I can try to address some of your arguments one by one: > How would you gather labels for every possible board state? It would require 768 factorial labels to

I can try to address some of your arguments one by one: > How would you gather labels for every possible board state? It would require 768 factorial labels to represent every possibility. You don't need to represent every possibility. Just a sufficiently large dataset and a neural network with a sufficient amount of prior and size. Note that e.g. video continuation networks already exist and deals with comparable data sizes. > But game of life is nothing like that. Every board is a valid board. Yes, but given the previous board (or the board N steps ago) there is only one valid board. Hence, a supervised learning problem. > Without self-play, your learned network will always overfit or underfit different scenarios. This confuses me. Why do you think self-play avoids over- and underfitting? How could one approach even solve both over- and underfitting at the same time? > Minesweeper is another example: it's possible to win every game using nothing but logic (disregarding tiebreakers), so therefore the solution is known. But I don't think it can be formulated as a supervised learning problem. Sure it can. If the solution is known, just train a neural network to mimic the solution. That's what network distillation is all about.