The spatiotemporal game between predators and prey is a fundamental process governing their distribution dynamics. Players may adopt different tactics as the associated costs and benefits change through time. Yet few studies have investigated the potentially simultaneous and dynamic nature of movement tactics used by both players. It is particularly unclear to what extent perceived predation risk mediates the fine‐scale distribution of large and dangerous prey, which are mostly driven by bottom–up, resource‐related processes. We built habitat use and movement models based on 10 years of monitoring GPS‐collared grey wolves Canis lupus and plains bison Bison bison bison in Prince Albert National Park, Canada, to investigate the predator–large prey game in a multi‐prey system. Bison did not underuse patches of high‐quality vegetation at any time during the seasonal cycle even though wolves were selectively patrolling these areas. Rather, in at least one season, bison engaged in complex tactics comprised of proactive responses to the long‐term distribution (risky places) and reactive responses to the immediate proximity (risky times) of their opponent. In summer–autumn, bison reduced the time spent in food‐rich patches as both the long‐term use and the immediate proximity of wolves increased. By demonstrating that wolf distribution triggers patch abandonment by bison, we provide a key element in support of the shell game hypothesis – where prey move constantly to avoid predators attempting to anticipate their location. In winter, a season of relatively high energetic stress, bison no longer abandoned food‐rich patches as predation risk increased, while no bison responses to wolves were observed in spring–summer. Our work demonstrates the highly dynamic and complex nature of the predator–large prey spatiotemporal game, a key trait‐mediated mechanism by which trophic interactions structure ecological communities.