Prime Rib versus New York Strip Roast
I know many people say the same thing over and over for questions like this, but: Probe thermometer.  They aren't expensive.  You can set them for a temperature so that you pull your roast at exactly the doneness you want.  (Well, generally pull it a few degrees below that, and let it coast upward while it rests.)

Heat transfer to roasts does not mathematically work out very well for "time per pound" formulas -- generally these only seem to "work" for a certain range of weights, but they don't work in general.  Adding in an uncontrolled "leave oven shut" (presumably turned off?) makes the method even more prone to imprecision.

Bottom line: Use a probe thermometer.  It makes no sense to risk screwing up a $100+ cut of beef rather than buy a $20 thermometer which you can reuse every time and always be certain of results.