Maharaj Shiva, Polson Nick, Turk Alex
ChessEd, 729 Colby Ct, Gurnee, IL 60031, USA.
Booth School of Business, University of Chicago, Chicago, IL 60637, USA.
Entropy (Basel). 2022 Apr 14;24(4):550. doi: 10.3390/e24040550.
Endgame studies have long served as a tool for testing human creativity and intelligence. We find that they can serve as a tool for testing machine ability as well. Two of the leading chess engines, Stockfish and Leela Chess Zero (LCZero), employ significantly different methods during play. We use Plaskett's Puzzle, a famous endgame study from the late 1970s, to compare the two engines. Our experiments show that Stockfish outperforms LCZero on the puzzle. We examine the algorithmic differences between the engines and use our observations as a basis for carefully interpreting the test results. Drawing inspiration from how humans solve chess problems, we ask whether machines can possess a form of imagination. On the theoretical side, we describe how Bellman's equation may be applied to optimize the probability of winning. To conclude, we discuss the implications of our work on artificial intelligence (AI) and artificial general intelligence (AGI), suggesting possible avenues for future research.
残局研究长期以来一直是测试人类创造力和智力的工具。我们发现它们也可以作为测试机器能力的工具。两款领先的国际象棋引擎，Stockfish和Leela Chess Zero（LCZero），在比赛过程中采用了截然不同的方法。我们使用普拉斯基特谜题（Plaskett's Puzzle），这是一个20世纪70年代末著名的残局研究，来比较这两款引擎。我们的实验表明，在这个谜题上Stockfish比LCZero表现更优。我们研究了这两款引擎之间的算法差异，并将我们的观察结果作为仔细解读测试结果的基础。从人类解决国际象棋问题的方式中获取灵感，我们提出机器是否能够拥有某种形式的想象力这一问题。在理论方面，我们描述了如何应用贝尔曼方程来优化获胜概率。最后，我们讨论了我们的工作对人工智能（AI）和通用人工智能（AGI）的影响，提出了未来研究可能的方向。
