Humans have great difficulty comparing quotients including fractions, proportions, and probabilities and often erroneously isolate the whole numbers of the numerators and denominators to compare them. Some have argued that the whole number bias is a compensatory strategy to deal with difficult comparisons. We examined adult humans' preferences for gambles that differed only in numerosity, and not in factors that influence their expected value (probabilities and stakes). Subjects consistently preferred gambles with more winning balls to ones with fewer, even though the probabilities were mathematically identical, replicating prior results. In a second experiment, we found that subjects accurately represented the relative probabilities of the choice options during rapid nonverbal probability judgments but nonetheless showed biases based on whole numbers. We mathematically formalized and quantitatively evaluated cognitive rules based on existing hypotheses that attempt to explain subjects' whole number biases during quotient comparisons. The results show that the whole number bias is intrinsic to the way humans solve quotient comparisons rather than a compensatory strategy. (PsycINFO Database Record