Structurally complex life and intelligence evolved late on Earth; models for the evolution of global temperature suggest that, due to the increasing solar luminosity, the future life span of the (eukaryote) biosphere will be “only” about another billion years, a short time compared to the ∼4 Ga since life began. A simple stochastic model (Carter, 1983) suggests that this timing might be governed by the necessity to pass a small number, n, of very difficult evolutionary steps, with n < 10 and a best guess of n = 4, in order for intelligent observers like ourselves to evolve. Here I extend the model analysis to derive probability distributions for each step. Past steps should tend to be evenly spaced through Earth's history, and this is consistent with identification of the steps with some of the major transitions in the evolution of life on Earth. A complementary approach, identifying the critical steps with major reorganizations in Earth's biogeochemical cycles, suggests that the Archean-Proterozoic and Proterozoic-Phanerozoic transitions might be identified with critical steps. The success of the model lends support to a “Rare Earth” hypothesis (Ward and Brownlee, 2000): structurally complex life is separated from prokaryotes by several very unlikely steps and, hence, will be much less common than prokaryotes. Intelligence is one further unlikely step, so it is much less common still.