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Experimental conditions explored the development of fallacious rules and assessed the rates and durations of superstitious responding by children under the influence of standard and second-order response-independent reinforcement. During the presentation of computer-generated math problems, subjects in Experiment 1 had access to a computer and keyboard. Group 1 received second-order, random-time (RT) reinforcement by way of a coin toss graphic procedure (mean reinforcement rate of 1/min). This procedure rendered an effect analogous to a "slot-machine" and matching icons produced monetary reinforcement displayed on the computer screen. A second group obtained response-independent reinforcement according to a standard random-time (RT) 30-s schedule (mean reinforcement rate of 2/min). A control group received no scheduled consequences but was exposed to the same demand conditions. After 10 min, students in all groups answered questions regarding "why" they had performed problems. Subsequently, experimental subjects were exposed to the same conditions for 10 min after which reinforcement was terminated; however, a series of problems remained available for solving. Over the course of the experiment, and particularly during extinction, Group 1 subjects performed at higher rates and longer durations. Experiment 2 replicated Experiment 1, but it examined the effects of second-order response-independent reinforcement on fixed-time (FT) schedules. Students who had been exposed to second-order response-independent reinforcement demonstrated higher rates and longer durations of problem solving. Outcomes suggest that, -independent of FT or RT schedules, second-order response-independent contingencies appear to generate elaborate fallac ious rules and particularly long durations of superstitious responding.