I had claude code implement minimax (w/ alpha-beta pruning) for the general n cells version of the game.

I checked n=6...20. It looks like white wins for n=6 and n=8 with perfect play, otherwise it is a draw.

With random play, black seems to have the edge regardless of board size. About 2/3 of the games end in a draw, but black wins 20% and white 13%.