Occupation density of every chess piece by phases, levels of game, outcomes and phase-space according to their entropy differences

Abstract

In this paper, we statistically analyze the density of each chess piece in four square concentric frames for different skill levels (according to the Elo ranking system), phases (opening, middlegame and endgame) and outcomes. The results indicate a tendency for pawns, knights and bishops to move towards the central areas, particularly during the opening phase. Additionally, we identified intrinsic entropy patterns for each piece throughout the entire game, independent of player skill level. We constructed a phase-space from entropy delay time series to provide probabilistic predictions for game outcomes.