Abstract-Games are one of the most popular and at the same time most computation intensive and energy consuming class of applications on mobile devices like smartphones and tablets. Dynamic voltage and frequency scaling (DVFS) is a common technique for reducing the processing power. However, highly variable and non-deterministic workload characteristics of mobile games mandate sophisticated workload prediction models to predict low-utilization phases of games during which the processor's frequency can be decreased to save energy. While prior works exhibit significant improvements, one main question is left open: How large is the gap between the developed techniques and the theoretically optimal power manager, i.e., a power manager which exactly knows the future workload and, hence, can select the optimal sequence of frequencies that minimizes the power consumption under given timing constraints. In this paper, we discuss that estimating the savings from such an optimal power manager is non-trivial due to the non-deterministic nature of games and the underlying system. In order to address this, we suggest a statistical model of the optimal power manager using which we estimate the potential savings of popular closed-source games. The results of our work have several implications: We reveal a significant gap between savings obtained from recently proposed game power managers and the theoretically optimum savings (up to 54.4 % energy savings are possible). Our work strongly motivates future research endeavors to minimize the gap between the optimum and the existing power managers.