Fragility of Chess positions: measure, universality and tipping points
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909466202472448 |
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| author | Barthelemy, Marc |
| author_facet | Barthelemy, Marc |
| contents | We introduce a novel metric to quantify the fragility of chess positions using the interaction graph of pieces. This fragility score $F$ captures the tension within a position and serves as a strong indicator of tipping points in a game. In well-known games, maximum fragility often aligns with decisive moments marked by brilliant moves. Analyzing a large dataset of games, we find that fragility typically peaks around move $15$, with pawns ($\approx 60\%$) and knights ($\approx 20\%$) frequently involved in high-tension positions. Comparing the Stockfish evaluation with the fragility score, we observe that the maximum fragility ply often serves as a critical turning point, where the moves made afterward can determine the outcome of the game. Remarkably, average fragility curves show a universal pattern across a wide range of players, games, and openings, with a subtle deviation observed in games played by the engine Stockfish. Our analysis reveals a gradual buildup of fragility starting around $8$ moves before the peak, followed by a prolonged fragile state lasting up to $15$ moves. This suggests a gradual intensification of positional tension leading to decisive moments in the game. These insights offer a valuable tool for both players and engines to assess critical moments in chess. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fragility of Chess positions: measure, universality and tipping points Barthelemy, Marc Physics and Society Disordered Systems and Neural Networks We introduce a novel metric to quantify the fragility of chess positions using the interaction graph of pieces. This fragility score $F$ captures the tension within a position and serves as a strong indicator of tipping points in a game. In well-known games, maximum fragility often aligns with decisive moments marked by brilliant moves. Analyzing a large dataset of games, we find that fragility typically peaks around move $15$, with pawns ($\approx 60\%$) and knights ($\approx 20\%$) frequently involved in high-tension positions. Comparing the Stockfish evaluation with the fragility score, we observe that the maximum fragility ply often serves as a critical turning point, where the moves made afterward can determine the outcome of the game. Remarkably, average fragility curves show a universal pattern across a wide range of players, games, and openings, with a subtle deviation observed in games played by the engine Stockfish. Our analysis reveals a gradual buildup of fragility starting around $8$ moves before the peak, followed by a prolonged fragile state lasting up to $15$ moves. This suggests a gradual intensification of positional tension leading to decisive moments in the game. These insights offer a valuable tool for both players and engines to assess critical moments in chess. |
| title | Fragility of Chess positions: measure, universality and tipping points |
| topic | Physics and Society Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2410.02333 |