Animal choices depend on direct sensory information, but also on the dynamic changes in the magnitude of reward. In visual discrimination tasks, the emergence of lateral biases in the choice record from animals is often described as a behavioral artifact, because these are highly correlated with error rates affecting psychophysical measurements. Here, we hypothesized that biased choices could constitute a robust behavioral strategy to solve discrimination tasks of graded difficulty. We trained mice to swim in a two-alterative visual discrimination task with escape from water as the reward. Their prevalence of making lateral choices increased with stimulus similarity and was present in conditions of high discriminability. While lateralization occurred at the individual level, it was absent, on average, at the population level. Biased choice sequences obeyed the generalized matching law and increased task efficiency when stimulus similarity was high. A mathematical analysis revealed that strongly-biased mice used information from past rewards but not past choices to make their current choices. We also found that the amount of lateralized choices made during the first day of training predicted individual differences in the average learning behavior. This framework provides useful analysis tools to study individualized visual-learning trajectories in mice.