Classical models of perceptual decision-making assume that subjects use a single, consistent strategy to form decisions, or that decision-making strategies evolve slowly over time. Here we present new analyses suggesting that this common view is incorrect. We analyzed data from mouse and human decision-making experiments and found that choice behavior relies on an interplay among multiple interleaved strategies. These strategies, characterized by states in a hidden Markov model, persist for tens to hundreds of trials before switching, and often switch multiple times within a session. The identified decision-making strategies were highly consistent across mice and comprised a single 'engaged' state, in which decisions relied heavily on the sensory stimulus, and several biased states in which errors frequently occurred. These results provide a powerful alternate explanation for 'lapses' often observed in rodent behavioral experiments, and suggest that standard measures of performance mask the presence of major changes in strategy across trials.