In this paper, we investigate how people use mental simulations: do people vary the number of simulations that they run in order to optimally balance speed and accuracy? We combined a model of noisy physical simulation with a decision making strategy called the sequential probability ratio test, or SPRT (Wald, 1947). Our model predicted that people should use more samples when it is harder to make an accurate pre- diction due to higher simulation uncertainty. We tested this through a task in which people had to judge whether a ball bouncing in a box would go through a hole or not. We var- ied the uncertainty across trials by changing the size of the holes and the margin by which the ball went through or missed the hole. Both people’s judgments and response times were well-predicted by our model, demonstrating that people have a systematic strategy to allocate resources for mental simulation.