Fragility of Chess positions: measure, universality and tipping points
| Autor: | Barthelemy, Marc |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. 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. Comment: 7 pages, 6 figures, 1 table (Revised version) |
| Databáze: | arXiv |
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