Abstract: Single-particle escape in tri-stellar gravitational systems is investigated using large ensembles of direct integrations that sample broad ranges of initial specific energy E and angular momentum L. It constructs outcome maps over (E, L) and interprets their structure with the aid of a co-rotating (synodic) frame, where the Jacobi-like integral and zero-velocity surfaces (ZVS) provide geometric diagnostics of accessible channels near the classical L1, 2 necks. Two outcome regimes emerge robustly across our experiments: (i) prompt ejection following a single strong passage and (ii) long-lived chaotic transients that persist for many binary periods before escaping. Ensemble statistics show an early-time peak in escape events accompanied by a heavy tail in residence times. The escape probability increases systematically with higher initial energy and lower angular momentum, reflecting the combined roles of surplus kinetic energy and a reduced centrifugal barrier. By coarse-graining the (E, L) plane, it resolves fractal-like escape basins bounded by trapped regions, consistent with sensitive dependence on initial conditions. Throughout, Jacobi/ZVS arguments are used as geometric guides rather than strict invariants, allowing a unified description that connects inertial-frame energy criteria to rotating-frame accessibility. The approach is intentionally minimal—Newtonian point masses and idealized initial families—yet yields practical summaries for evaporation, capture/escape statistics, and rapid screening of initial conditions in multi-body environments.