Othello is Solved

Abstract: The game of Othello is one of the world's most complex and popular games that has yet to be computationally solved. Othello has roughly ten octodecillion (10 to the 58th power) possible game records and ten octillion (10 to the 28th power) possible game positions. The challenge of solving Othello, determining the outcome of a game with no mistake made by either player, has long been a grand challenge in computer science. This paper announces a significant milestone: Othello is now solved. It is computationally proved that perfect play by both players lead to a draw. Strong Othello software has long been built using heuristically designed search techniques. Solving a game provides a solution that enables the software to play the game perfectly.

• The paper announces that the game of Othello has been weakly solved, demonstrating that perfect play from both sides results in a draw.
• A weak solution was achieved using a sophisticated alpha-beta search algorithm with modified Edax software, requiring monumental computational resources to verify.
• This achievement advances the field of game-solving AI, proving that complex games with vast search spaces can be weakly solved, and provides methods applicable to other games.

Solving the Game of Othello

The paper "Othello is Solved" by Hiroki Takizawa presents a significant advancement in the field of artificial intelligence and computational game theory, asserting that Othello, a complex and globally popular board game, has been computationally solved. This work confirms that perfect play by both players in Othello results in a draw, marking a historical leap in solving strategic board games. The intricacy of Othello is underscored by its immense search space, with approximately $10^{58}$ possible game records and $10^{28}$ possible game positions. Despite these overwhelming possibilities, the authors successfully achieved a weak solution for Othello, providing insights into both computational strategies and Othello’s game-theoretic properties.

The paper delineates the process of categorizing solved games—ultra-weakly, weakly, and strongly solved—and situates Othello in the weakly solved category. Unlike a strong solution, which would involve computing outcomes for all potential board states, a weak solution allows for accurate predictions from the initial game state under perfect play. This solution was achieved using a sophisticated search algorithm combined with the alpha-beta search method, significantly refining search efficiency compared to precedent heuristic-based approaches.

In tackling this formidable challenge, Takizawa employed modified existing Othello software, particularly Edax, which is backed by alpha-beta search algorithms. The paper explains various algorithm refinements necessary for thorough exploration and efficient problem-solving, including adjustments in iterative deepening and move ordering. The modifications ensured Edax’s performance was optimized for handling large search depths and computational demand specific to solving Othello.

Numerical results demonstrate the monumental computational efforts involved in the solving process. Approximately 1.5 billion positions with 36 empty squares were solved to verify the solution with high certainty, involving a computational expense of roughly $1.5 \times 10^{18}$ positions. This vast computational endeavor was supported by a supercomputer cluster, equipped with hardware enabling precise calculations, such as CPUs featuring ECC memory. Such provisions minimized errors and bolstered confidence in the results.

The implications of this study extend beyond its immediate findings. Successfully solving Othello contributes significantly to our understanding of strategic games and computational intelligence. It exemplifies that weakly solving games, even those with massive search spaces like Othello, is within reach using current algorithmic strategies and computational resources. While strongly solving Othello remains a distant goal due to the game's complexity, the study proposes the concept of "semi-strong solving," which could involve creating software capable of making optimal moves consistently.

Looking forward, the techniques and insights gained from solving Othello may invigorate efforts towards weakly solving other strategically rich games, such as chess, which possesses a comparably expansive decision tree. This paper signifies a methodological triumph and advances the conversation about future potential breakthroughs in AI-driven game-solving contexts. It stands as an inspiring example of how computational power and algorithmic precision can address the grand challenges of computer science, paving the way for further exploration and development in the field.