Accurate decisions require knowledge of prior probabilities (e.g., prevalence or base rate), but it is unclear how prior probabilities are learned in the absence of a teacher. We hypothesized that humans could learn base rates from experience making decisions, even without feedback. Participants made difficult decisions about the direction of dynamic random dot motion. Across blocks of 15-42 trials, the base rate favoring left or right varied. Participants were not informed of the base rate or choice accuracy, yet they gradually biased their choices and thereby increased accuracy and confidence in their decisions. They achieved this by updating knowledge of base rate after each decision, using a counterfactual representation of confidence that simulates a neutral prior. The strategy is consistent with Bayesian updating of belief and suggests that humans represent both true confidence, which incorporates the evolving belief of the prior, and counterfactual confidence, which discounts the prior.