Breakthrough is a well-known abstract board game played regularly at the Computer Games Olympiad. Despite the straightforward gameplay mechanics of the game, determining optimal play strategies poses significant challenges. We have (weakly) solved a variant of the game played on the 6 × 6 board, representing the largest board instance of the game solved to date. The game is a win for the first player. We apply a hybrid approach of computing endgame tablebases, defining game-specific race patterns, using a family of parallelizable proof-number-based solvers, and training a neural-network-based heuristic job scheduler to construct a solution tree and proof of the game’s game-theoretic value. This approach allowed us to not only solve the 6 × 6 game variant, but also lays the foundation for solving the game’s larger board-size variants.
2048 is a stochastic single-player game involving 16 cells on a 4 & times; 4 grid, where a player chooses a direction among up, down, left, and right to obtain a score by merging two tiles with the same number located in neighboring cells along the chosen direction. This paper presents that a variant 2048(4 & times;3) with 12 cells on a 4 & times; 3 board, one row smaller than the original, has been strongly solved. In this variant, the expected score achieved by an optimal strategy is about 50, 724.26 for the most common initial states: ones with two tiles of number 2. The number of reachable states and afterstates are identified to be 1, 152, 817, 492, 752 and 739, 648, 886, 170, respectively. The key technique is to partition the state space by the sum of tile numbers on a board, which we call the age of a state. An age is invariant between a state and its successive afterstate after any valid action and is increased by two or four by a stochastic response from the environment. Therefore, we can partition the state space by ages and enumerate all (after)states of an age depending only on states with the recent ages. Similarly, we can identify (after)state values by going along with ages in decreasing order.
On the 19th and 20th of February 2026, the GameTable COST Action held a meeting in Prague to kick off its third grant period. This meeting focused on discussions around joint projects between researchers in the humanities and game-playing artificial intelligence (AI) agents, as well as projects specific to one of the disciplines. A key point of discussion was the main goal of the COST Action: advancing research in human-like game AI. Additionally, as the GameTable COST Action approaches its conclusion in 2027, participants discussed future prospects for collaboration between humanities and computer science scholars to further our understanding of games, both past and present.
Breakthrough is a well-known abstract board game played regularly at the Computer Games Olympiad. Despite the straightforward gameplay mechanics of the game, determining optimal play strategies poses significant challenges. We have (weakly) solved a variant of the game played on the 6 & times; 6 board, representing the largest board instance of the game solved to date. The game is a win for the first player. We apply a hybrid approach of computing endgame tablebases, defining game-specific race patterns, using a family of parallelizable proof-number-based solvers, and training a neural-network-based heuristic job scheduler to construct a solution tree and proof of the game's game-theoretic value. This approach allowed us to not only solve the 6 & times; 6 game variant, but also lays the foundation for solving the game's larger board-size variants.
Endgames do help improve the playing strength of computer Chinese chess programs. However, due to their large size, human players benefit minorly. Distance-to-mate (DTM) or distance-to-conversion (DTC) values computed for endgames do not capture the idea of human playing style. Typically, human players develop a high-level strategy during a game, which consists of a sequence of captures or piece exchanges. The capture process may not follow DTC or DTM values but aims at simplifying the game without creating risks. The process of piece exchanges is not recorded in any endgame databases. We propose a systematic method for finding important winning tactics in endgame studies, which may be useful in studying other endgames. As an illustration, we study the Chinese chess KN P kgm endgame and find winning tactics that are beneficial for human players. Although many winning tactics are known for RED to win, such as exchanging the red pawn for the black guard or minister, human players only need to focus on two tactics, namely to capture the black guard or minister to ensure a win when playing this endgame.
In this article, I argue that powerful modern chess tools-including neural network engines, cloud-based databases, and endgame tablebases-now enable a human player to play consistently "error-free" chess. I begin with a personal history of my correspondence chess career, which spans over 50 years. Then, I detail the specific tools that contribute to what I call the methodological solution to chess. These tools apply across the Opening, Middlegame, and Endgame. My conclusion is that the resources currently available are fully adequate to achieve accurate evaluations for virtually all remaining unanalyzed middlegame positions. The only possible counterargument is the existence of long, maneuvering positions that might still challenge today's neural networks. However, I have yet to find one that does not ultimately result in a draw. The methodological solution to chess has significant implications for the future of the game. The ability to analyze with confidence and understand optimal play will accelerate the learning process for players at all levels. Looking forward, the remaining challenge is to determine whether truly unique structural positions exist that remain beyond the reach of current neural networks.
