A detailed observational treatment of bidirectional electrons (~50 to 50 eV)in the distant magnetotail (r>100 RE) is presented. It is found that electrons in this energy range commonly exhibit strong, field-aligned anisotropies in the tail lobes. Because of large tail motions, the ISEE 3 data provide extensive sampling of both the north and south lobes in rapid succession. These data demonstrate directly the strong asymmetries that exist between the north and south lobes at any one time. The bidirectional fluxes are found to occur predominantly in the lobe directly connected to the sunward interplanetary magnetic field in the open magnetosphere model (north lobe for away sectors and south lobe for toward sectors). Electron anisotropy and magnetic field data are presented which show the transition from unidirectional (sheath) electron populations to bidirectional (lobe) populations. Thus we demonstrate the open nature of the distant magnetopause and show that the source of the higher-energy, bidirectional lobe electrons is the tailward directed electron heat flux population in the distant magnetosheath. Taken together, the present evidence suggests that the bidirectional electrons that we observe in the distant tail are closely related to the polar rain electrons observed previously at lower altitudes. Furthermore, these data provide strong evidence that the distant tail is composed largely of open magnetic field lines in contradistinction to some recently advanced models.