When choosing to be almost certain of winning can be better than choosing to win with certainty

•Dictators prefer to choose probabilities of outcomes over choosing the outcomes.•Dictators choosing probabilities assign themselves almost everything.•The dictators' choices are not affected by the receivers' information.•Dictators signal to themselves and not the receivers.•Receivers anticipate dictators, but not always vice versa.

Participants in dictator games often contribute significant sums to unknown beneficiaries. This has been interpreted as suggesting that participants like to be perc.eived as generous even in anonymous situations.We show that when participants choose the probabilities with which they contribute, they tend to bias the probabilities in their favor without respect to whether others know only the outcomes or also the probabilities assigned. These results, together with the results of ultimatum games with similar frameworks, suggest that participants that choose probabilities make self-oriented choices even when others are likely to blame them rather than the random mechanism for the outcomes.