Race is a social construction whose effects are real. Why then, can’t we end race? Here, in order to answer this question, we begin with the proposition that all racial theorizing centers either Black or White but not both. We trace this centering as it is reflected in the Critical Race (center Black) and Neo-assimilation (center White) traditions. We show that, while there is a fixed binary, the meaning of race, such as that race is about ethnicity, or about color, or about colonization, and the internal composition of the Black and White race categories keeps changing. We then show that this occurs because, triangulation, which is the invocation of a third position to explain the binary, invariably reproduces the same centering of Black or of White in a new form. Race, therefore, is a fixed game that can never be won.