arXiv subjects

Chung-Chin Shih

Publications and source records attributed to Chung-Chin Shih.

10 recordsLinked to original sources

arXiv2026

Evaluating Game Difficulty in Tetris Block Puzzle

Tetris Block Puzzle is a single player stochastic puzzle in which a player places blocks on an 8 x 8 grid to complete lines; its popular variants have amassed tens of millions of downloads. Despite this reach, there is little principled assessment of which rule sets are more difficult. Inspired by prior work that uses AlphaZero as a strong evaluator for chess variants, we study difficulty in this domain using Stochastic Gumbel AlphaZero (SGAZ), a budget-aware planning agent for stochastic environments. We evaluate rule changes including holding block h, preview holding block p, and additional Tetris block variants using metrics such as training reward and convergence iterations. Empirically, increasing h and p reduces difficulty (higher reward and faster convergence), while adding more Tetris block variants increases difficulty, with the T-pentomino producing the largest slowdown. Through analysis, SGAZ delivers strong play under small simulation budgets, enabling efficient, reproducible comparisons across rule sets and providing a reference for future design in stochastic puzzle games.

cs.AI↗

arXiv2025

A Study of Solving Life-and-Death Problems in Go Using Relevance-Zone Based Solvers

This paper analyzes the behavior of solving Life-and-Death (L&D) problems in the game of Go using current state-of-the-art computer Go solvers with two techniques: the Relevance-Zone Based Search (RZS) and the relevance-zone pattern table. We examined the solutions derived by relevance-zone based solvers on seven L&D problems from the renowned book "Life and Death Dictionary" written by Cho Chikun, a Go grandmaster, and found several interesting results. First, for each problem, the solvers identify a relevance-zone that highlights the critical areas for solving. Second, the solvers discover a series of patterns, including some that are rare. Finally, the solvers even find different answers compared to the given solutions for two problems. We also identified two issues with the solver: (a) it misjudges values of rare patterns, and (b) it tends to prioritize living directly rather than maximizing territory, which differs from the behavior of human Go players. We suggest possible approaches to address these issues in future work. Our code and data are available at https://rlg.iis.sinica.edu.tw/papers/study-LD-RZ.

cs.AI↗

arXiv2025

Relevance-Zone Reduction in Game Solving

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.

cs.AI↗

arXiv2025

Bridging Local and Global Knowledge via Transformer in Board Games

Although AlphaZero has achieved superhuman performance in board games, recent studies reveal its limitations in handling scenarios requiring a comprehensive understanding of the entire board, such as recognizing long-sequence patterns in Go. To address this challenge, we propose ResTNet, a network that interleaves residual and Transformer blocks to bridge local and global knowledge. ResTNet improves playing strength across multiple board games, increasing win rate from 54.6% to 60.8% in 9x9 Go, 53.6% to 60.9% in 19x19 Go, and 50.4% to 58.0% in 19x19 Hex. In addition, ResTNet effectively processes global information and tackles two long-sequence patterns in 19x19 Go, including circular pattern and ladder pattern. It reduces the mean square error for circular pattern recognition from 2.58 to 1.07 and lowers the attack probability against an adversary program from 70.44% to 23.91%. ResTNet also improves ladder pattern recognition accuracy from 59.15% to 80.01%. By visualizing attention maps, we demonstrate that ResTNet captures critical game concepts in both Go and Hex, offering insights into AlphaZero's decision-making process. Overall, ResTNet shows a promising approach to integrating local and global knowledge, paving the way for more effective AlphaZero-based algorithms in board games. Our code is available at https://rlg.iis.sinica.edu.tw/papers/restnet.

cs.LG↗

arXiv2025

Strength Estimation and Human-Like Strength Adjustment in Games

Strength estimation and adjustment are crucial in designing human-AI interactions, particularly in games where AI surpasses human players. This paper introduces a novel strength system, including a strength estimator (SE) and an SE-based Monte Carlo tree search, denoted as SE-MCTS, which predicts strengths from games and offers different playing strengths with human styles. The strength estimator calculates strength scores and predicts ranks from games without direct human interaction. SE-MCTS utilizes the strength scores in a Monte Carlo tree search to adjust playing strength and style. We first conduct experiments in Go, a challenging board game with a wide range of ranks. Our strength estimator significantly achieves over 80% accuracy in predicting ranks by observing 15 games only, whereas the previous method reached 49% accuracy for 100 games. For strength adjustment, SE-MCTS successfully adjusts to designated ranks while achieving a 51.33% accuracy in aligning to human actions, outperforming a previous state-of-the-art, with only 42.56% accuracy. To demonstrate the generality of our strength system, we further apply SE and SE-MCTS to chess and obtain consistent results. These results show a promising approach to strength estimation and adjustment, enhancing human-AI interactions in games. Our code is available at https://rlg.iis.sinica.edu.tw/papers/strength-estimator.

