We introduce LudoBench, a benchmark for evaluating LLM strategic reasoning in Ludo, a stochastic multi-agent board game whose dice mechanics, piece capture, safe-square navigation, and home-path progression introduce meaningful planning complexity. LudoBench comprises 480 handcrafted spot scenarios across 12 behaviorally distinct decision categories, each isolating a specific strategic choice. We additionally contribute a fully functional 4-player Ludo simulator supporting Random, Heuristic, Game-Theory, and LLM agents. The game-theory agent uses Expectiminimax search with depth-limited lookahead to provide a principled strategic ceiling beyond greedy heuristics. Evaluating six models spanning four model families, we find that all models agree with the game-theory baseline only 40-46% of the time. Models split into distinct behavioral archetypes: finishers that complete pieces but neglect development, and builders that develop but never finish. Each archetype captures only half of the game theory strategy. Models also display measurable behavioral shifts under history-conditioned grudge framing on identical board states, revealing prompt-sensitivity as a key vulnerability. LudoBench provides a lightweight and interpretable framework for benchmarking LLM strategic reasoning under uncertainty. All code, the spot dataset (480 entries) and model outputs are available at https://anonymous.4open.science/r/LudoBench-5CBF/

翻译：我们提出了LudoBench，一个用于评估大语言模型在飞行棋中策略推理能力的基准测试。飞行棋是一种随机性多智能体棋类游戏，其骰子机制、棋子捕获、安全格导航以及归途路径推进构成了有意义的规划复杂度。LudoBench包含480个手工设计的局部场景，覆盖12个行为差异明显的决策类别，每个类别独立聚焦一种特定策略选择。我们额外提供一个功能完整的四玩家飞行棋模拟器，支持随机智能体、启发式智能体、博弈论智能体和LLM智能体。其中博弈论智能体采用深度受限前瞻的期望极小化极大搜索，为超越贪心启发式提供了理论化的策略天花板。在评估涵盖四个模型家族的六种模型后，我们发现所有模型仅在与博弈论基线一致性的40-46%时间内达成共识。模型可分为两种行为原型：“完成型”倾向于完成棋子但忽视发展，“建设型”注重发展但从未完成棋子。每种原型仅捕捉了博弈论策略的一半。同时，模型在相同棋盘状态下受到历史条件驱动的怨恨框架影响时，表现出可测量的行为偏移，揭示出提示敏感性这一关键脆弱性。LudoBench为在不确定性环境下评估LLM策略推理提供了一个轻量级且可解释的基准框架。全部代码、局部场景数据集（480条）及模型输出已公开于https://anonymous.4open.science/r/LudoBench-5CBF/