We find that free-floating planets can remain bound to an open cluster for much longer than was previously calculated: of the order of the cluster half-mass relaxation timescale as opposed to the crossing time. This result is based on N-body simulations performed with the new GRAPE-6 special purpose hardware and is important in the context of the preliminary detection of a population of free-floating, substellar objects in the globular cluster M22. The planets in our N-body study are of Jupiter mass and are initially placed in circular orbits of between 0.05 and 50 AU about a parent star whose mass is chosen from a realistic initial mass function. The presence of the free-floating planets is the result of dynamical encounters between planetary systems and the cluster stars. Most planets are liberated from their parent star in, or near, the cluster core, and then drift outward on a timescale of similar to10(8)-10(9) yr. This still implies the existence of many (similar to100) planets per star if the M22 result is confirmed.