What makes sense to me is to think about something that DOESN'T roll.
Suppose I start in Greenwich, walk - without rolling - down the prime meridian to the south pole, up the international date line to the north pole, and back down the prime meridian to Greenwich.
How many rotations do I go through? One. I get a full rotation because I've followed the earth's curvature all the way around the globe once, even though I'm walking straight without rolling.
So the answer is "how many rotations due to rolling" plus "one bonus rotation for passing around the curvature of the circle."
Suppose I start in Greenwich, walk - without rolling - down the prime meridian to the south pole, up the international date line to the north pole, and back down the prime meridian to Greenwich.
How many rotations do I go through? One. I get a full rotation because I've followed the earth's curvature all the way around the globe once, even though I'm walking straight without rolling.
So the answer is "how many rotations due to rolling" plus "one bonus rotation for passing around the curvature of the circle."