While most of crystalline wide gap oxides are both stoichiometric and insulating, a handful of them including ZnO and In2O3 are naturally anion-deficient and electron conductors. Even fewer of the oxides are naturally cation-deficient and hole conductors, the arch-type of which is Cu2O. Based on first principles calculation of equilibrium nonstoichiometry and defect stability, we explain why the Cu(I)(d10) oxide-based materials are both p-type and naturally cation-deficient, and why cation vacancies lead to delocalized, conductive states, whereas in other oxides (e.g., ZnO and MgO), they lead to localized, nonconductive states.