There's an old problem concerning an old drunken person who is so sloshed he can't walk properly: he's got a 50/50 chance of stepping a metre forwards; otherwise he moves a metre backwards. It can be shown that he winds up where he started infinitely many times and that his average displacement from the origin is zero. Let's say that his displacement from the origin is positive in the forward direction and negative in the backwards direction. Now suppose we put a wall at the origin so that he can't move into the negative area. If he's at zero and tries to move backwards he just stays where he is. What then is his average displacement? I have a feeling it's a positive constant but have no idea how to go about showing that. Does anyone have any ideas?