I've seen data sets for classification / regressions tasks in domains such as credit default detection, object identification in an image, stock price prediction etc. All of these data sets could simply be represented as an input matrix of size (n_samples, n_features) and fed into your machine learning algorithm to ultimately yield a trained model offering some predictive capability. Intuitively and mathematically this makes sense to me.
However, I'm really struggling with how to think about the structure of an input matrix for game-like tasks (Chess, Go, Seth Blings Mario Kart AI) specifically (using the Chess example):
How would you encode the state of the board to something that a model could train on? Is it reasonable to think about the board state as a 8x8 matrix (or 1x64) vector with each point being encoded by a numerical value dependent on the type of piece and color?
Assuming a suitable representation of the board state, how would the model be capable of making a recommendation given that each piece type moves differently? Would it not have to evaluate the different move possibilities for each piece and propose which move it "thinks" would have the best long term outcome for the game?
A follow up on 2 - given the interplay between a moves made now and moves made n moves into the future how would the model be able to recognize and make trade-offs between moves which may offer a better position now vs those that offer a position n moves in the future - would one have to extend the board state input to a vector of length 1x64n where n is the total number of moves for expected for an individual player or is this a function of a different algorithm which should be able to capture historical information which training?
I am unsure if I'm overthinking this and am missing something really obvious but I would appreciate any guidance in terms of how to approach thinking about this.