God and the Devil decide to play a game. God will start by picking an infinite sequence of moves of the form "left", "right", "up", and "down". The Devil responds by creating a finite maze with an exit and by placing God somewhere inside. God then follows His pre-selected sequence to traverse the maze. Unmakable moves are ignored; for example, if the next move is "left" and there is a wall to the left of the current square, God goes on to the next move in the sequence without moving.
If God escapes the maze in finite time, He wins. Otherwise, the Devil wins.
Assuming both agents act optimally, who will win?
(assume that the maze is formed by deleting some edges from a rectangular grid, and that it has no isolated regions; i.e., it is always possible to get to the exit from any point inside the maze)
(In reply to re: Regarding randomness
Hmm, this is an interesting thought. You still need to prove that normality leads to a guaranteed exit from any maze - John hinted at such a proof in his earlier posts.