We ask if participants in a choice experiment with repeated presentation of the same menus and no feedback provision: (i) learn to behave in ways that are closer to the predictions of ordinal and expected utility theory under *strict* preferences
or (ii) exhibit overall behaviour that is consistent with utility theory under *weak* preferences. To answer these questions we designed and implemented a free-choice lab experiment with 15 distinct menus. Each menu contained two, three and four lotteries with three monetary outcomes, and was shown five times. Subjects were not forced to make an active choice at any menu but could avoid/defer doing so at a positive expected cost. Among our 308 subjects from the UK and Germany, significantly more were ordinal- and expected-utility maximizers in their last 15 than in their first 15 identical decision problems. Around a quarter and a fifth of all subjects, respectively, decided in those modes *throughout* the experiment, with nearly half revealing non-trivial indifferences. A considerable overlap is found between those consistently rational individuals and the ones who satisfied core principles of*random* utility theory. Finally, choice consistency is positively correlated with cognitive ability, while subjects who learned to maximize utility were more cognitively able than those who did not. We discuss potential implications of our study's novel set of findings.