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 Gambling and Charity by David Shin)

When you gamble and feel your position is getting weaker, then the thought behind it is: Well if I'm gone loose, let's give it to charity, then at least they benefit.
I looked at WordVision and they indeed have a lot to offer. Problem is that they are not represented over here and money transfer costs will eat away most or all of my $20, so I'll give it to Médecins sans Frontières. 

Although you will have to refund me if my questions are unanswered.
Wait: I just saw the light: God is indeed allowed to give an infinite list, as long as it is only necessary to complete part of it before getting out.  Stronger: it would have to be an infinte list.

David, I have one more question you probably can answer right away.  A couple of years ago I read about the Devil and God playing another game.  On an infinite chessboard, the Devil does one unit moves, then God places one unit walls.  The question was: Is it possible to capture the Devil?  At that moment, math science did not have an answer yet to the problem, is it solved now?

Thanks to Ken Haley for putting up the work in answering me.

Posted by Hugo on 2005-02-16 18:36:58