This paper reports the results of a ‘probabilistic dictator game’ experiment in which subjects were given an option to share chances to win a prize with a dummy player. Using a within-subject design we manipulated two aspects of the decision, the relative cost of sharing and the nature of the lottery: the draws were either independent for the two players (‘noncompetitive’ condition) or one's success meant other's failure (‘competitive’ condition). We also asked for decisions in a standard, non-probabilistic, setting. The main results can be summarized as follows: first, a substantial fraction of subjects do share chances to win, also in the competitive treatments, thus showing concern for the other player that cannot be explained by outcome-based models. Second, subjects share less in the competitive treatment than in other treatments, indicating that procedural fairness alone cannot explain the data. Overall, these results suggest that models aiming at generalizing social concerns to risky environments will have to rely on a mix of distributive and procedural fairness.