Abstract. We study strategy synthesis for stochastic two-player games with multiple objectives expressed as a conjunction of LTL and expected total reward goals. For stopping games, the strategies are constructed from the Pareto frontiers that we compute via value iteration. Since, in general, infinite memory is required for deterministic winning strategies in such games, our construction takes advantage of randomised memory updates in order to provide compact strategies. We implement our methods in PRISM-games, a model checker for stochastic multi-player games, and present a case study motivated by the DARPA Urban Challenge, illustrating how our methods can be used to synthesise strategies for high-level control of autonomous vehicles.