People simulating a random generator fail in the rate of each event, which is too close to the theoretical rate, and in overalternation between events. It is suggested that both failures stem from attempts to produce within short-term memory (STM) limitations a typical sequence in the standard task. 398 Ss of 3 age groups performed 3 coin-tossing tasks: standard, guessing, and guessing with feedback. The proportion of events was more variable and alternation rate was higher in the guessing than in the standard task. High alternation rates are shown to be by-products of typical sequences. An estimate of the window size within which people operate highly correlated with age (corresponding to changes in STM capacity), further supporting the typicality assumption. People's grasp of randomness is therefore concluded to be better than hitherto believed.