Just goes to prove that there are always multiple logical pathways to solve a problem.
My first question to myself when I saw your post was, "What constitutes a valid hit, and how to give at least a 50-50 chance?"
The +2 actually made it pretty easy to win consistently. Using just the Width of the cone would mean touching, because the cone is the smaller of the circles and touching would be the sum of the two radii. Also makes it pretty hard to win without changing other stuff.