AAI_2025_Capstone_Chronicles_Combined

Evaluating Deep Learning Model Convergence in Chess via Nash Equilibria

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Figure 2: The histograms with KDE density estimations express the relationships between traditional heuristic material imbalance and class. For Hero Win and Villain Win, notice how material imbalance distribution swings to the hero or villain, respectively. However, these distributions have relatively high entropy, which may allude to the complexity of positions found in the dataset. These positions are sampled from 1800+ elo games, the players may engage in tactics or long-term positional play that justify material imbalance. Material Imbalance is often taught to chess beginners to quickly assess a position. By assigning values to each piece (1 for pawns, 3 for knights, 3.5 for bishops, 9 for queens, etc.) we can generate a heuristic for who is better by subtracting each side’s total material count. The histogram in the top right showcases how winning positions (for the hero) are skewed in material for the hero and vice versa. One interesting nuance of the dataset is that since the chess games are played by expert level players and above, the positions entered may often have unfavorable material imbalance despite the true evaluation of the position and game result. This fact is seen in the histograms, there are still a large number of games for both sides where an unfavorable material balance is observed.

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