An orchestration is a multi-threaded computation that invokes a number of remote services. In practice, the responsiveness of a web-service fluctuates with demand; during surges in activity service responsiveness may be degraded, perhaps even to the point of failure. An uncertainty profile formalizes a user's perception of the effects of stress on an orchestration of web-services; it describes a strategic situation, modelled by a zero-sum angel-daemon game. Stressed web-service scenarios are analysed, using game theory, in a realistic way, lying between over-optimism (services are entirely reliable) and over-pessimism (all services are broken). The 'resilience' of an uncertainty profile can be assessed using the valuation of its associated zero-sum game. In order to demonstrate the validity of the approach, we consider two measures of resilience and a number of different stress models. It is shown how (i) uncertainty profiles can be ordered by risk (as measured by game valuations) and (ii) the structural properties of risk partial orders can be analysed.