  Let x and y be points in a billiard table M that is bounded by a curve sigma.
We assume that sigma is a simple closed C^r curve with positive curvature,
where r is at least 2. A subset B of M\{x,y} is called a blocking set for the
pair (x,y) if every billiard path in M from x to y passes through a point in B.
If a finite blocking set exists, the pair (x,y) is called secure in M; if not,
it is called insecure. We show that for the generic (in the sense of Baire
category) curve sigma, the generic pair of interior points is insecure.
