The study of social justice asks: what sorts of social arrangements are equitable ones? But also: how do we derive the inequitable arrangements we often observe in human societies? In particular, in spite of explicitly stated equity norms, categorical inequity tends to be the rule rather than the exception. The cultural Red King hypothesis predicts that differentials in group size may lead to inequitable outcomes for minority groups even in the absence of explicit or implicit bias. We test this prediction in an experimental context where subjects divided into groups engage in repeated play of a bargaining game. We ran 14 trials involving a total of 112 participants. The results of the experiments are statistically significant and suggestive: individuals in minority groups in these experiments end up receiving fewer resources than those in majority groups. Combined with previous theoretical findings, these results give some reason to think that the cultural Red King may occur in real human groups.