Use StockFish to predict the next move, and only store the diff between the actual move and the prediction.
Or, better, get a ranked list of all possible moves from stockfish, and use a variable-length integer to encode the position in the list. Then the best move takes ~1 bit, and worse moves take more bits. (And we can do fun things like compute how bad a player is by how big their game is after compression.)
Or, better, get a ranked list of all possible moves from stockfish, and use a variable-length integer to encode the position in the list. Then the best move takes ~1 bit, and worse moves take more bits. (And we can do fun things like compute how bad a player is by how big their game is after compression.)