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 Regarding randomness by David Shin)

While God may not play dice with the universe, and probability zero is not "impossible", there's also the concept of a normal number, whose digits behave the way we'd expect random numbers to behave.  While I don't think even pi or e have been proved to be normal though they are suspected to be.  You might say, "God knows what numbers are normal", and could use one to determine up, down, left, right. (Odd-Odd = up; odd-even = right; even-even=left; even-odd = down).

Posted by Charlie on 2005-02-09 02:11:30