Human beings do assess probabilities. Their judgments are however sometimes at odds with probability theory. One possibility is that human cognition is imperfect or flawed in the probability domain, showing biases and errors. Another possibility, that we explore here, is that human probability judgments do not rely on a weak version of probability calculus, but rather on complexity computations. This hypothesis is worth exploring, not only because it predicts some of the probability ‘biases’, but also because it explains human judgments of uncertainty in cases where probability calculus cannot be applied. We designed such a case in which the use of complexity when judging uncertainty is almost transparent.