We analyze strategic complexity across all 960 Chess960 (Fischer Random Chess) starting positions. Stockfish evaluations show a near-universal first-move advantage for White ($\langle E \rangle = +0.30 \pm 0.14$ pawns), indicating that the advantage conferred by moving first is a robust structural feature of the game. To quantify decision difficulty, we introduce an information-based measure $S(n)$ describing the cumulative information required to identify optimal moves over the first $n$ plies. This measure decomposes into contributions from White and Black, $S_W$ and $S_B$, yielding a total opening complexity $S_{\mathrm{tot}} = S_W + S_B$ and a decision asymmetry $A=S_B-S_W$. Across the ensemble, $S_{\mathrm{tot}}$ varies by a factor of three, while $A$ spans from $-2.5$ to $+1.8$ bits, showing that some openings burden White and others Black. The mean $\langle A \rangle = -0.25$ bits indicates a slight tendency for White to face harder opening decisions. Standard chess (position \#518, \texttt{RNBQKBNR}) exhibits above-average asymmetry (91st percentile) but typical overall complexity (47th percentile). The most complex opening is \#226 (\texttt{BNRQKBNR}), whereas \#198 (\texttt{QNBRKBNR})is the most balanced, with both evaluation and asymmetry near zero. These results reveal a highly heterogeneous Chess960 landscape in which small rearrangements of the back-rank pieces can significantly alter strategic depth and competitive fairness. Remarkably, the classical starting position-despite centuries of cultural selection-lies far from the most balanced configuration.

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评估显示白方几乎在所有局面中均具有先手优势（$\langle E \rangle = +0.30 \pm 0.14$兵），表明先手优势是游戏固有的稳健结构特征。为量化决策难度，我们引入基于信息的度量$S(n)$，该指标描述了在前$n$步内识别最优着法所需的累积信息量。该度量可分解为白方与黑方的贡献$S_W$和$S_B$，由此得到开局总复杂度$S_{\mathrm{tot}} = S_W + S_B$及决策不对称性$A=S_B-S_W$。在全样本中，$S_{\mathrm{tot}}$存在三倍差异，而$A$的分布范围为$-2.5$至$+1.8$比特，表明某些开局对白方构成决策负担，另一些则对黑方形成压力。均值$\langle A \rangle = -0.25$比特表明白方倾向于面临稍显困难的开局决策。传统象棋（第518号局面，\texttt{RNBQKBNR}）表现出高于平均水平的不对称性（第91百分位）但具有典型的总体复杂度（第47百分位）。最复杂的开局是第226号局面（\texttt{BNRQKBNR}），而第198号局面（\texttt{QNBRKBNR}）最为均衡，其评估值与不对称性均接近零。这些结果揭示了Chess960存在高度异质化的局面谱系，底排棋子的微小重排即可显著改变策略深度与竞技公平性。值得注意的是，尽管经历了数个世纪的文化选择，经典初始局面仍远未达到最均衡的构型。