Pigeons were presented with an operant simulation of two prey patches using concurrent randomratio schedules of reinforcement. An unstable patch offered a higher initial reinforcement probability, which then declined unpredictably to a zero reinforcement probability in each session. A stable patch offered a low but unvarying reinforcement probability. When the reinforcement probability declined to zero in a single step, the birds displayed shorter giving-up times in the unstable patch when the ratio between the initial reinforcement probabilities in the unstable and stable patches was greater and when the combined magnitude of the reinforcement probabilities in the two patches was greater. When the unstable patch declined in two steps, the birds behaved as if their giving-up times were influenced heavily by events encountered during the most recent step of the double-step change. This effect was observed, however, only when the reinforcement probability in that step was .04, not when it was .06. All of these data agree with the predictions of a capture-probability model based on a comparison of the estimated probability of receiving a reinforcer in the current patch with that in alternative patches.