We studied how people attribute action outcomes to their own actions under conditions of uncertainty. Participants chose between left and right keypresses to produce an action effect (a corresponding left or right light), while a computer player made a simultaneous keypress decision. In each trial, a random generator determined which of the players controlled the action effect at varying probabilities, and participants then judged which player had produced it. Participants' effect control ranged from 20% to 80%, varied blockwise, and they could use trial-by-trial feedback to optimize the accuracy of their agency judgments. Participants tended to attribute action effects to themselves (agency bias), probably reflecting a rational guessing strategy of always naming the more likely player. However, participants systematically neglected information favoring the computer player as the agent, even under conditions where this bias could only harm judgment accuracy. We conclude that agency biases have both rational and irrational components.