People's choices between prospects with relatively affect‐rich outcomes (e.g., medical side effects) can diverge markedly from their choices between prospects with relatively affect‐poor outcomes (e.g., monetary losses). We investigate the cognitive mechanisms underlying this “affect gap” in risky choice. One possibility is that affect‐rich prospects give rise to more distortion in probability weighting. Another is that they lead to the neglect of probabilities. To pit these two possibilities against each other, we fitted cumulative prospect theory (CPT) to the choices of individual participants, separately for choices between options with affect‐rich outcomes (adverse medical side effects) and options with affect‐poor outcomes (monetary losses); additionally, we tested a simple model of probability neglect, the minimax rule. The results indicated a qualitative difference in cognitive mechanisms between the affect‐rich and affect‐poor problems. Specifically, in affect‐poor problems, the large majority of participants were best described by CPT; in affect‐rich problems, the proportion of participants best described by the minimax rule was substantially higher. The affect gap persisted even when affect‐rich outcomes were supplemented by numerical information, thus providing no support for the thesis that choices in affect‐rich and affect‐poor problems diverge because the information provided in the former is nonnumerical. Our findings suggest that the traditional expectation‐based framework for modeling risky decision making may not readily generalize to affect‐rich choices. Copyright © 2015 John Wiley & Sons, Ltd.