The Algorithm gives a location within a 1°x1° spherical quadrilateral, relative to the quadrilateral's borders. The user picks whichever 1°x1° spherical quadrilateral which they are in.
Certain cities are located across more than one graticule. In most cases, such a city will be divided across two graticules, but Calgary, Alberta, is one of the few cities quartered amongst four. On the xkcd blag, Gylbert suggested  that each week, Calgarians pick the location which is closest to exactly 51°N, 114°W, a spot near the center of the city.
This effectively uses a re-centered graticule, centered on 51°N, 114°W, and bounded by 51°30'N, 113°30'W, 50°30'N and 114°30'W on the North, East, South and West, respectively. Every day, one (and only one) of the four designated locations will fall within this area. Gylbert suggested envisioning this concept as one Mah-Jongg tile covering four other tiles beneath.
The Gylbert Algorithm is not equivalent to running the Algorithm hash on the shifted graticule, which would get you a fifth location different from all four surrounding locations. No one else is likely to be there.
The Gylbert Algorithm may be used at the discretion of individuals, because it does not change the target locations, it merely picks the one closest to the intersection of 51°N and 114°W.