Worldwide transport projects repeatedly exceed their budgets. This problem has received widespread attention over several decades, with little progress made to improve project cost performance. Consequently, this has led to the emergence of the following recurring question: How can public agencies responsible for delivering transport projects improve the estimation accuracy of their actual construction costs? We use the metaphor of the Sisyphean task to assist us in suggesting that the conflation of risk and uncertainty results in an inability to estimate actual construction costs accurately. Ambiguity aversion, an illusion of certainty, and the repeated occurrence of cost deviations, as demonstrated by our illustrative example and analysis of the elemental cost models of 39 transport projects, collectively create a Sisyphean loop that is impossible to break. Thus, we question the prevailing conceptualisation and treatment of risk and uncertainty used to estimate the actual construction costs of projects. We offer a new theoretical lens framed around ecologically rational heuristics and provide suggestions to reconceptualize and recalibrate the treatment and assessment of uncertainty in cost estimates. We hope this paper provides a much-needed circuit breaker to public agencies’ prevailing treatment of risk and uncertainty and stimulates new lines of inquiry to improve the cost performance of transport projects.