Both normative and many descriptive theories of decision making under risk are based on the notion that outcomes are weighted by their probability, with subsequent maximization of the (subjective) expected outcome. Numerous investigations from psychology, economics, and neuroscience have produced evidence consistent with this notion. However, this research has typically investigated choices involving relatively affect-poor, monetary outcomes. We compared choice in relatively affect-poor, monetary lottery problems with choice in relatively affect-rich medical decision problems. Computational modeling of behavioral data and model-based neuroimaging analyses provide converging evidence for substantial differences in the respective decision mechanisms. Relative to affect-poor choices, affect-rich choices yielded a more strongly curved probability weighting function of cumulative prospect theory, thus signaling that the psychological impact of probabilities is strongly diminished for affect-rich outcomes. Examining task-dependent brain activation, we identified a region-by-condition interaction indicating qualitative differences of activation between affect-rich and affect-poor choices. Moreover, brain activation in regions that were more active during affect-poor choices (e.g., the supramarginal gyrus) correlated with individual trial-by-trial decision weights, indicating that these regions reflect processing of probabilities. Formal reverse inference Neurosynth meta-analyses suggested that whereas affect-poor choices seem to be based on brain mechanisms for calculative processes, affect-rich choices are driven by the representation of outcomes' emotional value and autobiographical memories associated with them. These results provide evidence that the traditional notion of expectation maximization may not apply in the context of outcomes laden with affective responses, and that understanding the brain mechanisms of decision making requires the domain of the decision to be taken into account.