https://arxiv.org/abs/2512.14319 Skip to main content Cornell University We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate arxiv logo > physics > arXiv:2512.14319 [ ] Help | Advanced Search [All fields ] Search arXiv logo Cornell University Logo [ ] GO quick links * Login * Help Pages * About Physics > Physics and Society arXiv:2512.14319 (physics) [Submitted on 16 Dec 2025 (v1), last revised 13 Jan 2026 (this version, v2)] Title:Not all Chess960 positions are equally complex Authors:Marc Barthelemy View a PDF of the paper titled Not all Chess960 positions are equally complex, by Marc Barthelemy View PDF HTML (experimental) Abstract: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. Comments: Revised version including a discussion of thinking time and complexity (11 pages, 8 figures) Physics and Society (physics.soc-ph); Disordered Systems Subjects: and Neural Networks (cond-mat.dis-nn); Human-Computer Interaction (cs.HC) Cite as: arXiv:2512.14319 [physics.soc-ph] (or arXiv:2512.14319v2 [physics.soc-ph] for this version) https://doi.org/10.48550/arXiv.2512.14319 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Marc Barthelemy [view email] [v1] Tue, 16 Dec 2025 11:33:37 UTC (1,703 KB) [v2] Tue, 13 Jan 2026 15:18:15 UTC (1,800 KB) Full-text links: Access Paper: View a PDF of the paper titled Not all Chess960 positions are equally complex, by Marc Barthelemy * View PDF * HTML (experimental) * TeX Source view license Current browse context: physics.soc-ph < prev | next > new | recent | 2025-12 Change to browse by: cond-mat cond-mat.dis-nn cs cs.HC physics References & Citations * NASA ADS * Google Scholar * Semantic Scholar export BibTeX citation Loading... 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