How many e-folds should we expect from high-scale inflation?

We address the issue of how many e-folds we would naturally expect if inflation occurred at an energy scale of order 1016 GeV. We use the canonical measure on trajectories in classical phase space, specialized to the case of flat universes with a single scalar field. While there is no exact analytic expression for the measure, we are able to derive conditions that determine its behavior. For a quadratic potential V(phi) = m(2)phi(2)/2 with m = 2 x 10(13) GeV and cutoff at M-Pl = 2.4 x 10(18) GeV, we find an expectation value of 2 x 10(10) e-folds on the set of Friedmann-Robertson-Walker trajectories. For cosine inflation V(phi) = Lambda(4)[1 - cos(phi/f)] with f = 1.5 x 10(19) GeV, we find that the expected total number of e-folds is 50, which would just satisfy the observed requirements of our own Universe; if f is larger, more than 50 e-folds are generically attained. We conclude that one should expect a large amount of inflation in large-field models and more limited inflation in small-field (hilltop) scenarios.