How often does a randomly chosen variety have a point? Answering this question depends on the family of varieties in question, how we decide to order them, and what kinds of points we are looking for. Motivated by rational points, we endeavor to explicitly describe how often a randomly chosen variety is everywhere locally soluble. When our family is described by the fibers of a suitable morphism, this likelihood is equal to the product of local probabilities at each place and in some cases may be computed exactly. In particular, in joint work with Lea Beneish we find that for almost 97% of integral binary sextic forms f(x,z), the superelliptic curve y^3 = f(x,z) is everywhere locally soluble, with the local factors described explicitly by rational functions. Time permitting, we will discuss ongoing work on determining how often a cubic hypersurface has a rational point.