We consider robust resource allocation of services in Clouds. More specifically, we consider the case of a large public or private Cloud platform that runs a relatively small set of large and independent services. These services are characterized by their demand along several dimensions (CPU, memory,...) and by their quality of service requirements, that have been defined through an SLA in the case of a public Cloud or fixed by the administrator in the case of a private Cloud. This quality of service defines the required robustness of the service, by setting an upper limit on the probability that the provider fails to allocate the required quantity of resources. This maximum probability of failure can be transparently turned into a pair (price,penalty). Failures can indeed hit the platform, and resilience is provided through service replication. Our contribution is two-fold. First, we propose a resource allocation strategy whose complexity is logarithmic in the number of resources, what makes it very efficient for large platforms. Second, we propose an efficient algorithm based on rare events detection techniques in order to estimate the robustness of an allocation, a problem that has been proven to be P-complete. Finally, we provide an analysis of the proposed strategy through an extensive set of simulations, both in terms of the overall number of allocated resources and in terms of time necessary to compute the allocation.