Preference for working on variable schedules and temporal discrimination were simultaneously examined in two experiments using a discrete-trial, concurrent-chains arrangement with fixed interval (FI) and random interval (RI) terminal links. The random schedule was generated by first sampling a probability distribution after the programmed delay to reinforcement on the FI schedule had elapsed, and thus the RI never produced a component schedule value shorter than the FI and maintained a rate of reinforcement half that of the FI. Despite these features, the FI was not strongly preferred. The probability of obtaining the smallest programmed delay to reinforcement on the RI schedule was manipulated in Experiment 1, and the interaction of this probability and initial link length was examined in Experiment 2. As the probability of obtaining small values in the RI increased, preference for the schedule increased while the discriminated time of reinforcer availability in the terminal link decreased. Both of these effects were attenuated by lengthening the initial links. The results support the view that in addition to the delay to reinforcement, the probability of obtaining a short delay is an important choice-affecting variable that likely contributes to the robust preferences for variable, as opposed to fixed, schedules of reinforcement. (Contains 2 tables and 6 figures.)