Alice and Bob play a game with an 8×8 grid of lights, all initially on. They take turns choosing a light which is on and turning it off, with Alice going first. However, the grid is rigged such that choosing a light toggles the entire 3×3 square to its bottom and left. Therefore, nine lights are toggled each turn, unless the selected light is close to the bottom or left border. If a player turns off all the lights, they lose.
Does this game favor Alice or Bob?
What is the optimal strategy of the winning player?