Medicaid was primarily designed to protect and insure the poor. However, the poor tend to live much shorter lifespans and thus incur much lower medical expenses before death. In this paper, we assess the insurance and redistributive properties of Medicaid, taking these dimensions of heterogeneity into account for single retirees. The Medicaid recipiency rate for those at the bottom income quintile stays around 60%-70% throughout their retirement. In contrast, Medicaid recipiency by higher-income retirees is much lower but increases by age, especially after age 90. Our preliminary results show that the annuity value of Medicaid payments is a hump-shaped function of permanent income. People in the middle of the income distribution receive more than those at the top or the bottom. Once one takes into account that the rich live longer, Medicaid is even less redistributive: in terms of present discounted value, the richest people receive almost as much the poorest ones, and the middle income people still benefit the most. Accounting for risk makes Medicaid less redistributive further still. Compensating differential calculations show that Medicaid insurance is valued most highly by the most rich, who have the most to lose.