We use logistic regression to estimate the value of the pieces in standard chess and several chess variants, namely Chess 960, Atomic chess, Antichess, and Horde chess. We perform our regressions on several years of data from Lichess, the free and open-source internet chess server. We use the published player ratings to control for the confounding effect of differential player skill. We adjust for the attenuation bias in regressions due to the noise in observed ratings. We find that major piece values, relative to the value of a pawn, are fairly consistent with historical valuation systems. However we find slightly higher value to bishops than knights. We find that piece values are smaller, in absolute value, in Atomic and Antichess than standard chess. We also present approximate values of the pieces to equalize odds when players of varying skill face off.

翻译：本文采用逻辑回归方法，估算了标准国际象棋及多种变体（包括Chess 960、原子象棋、弃兵象棋和部落象棋）中棋子的价值。回归分析基于免费开源国际象棋服务器Lichess多年积累的对局数据，并利用公开的玩家评级数据控制玩家技术水平差异带来的混杂效应。同时，我们针对观测评级噪声导致的回归衰减偏差进行了校正。研究发现，主要棋子的相对价值（以兵为基准）与历史估值体系基本一致，但象的价值略高于马。在原子象棋和弃兵象棋中，棋子的绝对价值普遍低于标准国际象棋。此外，本文还提出了在不同水平玩家对弈时使胜率均等化的棋子近似价值参数。