We analyze the reallocations of educational expenditures required to equalize opportunities across types of individuals using the theory developed in Roemer (1998). Based on data for black and white men from the national Longitudinal Survey of Young Men, we find that equalizing opportunity between races would require spending six to ten times as much on blacks as on whites. Efficiency losses from such a policy would be modest. However, this reallocation of spending per pupil would require either large expansions of total educational expenditures or large reductions in spending for white students, were school budgets held constant. We calculate, as well, optimal allocations of education, and on a two-type analysis that conditions of parental education alone. Strikingly, the optimal equal-opportunity policy in the case that ignores race, but conditions on parental education, leaves the distribution of black workers across earnings quintiles virtually unchanged, a finding with implications for the recent trend in California and Texas toward dropping race as a relevant factor in affirmative action policy.