We introduce a heuristic called pseudocontingencies (PCs) as an alternative account of various stereotyping phenomena. PCs give rise to the expectation that attributes are correlated based solely on asymmetries in attribute base rates. Attributes that are encountered frequently and attributes that are encountered rarely are perceived to be correlated with each other. Such differences in information densities are typical of many stereotyped targets, including the self vs. others, the in-group vs. out-groups and majority vs. minority groups. Evidence is reviewed for PCs underlying illusory correlations, confirmation biases, gender stereotypes, Simpson's paradox, and in procedures used for implicit stereotype measurement. PCs are shown to predict specific patterns of self-enhancement and self-depreciation, the effects of intergroup contact on in-group biases and the readiness to infer stereotypes from aggregated "big-data". Although PCs can lead to seriously flawed stereotypic expectations, they afford an efficient and possibly adaptive inference strategy.