Not all Chess960 positions are equally complex

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 ± 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, SW and SB, defining a total opening complexity Stot = SW + SB and a decision asymmetry A = SB - SW. Across the ensemble, Stot 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, textttRNBQKBNR) 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.