The game of life is interesting, because it's not reversible. It would then be possible to design an AI that does something (brings happiness to a small child or whatever) such that in a million iterations, the board is exactly as it would have been had the AI not existed.

But yes, counting the squares different might work in theory, though it might be too chaotic to be much use in practice. In our world, we use 'chaos' to get non-reversiblity, and coarse graining to measure the deviation.