This study presents a strong solution for the two-player, perfect-information, zero-sum board game PYLOS under three different rule sets: the rule set for children, the standard rule set, and the rule set for mature players. Using a zero-suppressed binary decision diagram, we systematically index all pseudo-reachable positions, that is, those that satisfy necessary structural constraints but may not be reachable during actual gameplay. Retrograde analysis is then executed on each rule set to assign game-theoretic values to all positions. A total of over 12 billion pseudo-reachable positions are considered. We also develop a method to extract truly reachable positions from this superset and verify the consistency of both indexing and value assignments. Experiments show that in all three rule sets, the first player is forced to lose, from the initial position, within 36, 40, and 46 moves, respectively. Furthermore, our analysis reveals that PYLOS has a higher proportion of zugzwang positions compared to previously solved games, emphasizing the strategic importance of conserving spheres. The mature players' rule set generated the greatest number of legal moves. This study demonstrates the feasibility of computing strong solutions to PYLOS, and highlights structural differences among the three rule sets in terms of reachability and strategy.
The Mijnlieff board game is solved using a modified alpha-beta algorithm with an appropriate move ordering. The perfect game is found to be won by the second player and a new variant is proposed, whose perfect game is draw.
Tibetan Jiu Chess, a recognized national intangible cultural heritage, is characterized by limited game data and significant parsing challenges. In this study, we leverage the retrieval-augmented generation (RAG) framework, prompt engineering, artificial intelligence (AI) agents, and large language models (LLMs) to construct a question-and-answer (Q&A) system tailored for Tibetan Jiu Chess. Additionally, we developed a specialized algorithm for Jiu Chess game parsing, which integrates with the LLM to enable intelligent and accurate game interpretation. Experimental results demonstrate that the Q&A system effectively addresses two types of Tibetan Jiu Chess questions, achieving notably higher accuracy in knowledge-based questions compared to baseline systems. This Q&A system not only addresses the gap in Tibetan Jiu Chess analysis but also pioneers a new approach to the preservation and transmission of Tibetan chess culture.
Chinese chess is an artificial intelligence (AI) domain that merges ancient culture with emerging technology. This article explores key aspects of current Chinese chess technology, including move generation, evaluation functions, and search techniques in the search engine, as well as developments in the opening knowledge base and endgame databases. We also examine parallelization techniques, which are essential for improving computational efficiency and performance. Inspired by AlphaZero's achievements in reinforcement learning, this article also explores its key concepts and impact on AI techniques. It further highlights the field's development and the notable performance of computer Chinese chess in international competitions, particularly in human versus computer matches and global tournaments. The article concludes with a discussion of future trends in computer Chinese chess technology.
Endgames do help improve the playing strength of computer Chinese chess programs. However, due to their large size, human players benefit minorly. Distance-to-mate (DTM) or distance-to-conversion (DTC) values computed for endgames do not capture the idea of human playing style. Typically, human players develop a high-level strategy during a game, which consists of a sequence of captures or piece exchanges. The capture process may not follow DTC or DTM values but aims at simplifying the game without creating risks. The process of piece exchanges is not recorded in any endgame databases. We propose a systematic method for finding important winning tactics in endgame studies, which may be useful in studying other endgames. As an illustration, we study the Chinese chess KNPkgm endgame and find winning tactics that are beneficial for human players. Although many winning tactics are known for RED to win, such as exchanging the red pawn for the black guard or minister, human players only need to focus on two tactics, namely to capture the black guard or minister to ensure a win when playing this endgame.
This paper presents a Go AI competition that aimed to advance AI research by developing models capable of mimicking human Go playing styles and recognizing different playing patterns within game records. The competition challenged participants to create AI models that could accurately replicate the playing styles of professional Go players at various skill levels, as well as classify specific moves based on different playing styles. Participants' models were evaluated on their ability to accurately imitate professional players and recognize playing styles. The results showed that the top-performing teams leveraged advanced techniques from state-of the-art Go AI systems, such as AlphaGo and AlphaZero, combined with deep learning architectures like convolutional neural networks (CNNs) and residual networks (ResNets). This competition highlights the potential of AI in replicating complex human behaviors and underscores the significance of large-scale datasets and advanced deep learning techniques in achieving this goal.
