Growing evidence suggests that behavioral variability plays a critical role in how humans manage the tradeoff between exploration and exploitation. In these decisions a little variability can help us to overcome the desire to exploit known rewards by encouraging us to randomly explore something else. Here we investigate how such 'random exploration' could be controlled using a drift-diffusion model of the explore-exploit choice. In this model, variability is controlled by either the signal-to-noise ratio with which reward is encoded (the 'drift rate'), or the amount of information required before a decision is made (the 'threshold'). By fitting this model to behavior, we find that while, statistically, both drift and threshold change when people randomly explore, numerically, the change in drift rate has by far the largest effect. This suggests that random exploration is primarily driven by changes in the signal-to-noise ratio with which reward information is represented in the brain.