Traditional game-theoretic research for security applications primarily focuses on the allocation of external protection resources to defend targets. This work puts forward the study of a new class of games centered around strategically arranging targets to protect them against a constrained adversary, with motivations from varied domains such as peacekeeping resource transit and cybersecurity. Specifically, we introduce Escape Sensing Games (ESGs). In ESGs, a blue player manages the order in which targets pass through a channel, while her opponent tries to capture the targets using a set of sensors that need some time to recharge after each activation. We present a thorough computational study of ESGs. Among others, we show that it is NP-hard to compute best responses and equilibria. Nevertheless, we propose a variety of effective (heuristic) algorithms whose quality we demonstrate in extensive computational experiments.