When given a choice between two alternatives, each offering food after the same delay with different but signaled probabilities, pigeons often prefer the low probability alternative. This preference is surprising because pigeons fail to maximize the rate of food intake; they exhibit a suboptimal preference. We advance a new explanation, the Δ–∑ hypothesis, in which the difference in probability of reinforcement within terminal links (Δ) and the overall reinforcement probability rate of each alternative (∑) are the key variables responsible for such suboptimal preference. We tested the Δ–∑ hypothesis in two experiments. In Experiment 1, we manipulated the Δs while maintaining constant all other parameters of the task, in particular the ∑s. We predicted a preference for the alternative with the larger Δ. In Experiment 2, we examined the effect of the overall reinforcement probabilities, the ∑s, while maintaining constant all other parameters of the task, in particular the Δs. We predicted a preference for the larger ∑. The results of both experiments support the Δ–∑ hypothesis.