Subjective expected utility, prospect theory and most other formal models of decision making under uncertainty are probabilistic: they assume that in making choices people judge the likelihood of relevant uncertainties. Clearly, in many situations people do indeed judge likelihood. However, we present studies suggesting that there are also many situations in which people do not judge likelihood and instead base their decisions on intuitively generated, non-probabilistic rules or rationales. Thus, we argue that real-world situations are of two types. In situations eliciting a probabilistic mindset, people rely on judgments of likelihood. In situations eliciting a non-probabilistic mindset, they neglect judgments of likelihood. We suggest three factors that may inXuence the tendency towards either probabilistic or non-probabilistic mindsets. We also outline how extant probabilistic theories may be complemented by non-probabilistic models. © 2006 Elsevier Inc. All rights reserved.