To enable sophisticated interactions between humans and robots in a shared environment, robots must infer the intentions and strategies of their human counterparts. This inference can provide a competitive edge to the robot or enhance human-robot collaboration by reducing the necessity for explicit communication about task decisions. In this work, we identify specific states within the shared environment, which we refer to as Critical Decision Points, where the actions of a human would be especially indicative of their high-level strategy. A robot can significantly reduce uncertainty regarding the human’s strategy by observing actions at these points. To demonstrate the practical value of Critical Decision Points, we propose a Receding Horizon Planning (RHP) approach for the robot to influence the movement of a human opponent in a competitive game of hide-and-seek in a partially observable setting. The human plays as the hider and the robot plays as the seeker. We show that the seeker can influence the hider to move towards Critical Decision Points, and this can facilitate a more accurate estimation of the hider’s strategy. In turn, this helps the seeker catch the hider faster than estimating the hider’s strategy whenever the hider is visible or when the seeker only optimizes for minimizing its distance to the hider.