The relationship between positive and negative reinforcement and the symmetry of Thorndike's law of effect are unresolved issues in operant psychology. Here we show that, for a given pattern of responding on variable interval (VI) schedules with the same programmed rate of food rewards (positive reinforcement VI) or electric shocks (negative reinforcement VI), there is a fundamental mathematical equivalence between reward gain and shock reduction. We also provide the first normative account of how animals should respond on a negative VI schedule, showing that it is better to space responses evenly than to respond with a variable inter-response time (IRT). Published data from rats, however, indicate that these animals respond irregularly, often with a burst of activity immediately following a shock. While this is irrational in the experimental setting, it may represent an appropriate response to the heterogeneity of stimuli commonly encountered in natural environments. We discuss the broader implications of our analysis for understanding how animals evaluate appetitive and aversive stimuli. (Contains 4 figures.)