A web-service is a remote computational facility which is made available for general use by means of the internet. An orchestration is a multi-threaded computation which invokes remote services. In this paper game theory is used to analyse the behaviour of orchestration evaluations when underlying web-services are unreliable. Uncertainty profiles are proposed as a means of defining bounds on the number of service failures that can be expected during an orchestration evaluation. An uncertainty profile describes a strategic situation that can be analyzed using a zero-sum angel-daemon game with two competing players: an angel whose objective is to minimize damage to an orchestration and a daemon who acts in a destructive fashion. An uncertainty profile is assessed using the value of its angel daemon game. It is shown that uncertainty profiles form a partial order which is monotonic with respect to assessment.