We investigate how the dependence of payoffs affects preferences for redistribution. For a fixed outcome, we experimentally implement and compare a zero-sum world and a setting in which everyone can be simultaneously successful. First, two subjects’ performances in a real effort task translate into chances of gaining a prize. Across treatments we then vary the interdependence of payoffs: either, there is only a single prize, or both subjects can potentially gain a prize at the same time. Afterwards, a third subject can redistribute the prize money. Removing the direct dependency of subjects’ payoffs decreases the average amount of redistribution by 14-22%. If the outcome of the allocation process solely hinges on relative performance and not partially on chance, the role of payoff dependence remains unchanged. However, we find that the mere presence of randomness increases redistribution – even though there is no uncertainty about the (relative) performance of the two subjects.