This reminds me of two things. The first is the intro to statistics exercise on how you can't have uniform probability on a continuous domain, since you will almost surely miss any particular point on the board. It is often illustrated with dart boards, and caused me great consternation once.

The second is that in my experience, dart throws aren't normally distributed: they're skewed towards the bottom, because I don't throw very hard. I wonder if that effect goes away with practise.