We propose a neural network-based approach to calculate the value of a chess square–piece combination. Our model takes a triplet (color, piece, square) as the input and calculates a value that measures the advantage/disadvantage of having this piece on this square. Our methods build on recent advances in chess AI, and can accurately assess the worth of positions in a game of chess. The conventional approach assigns fixed values to pieces (Entropy 25 01374 i001= ∞, Entropy 25 01374 i002= 9, Entropy 25 01374 i003= 5, Entropy 25 01374 i004= 3, Entropy 25 01374 i005= 3, Entropy 25 01374 i006= 1). We enhance this analysis by introducing marginal valuations. We use deep Q-learning to estimate the parameters of our model. We demonstrate our method by examining the positioning of knights and bishops, and also provide valuable insights into the valuation of pawns. Finally, we conclude by suggesting potential avenues for future research. [Note: Please download the article to see the special symbols in the abstract.]