Scientific advice is increasingly used to inform policy. Often, experts are asked to give advice when stakes are high, time pressure is severe and uncertainty looms. In such environments, decisions may be guided by instincts and priors, rather than reason. Yet, the extent of these intuitive judgements is unknown. We use a database of fish stock assessments to detect and quantify the systematic tendency to put too much weight on previous information, known as anchoring, in scientific advice. By exploiting exogenous variation in procedures and possibilities to vary model assumptions, we find consistent evidence for intuitive judgement. We find that anchoring is strongest if model choices are flexible and the fish stock is in crisis, potentially increasing pressure and stakes. By providing advice that is biased towards previous results, the stock assessments may be more robust but may also give a false sense of security as more drastic changes may go undetected.