Intracellular transport is mediated by molecular motors that pull cargos along cytoskeletal filaments. Many cargos move bidirectionally and are transported by two teams of motors which move into opposite directions along the filament. We have recently introduced a stochastic tug-of-war model for this situation. This model describes the motion of the cargo as a Markov process on a two-dimensional state space defined by the numbers of active plus and active minus motors. In spite of its simplicity, this tug-of-war model leads to a complex dependence of the cargo motility on the motor parameters. We present new numerical results for the dependence on the number of involved motors. In addition, we derive a simple and intuitive sharp maxima approximation, from which one obtains the cargo motility state from only four simple inequalities. This approach provides a fast and reliable method to determine the cargo motility.