Not all Chess960 positions are equally complex
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910045685415936 |
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| author | Barthelemy, Marc |
| author_facet | Barthelemy, Marc |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Not all Chess960 positions are equally complex Barthelemy, Marc Physics and Society Disordered Systems and Neural Networks Human-Computer Interaction 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. |
| title | Not all Chess960 positions are equally complex |
| topic | Physics and Society Disordered Systems and Neural Networks Human-Computer Interaction |
| url | https://arxiv.org/abs/2512.14319 |