cs.AI↗

arXiv2024

A Novel Approach to Solving Goal-Achieving Problems for Board Games

Goal-achieving problems are puzzles that set up a specific situation with a clear objective. An example that is well-studied is the category of life-and-death (L&D) problems for Go, which helps players hone their skill of identifying region safety. Many previous methods like lambda search try null moves first, then derive so-called relevance zones (RZs), outside of which the opponent does not need to search. This paper first proposes a novel RZ-based approach, called the RZ-Based Search (RZS), to solving L&D problems for Go. RZS tries moves before determining whether they are null moves post-hoc. This means we do not need to rely on null move heuristics, resulting in a more elegant algorithm, so that it can also be seamlessly incorporated into AlphaZero's super-human level play in our solver. To repurpose AlphaZero for solving, we also propose a new training method called Faster to Life (FTL), which modifies AlphaZero to entice it to win more quickly. We use RZS and FTL to solve L&D problems on Go, namely solving 68 among 106 problems from a professional L&D book while a previous program solves 11 only. Finally, we discuss that the approach is generic in the sense that RZS is applicable to solving many other goal-achieving problems for board games.

cs.AI↗

arXiv2024

Solving 7x7 Killall-Go with Seki Database

Game solving is the process of finding the theoretical outcome for a game, assuming that all player choices are optimal. This paper focuses on a technique that can reduce the heuristic search space significantly for 7x7 Killall-Go. In Go and Killall-Go, live patterns are stones that are protected from opponent capture. Mutual life, also referred to as seki, is when both players' stones achieve life by sharing liberties with their opponent. Whichever player attempts to capture the opponent first will leave their own stones vulnerable. Therefore, it is critical to recognize seki patterns to avoid putting oneself in jeopardy. Recognizing seki can reduce the search depth significantly. In this paper, we enumerate all seki patterns up to a predetermined area size, then store these patterns into a seki table. This allows us to recognize seki during search, which significantly improves solving efficiency for the game of Killall-Go. Experiments show that a day-long, unsolvable position can be solved in 482 seconds with the addition of a seki table. For general positions, a 10% to 20% improvement in wall clock time and node count is observed.

cs.AI↗

arXiv2024

MiniZero: Comparative Analysis of AlphaZero and MuZero on Go, Othello, and Atari Games

This paper presents MiniZero, a zero-knowledge learning framework that supports four state-of-the-art algorithms, including AlphaZero, MuZero, Gumbel AlphaZero, and Gumbel MuZero. While these algorithms have demonstrated super-human performance in many games, it remains unclear which among them is most suitable or efficient for specific tasks. Through MiniZero, we systematically evaluate the performance of each algorithm in two board games, 9x9 Go and 8x8 Othello, as well as 57 Atari games. For two board games, using more simulations generally results in higher performance. However, the choice of AlphaZero and MuZero may differ based on game properties. For Atari games, both MuZero and Gumbel MuZero are worth considering. Since each game has unique characteristics, different algorithms and simulations yield varying results. In addition, we introduce an approach, called progressive simulation, which progressively increases the simulation budget during training to allocate computation more efficiently. Our empirical results demonstrate that progressive simulation achieves significantly superior performance in two board games. By making our framework and trained models publicly available, this paper contributes a benchmark for future research on zero-knowledge learning algorithms, assisting researchers in algorithm selection and comparison against these zero-knowledge learning baselines. Our code and data are available at https://rlg.iis.sinica.edu.tw/papers/minizero.

cs.AI↗

arXiv2023

Game Solving with Online Fine-Tuning

Game solving is a similar, yet more difficult task than mastering a game. Solving a game typically means to find the game-theoretic value (outcome given optimal play), and optionally a full strategy to follow in order to achieve that outcome. The AlphaZero algorithm has demonstrated super-human level play, and its powerful policy and value predictions have also served as heuristics in game solving. However, to solve a game and obtain a full strategy, a winning response must be found for all possible moves by the losing player. This includes very poor lines of play from the losing side, for which the AlphaZero self-play process will not encounter. AlphaZero-based heuristics can be highly inaccurate when evaluating these out-of-distribution positions, which occur throughout the entire search. To address this issue, this paper investigates applying online fine-tuning while searching and proposes two methods to learn tailor-designed heuristics for game solving. Our experiments show that using online fine-tuning can solve a series of challenging 7x7 Killall-Go problems, using only 23.54% of computation time compared to the baseline without online fine-tuning. Results suggest that the savings scale with problem size. Our method can further be extended to any tree search algorithm for problem solving. Our code is available at https://rlg.iis.sinica.edu.tw/papers/neurips2023-online-fine-tuning-solver.

cs.AI↗

arXiv2022

A Local-Pattern Related Look-Up Table

This paper describes a Relevance-Zone pattern table (RZT) that can be used to replace a traditional transposition table. An RZT stores exact game values for patterns that are discovered during a Relevance-Zone-Based Search (RZS), which is the current state-of-the-art in solving L&D problems in Go. Positions that share the same pattern can reuse the same exact game value in the RZT. The pattern matching scheme for RZTs is implemented using a radix tree, taking into consideration patterns with different shapes. To improve the efficiency of table lookups, we designed a heuristic that prevents redundant lookups. The heuristic can safely skip previously queried patterns for a given position, reducing the overhead to 10% of the original cost. We also analyze the time complexity of the RZT both theoretically and empirically. Experiments show the overhead of traversing the radix tree in practice during lookup remain flat logarithmically in relation to the number of entries stored in the table. Experiments also show that the use of an RZT instead of a traditional transposition table significantly reduces the number of searched nodes on two data sets of 7x7 and 19x19 L&D Go problems.

cs.AI↗