In human-in-the-loop systems, humans are often faced with making repeated choices among finite alternatives in response to observations of the evolving system performance. In order to design humans into such systems, it is important to develop a systematic description of human decision making in this context. We examine a commonly used, drift-diffusion, decision-making model that has been fit to human neural and behavioral data in sequential, two-alternative, forced-choice tasks. We show how this model and type of task together can be regarded as a Markov process, and we derive the steady-state probability distribution for choice sequences. Using the analytic expression for this distribution, we prove matching behavior for tasks that exhibit a matching point and we compute the sensitivity of steady-state choices to a model parameter that measures the decision maker's "exploratory" tendency.