Moving target search (MTS) or the game of cops and robbers has a broad field of application reaching from law enforcement to computer games. Within the recent years research has focused on computing move policies for one or multiple pursuers (cops). The present work motivates to extend this perspective to both sides, thus developing algorithms for the target (robber). We investigate the game with perfect information for both players and propose two new methods, named TrailMax and Dynamic Abstract Trailmax, to compute move policies for the target. Experiments are conducted by simulating games on 20 maps of the commercial computer game Baldur's Gate and measuring survival time and computational complexity. We test seven algorithms: Cover, Dynamic Abstract Minimax, minimax, hill climbing with distance heuristic, a random beacon algorithm, TrailMax and DA-TrailMax. Analysis shows that our methods outperform all the other algorithms in quality, achieving up to 98% optimality, while meeting modern computer game computation time constraints.