We asked participants to make simple risky choices while we recorded their eye movements. We built a complete statistical model of the eye movements and found very little systematic variation in eye movements over the time course of a choice or across the different choices. The only exceptions were finding more (of the same) eye movements when choice options were similar, and an emerging gaze bias in which people looked more at the gamble they ultimately chose. These findings are inconsistent with prospect theory, the priority heuristic, or decision field theory. However, the eye movements made during a choice have a large relationship with the final choice, and this is mostly independent from the contribution of the actual attribute values in the choice options. That is, eye movements tell us not just about the processing of attribute values, but also are independently associated with choice. The pattern is simple—people choose the gamble they look at more often, independently of the actual numbers they see—and this pattern is simpler than predicted by decision field theory, decision by sampling, and the parallel constraint satisfaction model.