We explore the ability to distinguish random from non-random events without invoking the randomness concept. Randomness is defined in terms of radioactive decay whereas non-randomness is quantified by excess repetitions (i.e., repeat) or alternations between successive bits (i.e., switch). In four experiments, participants completed tasks including identifying the boundary between random and non-random textures, distinguishing random from non-random movement, learning to classify patterns, and tracking changes in successive matrices. Importantly, in task instructions, no mention was made of randomness, probability, or related concepts. We found superior performance in distinguishing random stimuli from repeat stimuli compared to switch stimuli. Moreover, memory for repeat stimuli declined as stimuli became more random, whereas memory for switch stimuli did not vary with the degree of non-randomness.