Pigeons show a preference for an alternative that provides them with discriminative stimuli (sometimes a stimulus that predicts reinforcement and at other times a stimulus that predicts the absence of reinforcement) over an alternative that provides them with non discriminative stimuli, even if the non discriminative stimulus alternative is associated with 2.5 times as much reinforcement (Stagner & Zentall, 1910). In Experiment 1 we found that the delay to reinforcement associated with the non discriminative stimuli could be reduced by almost one half before the pigeons were indifferent between the two alternatives. In Experiment 2 we tested the hypothesis that the preference for the discriminative stimulus alternative resulted from the fact that, like humans, the pigeons were attracted by the stimulus that consistently predicted reinforcement (the Allais paradox). When the probability of reinforcement associated with the discriminative stimulus that predicted reinforcement was reduced from 100% to 80% the pigeons still showed a strong preference for the discriminative stimulus alternative. Thus, under these conditions, the Allais paradox cannot account for the sub-optimal choice behavior shown by pigeons. Instead we propose that sub-optimal choice results from positive contrast between the low expectation of reinforcement associated with the discriminative stimulus alternative and the much higher obtained reinforcement when the stimulus associated with reinforcement appears. We propose that similar processes can account for sub-optimal gambling behavior by humans.