The following uses 120 evenly spaced angular values, and 120 evenly spaced radial values. The dart throws are random, normalized to a gaussian around the aim point. I averaged 'throws' at each aim point, until the average converges to within 1 part in a thousand. I haven't yet included the possibility of bounce outs, but the next day I have some time free, I'll see about adding that.
I've run a few models for different throwing abilities. The two things that I see immediately are that a beginning thrower does score highest throwing at the bull, and throwing at the triple is always better than throwing at the large part of the number.
The first image is for a 'good' thrower, whose throws are confined to a gaussian with Full Width at Half Max equal to 10 percent of the width of the board.
The second image is for a 'mediocre' thrower, whose throws are confined to a gaussian with FWHM set equal to a quarter of the width of the board.
The final image is for a 'beginner' thrower, whose throws are confined to a gaussian with FHWM set equal to half the diameter of the board.
