Can you fling the fractal darts?

How many points will you asymptotically approach? - Question: You are playing darts with your friend, Apollonius, who has brought his own dartboard. However, this dartboard is somewhat … different. Instead of being a circle divided into concentric rings and sectors, the dartboard is a unit circle (i.e., with radius $1$) that’s divided via an Apollonian gasket. In...