Re: How far off? @Gomez Adams
The drunk can't take a shortcut in this metaphor, because he is bound to his sober friend. The sober friend is the true position of the walker, and the drunk is true position +/- some error. So in a working GPS drunk is always close to sober within the error margins (the high walls on the path.)
In the 10 metre box example, cutting the corner won't decrease the overall length measured as the next measurement is just as likely to be outside the box which increases the distance the error covers. For any path - square, circle or winding lane - the error has a 50/50 chance of being on one side or the other, which is what causes the zigzagging that increases perceived distance.