Redistributional issues are important in contemporary welfare states. These issues cannot be analyzed using the median voter theorem because preferences fail single-peakedness: Collective preferences are intransitive, giving rise to cyclical preferences. A suitable instrument for analyzing redistributional issues is the Colonel Blotto game. This game is older than the more familiar prisoner's dilemma, but it has been solved only recently. The article introduces the Colonel Blotto Game as well as the general structure of its solutions. Thereafter, the game's logic is illustrated using several policy examples. The two most fascinating results state that, in a political contest, it is never optimal to use pure strategies, and that the political process itself induces remarkable inequalities. © 2011 Verein für Socialpolitik.