Ad hoc teamwork exists when a team of agents needs to cooperate without being able to communicate or use coordination schemes that were designed a-priori. Sometimes ad hoc teamwork amounts to acting so as to bring out the best in your teammates by “leading” them to the optimal joint action. Doing so can be challenging even when their behavior is fully known. In this paper, we take the challenge to the next level by considering the situation in which there is uncertainty about the teammates’ behaviors. We discuss the problem of recursive modeling of the teammate’s uncertain behavior in two-agent teams and conclude not only that the depth that is useful to model is bounded, but also the number of models useful to consider is linear in the number of actions (and not exponential, as expected). We then show that adopting a naive perspective might lead to negative long-term results in large teams, and thus introduce REACT, an algorithm for determining the action an agent should perform in order to maximize the team’s expected utility. Finally, we show empirically that in randomly generated utility matrices, using REACT to select actions outperforms making incorrect assumptions about the identities of teammates.