There is some literature on this, yes. I don't know quite how general it gets. See for example several books by Elwyn Berlekamp. One outcome of this work was

There is some literature on this, yes. I don't know quite how general it gets. See for example several books by Elwyn Berlekamp. One outcome of this work was Berlekamp (IIRC) solving a small class of endgame problem that has eluded professional (full-time) go players for literally hundreds of years.