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Autonomous drone racing pushes the bound- aries of high-speed motion planning and multi-agent strategic decision-making. Success in this domain requires drones not only to navigate at their limits but also to anticipate and counteract competitors’ actions. In this paper, we study a fundamental question that arises in this domain: how deeply should an agent strategize before taking an action? To this end, we compare two planning paradigms: the Model Predictive Game (MPG), which finds interaction-aware strategies at the expense of longer computation times, and contouring Model Predictive Control (MPC), which computes strategies rapidly but does not reason about interactions. We perform extensive experiments to study this trade-off, revealing that MPG out- performs MPC at moderate velocities but loses its advantage at higher speeds due to latency. To address this shortcoming, we propose a Learned Model Predictive Game (LMPG) approach that amortizes model predictive gameplay to reduce latency. In both simulation and hardware experiments, we benchmark our approach against MPG and MPC in head-to-head races, finding that LMPG outperforms both baselines.