We introduce a new distinction between inequality in initial endowments (e.g., ability, inherited wealth) and inequality of what one can obtain as rewards (e.g., prestigious positions, money). We show that, when society allocates resources via tournaments, these two types of inequality have opposing effects on equilibrium behavior and well-being. Greater inequality of rewards hurts most people—both the middle class and the poor—who are forced into greater effort. Conversely, greater inequality of endowments benefits the middle class. Thus, the correctness of our intuitions about the implications of inequality is hugely affected by the type of inequality considered. (JEL D63, D82)