A curve over a field of characteristic $$p$$ is called ordinary if the $$p$$ torsion of its Jacobian is the largest possible. But what is the probability that a curve is ordinary? I will talk about various perspectives on this question, including some heuristics about how random $$p$$-divisible groups behave. I will also talk about cases for which the answer is known, namely Artin-Schreier and superelliptic curves.