Based on my extensive pizza eating experience, the average pizza slice is no wider than the distance between my thumb and forefinger, so start by wrapping the string around thumb & forefinger 11 times, leaving a bit dangling at the end. Then gradually expand the distance between the two fingers until the loose bit is eliminated.
I suspect you don't even have to mark the string with a pen (meaning the author possibly overthought the solution). You can just use the gap between your fingers. The chances are that the additional length added by the circumference of your fingers probably compensates for the curvature of the pizza circumference, depending on the size of the pizza and the size of your fingers. If you're doing this regularly you'll quickly learn the appropriate degree of compensation.
