Due to the recent remarkable advances in artificial intelligence, researchers have begun to consider challenging learning problems such as learning to generalize behavior from large offline datasets or learning online in non-Markovian environments. Meanwhile, recent advances in both of these areas have increasingly relied on conditioning policies on large context lengths. A natural question is if there is a limit to the performance benefits of increasing the context length if the computation needed is available. In this work, we establish a novel theoretical result that links the context length of a policy to the time needed to reliably evaluate its performance (i.e., its mixing time) in large scale partially observable reinforcement learning environments that exhibit latent sub-task structure. This analysis underscores a key tradeoff: when we extend the context length, our policy can more effectively model non-Markovian dependencies, but this comes at the cost of potentially slower policy evaluation and as a result slower downstream learning.