Fragility of chess positions: Measure, universality, and tipping points.

Abstract

We introduce a 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 (≈60%) and knights (≈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 eight 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.