Many psychological studies have shown that human-generated sequences are hardly ever random. However, what remains an open question is the degree to which this (in)ability varies between people and is affected by contextual factors. We used a modern, robust measure of randomness based on algorithmic information theory to assess human-generated series. In S1, we tested the effects of context and mental fatigue on human-generated randomness. In S2, we investigated the effect of mental fatigue on the randomness and the relationship between the need for cognition (NFC) and the ability to produce random-like series. Results of S1 show that the activation of the ability to produce random-like series depends on the relevance of the contextual cues, whether they activate known representations of a random series generator and consequently help to avoid the production of trivial sequences. Our findings from S1 and S2 on the effect of mental fatigue and cognitive motivation demonstrate that regardless of the context or task’s novelty people quickly lose interest in the random series generation. However, people high in the NFC can maintain cognitive motivation for a longer period and consequently on average generate more random series.