Abstract In probabilistic and nonstationary environments, individuals must use internal and external cues to flexibly make decisions that lead to desirable outcomes. To gain insight into the process by which animals choose between actions, we trained mice in a task with time-varying reward probabilities. In our implementation of such a “two-armed bandit” task, thirsty mice use information about recent action and action-outcome histories to choose between two ports that deliver water probabilistically. Here, we comprehensively modeled choice behavior in this task, including the trial-to-trial changes in port selection – i.e. action switching behavior. We find that mouse behavior is, at times, deterministic and, at others, apparently stochastic. The behavior deviates from that of a theoretically optimal agent performing Bayesian inference in a Hidden Markov Model (HMM). We formulate a set of models based on logistic regression, reinforcement learning, and ‘sticky’ Bayesian inference that we demonstrate are mathematically equivalent and that accurately describe mouse behavior. The switching behavior of mice in the task is captured in each model by a stochastic action policy, a history-dependent representation of action value, and a tendency to repeat actions despite incoming evidence. The models parsimoniously capture behavior across different environmental conditionals by varying the ‘stickiness’ parameter, and, like the mice, they achieve nearly maximal reward rates. These results indicate that mouse behavior reaches near-maximal performance with reduced action switching and can be described by a set of equivalent models with a small number of relatively fixed parameters. Significance To obtain rewards in changing and uncertain environments, animals must adapt their behavior. We found that mouse choice and trial-to-trial switching behavior in a dynamic and probabilistic two-choice task could be modeled by equivalent theoretical, algorithmic, and descriptive models. These models capture components of evidence accumulation, choice history bias, and stochasticity in mouse behavior. Furthermore, they reveal that mice adapt their behavior in different environmental contexts by modulating their level of ‘stickiness’ to their previous choice. Despite deviating from the behavior of a theoretically ideal observer, the empirical models achieve comparable levels of near-maximal reward. These results make predictions to guide interrogation of the neural mechanisms underlying flexible decision-making strategies.