量化少量作弊对国际象棋胜率的影响，为反作弊提供基准数据。
How Much Can a Few Engine Moves Help? Quantifying Limited Cheating in Chess
- 设计基于阈值和贝尔曼方程的作弊策略，模拟有限次数干预
- 1次或2次作弊可使胜率从0.51提升至0.71或0.82
- 提出无需引擎的快速仿真器，加速策略优化
国际象棋作弊问题日益严重，尤其在高水平比赛中频繁使用强大软件辅助。与以往侧重检测作弊的研究不同，本文评估在单局游戏中仅有限次数作弊所能带来的性能提升。我们设计了基于阈值和贝尔曼风格的干预策略，并在受控的Stockfish引擎对战环境中进行测试。结果显示，合理使用1次或2次作弊时，平均得分分别达到0.71和0.82，远高于无作弊时的0.51。此外，我们还提出一种无需引擎的快速仿真器，可在不运行实际对局的情况下完成超参数优化，其结果与基于引擎的最优解高度一致。本研究目的并非协助作弊，而是量化作弊效果，为反作弊机制的设计与检测提供关键参考。
原文摘要 · Abstract (English)
Cheating in chess, by using advice from powerful software, has become a major problem, reaching the highest levels. As opposed to the large majority of previous work, which concerned {\em detection} of cheating, here we try to evaluate the possible gain in performance, obtained by cheating a limited number of times during a game. We develop threshold-based and Bellman-style intervention policies, and test them in a controlled engine-vs-engine setting using Stockfish. A judicious choice of 1 or 2 cheats yields average scores of 0.71 and 0.82, respectively, compared to 0.51 with no cheats. We also introduce a fast, engine-free simulator that enables hyperparameter optimization without running games, closely matching the engine-based optimum. The goal of this work is not to assist cheaters, but to measure the effectiveness of cheating -- which is crucial as part of the effort to contain and detect it.
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