标题： 国际象棋变体熵和引擎对人类的相关性 显示英文标题

标题： Chess variation entropy and engine relevance for humans

摘要： 现代国际象棋引擎显著超越人类玩家，并且对于评估局面和走法质量至关重要。这些引擎为局面分配一个数值评估$E$，表明白方或黑方的优势，但相似的评估可能掩盖了不同层次的走法复杂性。一些走法序列很简单，而另一些则需要近乎完美的操作，这限制了这些评估对大多数玩家的实际价值。为了量化这个问题，我们使用熵来衡量主要变化（最佳走法序列）的复杂性。有强制走法的变化具有低熵，而有多条可行选择的变化具有高熵。我们的结果显示，除了专家外，大多数人类玩家在处理高熵变化时都存在困难，特别是在$|E|<100$厘帕时，这占所有局面的大约$2/3$。这突显了需要人工智能生成的评估来传达潜在走法序列的复杂性，因为它们通常超出典型人类的认知能力，从而降低了其实用性。 显示英文摘要

摘要： Modern chess engines significantly outperform human players and are essential for evaluating positions and move quality. These engines assign a numerical evaluation $E$ to positions, indicating an advantage for either white or black, but similar evaluations can mask varying levels of move complexity. While some move sequences are straightforward, others demand near-perfect play, limiting the practical value of these evaluations for most players. To quantify this problem, we use entropy to measure the complexity of the principal variation (the sequence of best moves). Variations with forced moves have low entropy, while those with multiple viable alternatives have high entropy. Our results show that, except for experts, most human players struggle with high-entropy variations, especially when $|E|<100$ centipawns, which accounts for about $2/3$ of positions. This underscores the need for AI-generated evaluations to convey the complexity of underlying move sequences, as they often exceed typical human cognitive capabilities, reducing their practical utility.