Scour poses a significant risk to infrastructure placed on mobile seabeds. Seabed mobility is common on the North West Shelf of Australia, in parts of the North Sea, and also occurs in the deepwater Gulf of Mexico, due to loop currents. Scour can undermine structures and, for shallow-skirted mudmat foundations, there can be significant consequences including excessive settlements, tilt and loss of bearing and sliding capacity. However, scour mitigation via engineered protection is costly, and to be avoided if possible. This paper describes a new quantitative risk-based approach for assessing the susceptibility of subsea infrastructure to scour processes. This probabilistic scour assessment accommodates measurable uncertainties in metocean and seabed conditions, using new characterization techniques. The approach allows operators and owners to better assess the optimum strategy to address scour risk, selecting from mitigation during installation or in-service monitoring, prediction and remediation. The paper describes (i) best practice approaches for assessing scour susceptibility and propagation rates with and without engineered protection, (ii) new methods for determining the applicable seabed and metocean inputs, (iii) a probabilistic framework for encompassing uncertainties, and (iv) how this approach can be applied in project applications. Our probabilistic method of assessing and presenting scour risk produces a distribution of estimates of scour depth and time rate. By capturing and quantifying the full range of uncertainties, this method facilitates decision-making by showing the range of potential outcomes and allowing the associated costs and consequences to be evaluated. This approach is superior to deterministic 'worst case' calculations, which are often used to assess scour susceptibility. In summary, this paper provides operators and owners with an improved methodology to unlock Capex and Opex savings through more accurate and informed scour assessments.