When all information is openly available in a decision problem and no biasing factors are manipulated, most people apply compensatory strategies in a quick and seemingly effortless manner. Choices thereby approximate closely a rational naive Bayes solution. In a pre-registered study (n = 212 participants, total = 55,640 choices), we investigated whether this finding also holds under a) increased complexity of the probabilistic inference tasks (6 vs. 12 cues) and b) if we manipulate processing fluency to include a well established biasing factor. Common decision models were compared in terms of their predictive power for choices, confidence, and decision times per individual. Across all levels of complexity and also when taking into account the fluency manipulation, most participants‘ behavior (> 70%) was best described by compensatory strategies. We furthermore show that also under such challenging conditions, a Parallel Constraint Satisfaction (PCS) Model of decision making provided the most accurate predictions of participants’ behavior. The predictive performance of PCS was thereby close to the upper benchmark provided by applying a machine learning approach to cross-predict the data. Accounting for interindividual differences significantly improved predictive accuracy in both the PCS model and the machine learning model, revealing considerable variation concerning the degree to which participants’ choices were affected by processing fluency.