Human beings perform well in uncertain environments, matching the performance of complex probabilistic models in complex tasks such as language or physical system prediction. Yet people’s judgments about probabilities also display well-known biases. How can this be? Recently cognitive scientists have explored the possibility that the same sampling algorithms that are used in computer science to approximate complex probabilistic models are also used in the mind and the brain. We the review experimental evidence that characterises the human sampling algorithm, and discuss how such an algorithm could potentially explain apects of the movement of asset prices in financial markets. We also discuss how many of the biases that people display may be the direct result of using only a small number of samples, but using them efficiently. As human beings make successful real-time decisions using only rough estimates of uncertainty, this suggests that machine intelligence could do the same.