AAI_2025_Capstone_Chronicles_Combined

Evaluating Deep Learning Model Convergence in Chess via Nash Equilibria

8

Figure 4: Piece density charts conditioned on each class were created to analyze how pieces may change location depending on class. These charts did not seem to yield much difference when conditioned on class. Chess is a sharp game, a single misplaced piece can mean the difference between a victory and loss. We would expect winning, drawn, and losing positions to not have much difference on aggregate. Instead, the charts reveal the positions biased in the dataset. The majority of positions have a kingside castle or a non-castle, with queenside castling being more rare. We can also observe that the light square bishop is fianchettoed much more than the dark square bishop in the dataset

shows the center pawns leaving their original squares to occupy more central ones, this is well known in opening theory.

Finally I created gifs to show how piece density evolves for each piece depending on how many pieces are actually present in total on the board. The gif for pawns shows how these pieces advance towards the other side of the board and slowly dissipate as games progress. The king gif showcases how kings are hidden in their castled positions in the early and middle stages of the game, but disperse themselves throughout the board as the piece count drops.

82