We analyze strategic complexity across all 960 Chess960 (Fischer Random Chess) starting positions. Stockfish evaluations reveal a near-universal first-move advantage for White ($\langle E \rangle = +0.33 \pm 0.12$ pawns), indicating that the initiative is a robust structural feature of the game. To quantify decision difficulty, we introduce an information-based measure $S(n)$ that captures the cumulative information required to identify optimal moves over the first $n$ plies. This measure decomposes into White and Black contributions, $S_W$ and $S_B$, defining a total opening complexity $S_{\mathrm{tot}} = S_W + S_B$ and a decision asymmetry $A = S_B - S_W$. Across the ensemble, $S_{\mathrm{tot}}$ ranges from $2.6$ to $17.2$ bits, while $A$ spans from $-4.5$ to $+4.2$ bits (mean $\langle A \rangle = -0.26$), showing that openings are nearly evenly split between those that burden White and those that burden Black, with a slight average excess complexity for White. Standard chess (position \#518, \texttt{RNBQKBNR}) exhibits near-average total complexity and asymmetry, yet lies far from the configuration that jointly minimizes evaluation imbalance and decision asymmetry. These results reveal a highly heterogeneous Chess960 landscape in which small rearrangements of back-rank pieces can substantially alter strategic depth and competitive balance. The classical starting position--despite centuries of refinement--appears not as an extremum, but as one configuration among many in a broad statistical ensemble.

翻译：我们分析了全部960种Chess960（菲舍尔任意制象棋）初始局面的策略复杂度。Stockfish评估显示白方首步优势近乎普遍存在（$\langle E \rangle = +0.33 \pm 0.12$兵），表明主动权是该游戏稳定的结构性特征。为量化决策难度，我们引入基于信息的度量$S(n)$，该度量捕捉前$n$步内识别最优着法所需的累积信息。此度量可分解为白方与黑方贡献$S_W$和$S_B$，由此定义开局总复杂度$S_{\mathrm{tot}} = S_W + S_B$与决策不对称性$A = S_B - S_W$。在整个集合中，$S_{\mathrm{tot}}$取值范围为$2.6$至$17.2$比特，$A$取值范围为$-4.5$至$+4.2$比特（均值$\langle A \rangle = -0.26$），表明开局体系中对白方构成负担与对黑方构成负担的局面近乎均等分布，仅白方平均承担略多复杂度。标准象棋（第518号局面，\texttt{RNBQKBNR}）展现出接近平均的总复杂度与不对称性，却远离同时最小化评估失衡与决策不对称性的构型。这些结果揭示了Chess960存在高度异质化的局面景观：底线棋子的细微重组即可显著改变策略深度与竞技平衡。经典初始局面——尽管历经数百年精研——并非作为极值存在，而是广泛统计集合中的众多构型之一。