Previous research on the effects of probability and delay on decision-making has focused on examining each dimension separately, and hence little is known about when these dimensions are combined into a single choice option. Importantly, we know little about the psychological processes underlying choice behavior with rewards that are both delayed and probabilistic. Using a process-tracing experimental design, we monitored information acquisition patterns and processing strategies. We found that probability and delay are processed sequentially and evaluations of risky delayed prospects are dependent on the sequence of information acquisition. Among choice strategies, directly comparing the values of each dimension (i.e., dimension-wise processing) appears to be most favored by participants. Our results provide insights into the psychological plausibility of existing computational models and make suggestions for the development of a process model for risky intertemporal choice.