Sampling has become an important strategy for inference in belief networks. It can also be applied to the problem of selecting actions in influence diagrams. In this paper, we present methods with probabilistic guarantees of selecting a near-optimal action. We establish bounds on the number of samples required for the traditional method of estimating the utilities of the actions, then go on to extend the traditional method based on ideas from sequential analysis, generating a method requiring fewer samples. Finally, we exploit the intuition that equally good value estimates for each action are not required, to develop a heuristic method that achieves major reductions in required sample size. The heuristic method is validated empirically.