemical synthesis (Heifets and Jurisica, 2012). All PNS variants share two features: (1) they are algorithms for solving binary goals, such as proving a win or a loss in a game position, and (2) they rely on the concept of proof and disproof numbers.…”