[gah44]

In the problem, the points are uniform randomly distributed. With a smaller number of points, the gap is, statistically, larger. Given N points, the line that created the classification could be anywhere in the gap. The SVM solution should be close to the center of the gap. My guess is that PLA can also be anywhere in the gap.

Given that, you can see that the SVM solution should be closer more often,
though not so easily to guess how often.