Game solving aims to find the optimal strategies for all players and determine the theoretical outcome of a game. However, due to the exponential growth of game trees, many games remain unsolved, even though methods like AlphaZero have demonstrated super-human level in game playing. The Relevance-Zone (RZ) is a local strategy reuse technique that restricts the search to only the regions relevant to the outcome, significantly reducing the search space. However, RZs are not unique. Different solutions may result in RZs of varying sizes. Smaller RZs are generally more favorable, as they increase the chance of reuse and improve pruning efficiency. To this end, we propose an iterative RZ reduction method that repeatedly solves the same position while gradually restricting the region involved, guiding the solver toward smaller RZs. We design three constraint generation strategies and integrate an RZ Pattern Table to fully leverage past solutions. In experiments on 7x7 Killall-Go, our method reduces the average RZ size to 85.95% of the original. Furthermore, the reduced RZs can be permanently stored as reusable knowledge for future solving tasks, especially for larger board sizes or different openings.

Solving combinatorial games has been a classic research topic in artificial intelligence because solutions can offer essential information to improve gameplay. Several definitions exist for `solving the game,' but they are markedly different regarding computational cost and the detail of insights derived. In this study, we introduce a novel definition called `semi-strongly solved' and propose an algorithm to achieve this type of solution efficiently. This new definition addresses existing gaps because of its intermediate computational cost and the quality of the solution. To demonstrate the potential of our approach, we derive the theoretical computational complexity of our algorithm under a simple condition, and apply it to semi-strongly solve the game of 6x6 Othello. This study raises many new research goals in this research area.

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.

Mirowski cites Turing as author of the paragraph containing this remark. The paragraph appeared in [46], in a chapter with Turing listed as one of three contributors. Which parts of the chapter are the work of which contributor, particularly the introductory material containing this quote, is not made explicit.