A magnitude effect in probability discounting is well established with humans, in which the value of a larger reward decreases more with uncertainty than the value of a smaller reward. We report two experiments which show that an analogous result is obtained with pigeons choosing between probabilistic food rewards in a two-component concurrent-chains procedure. In Experiment 1, the terminal links delivered large (4-s access to food) and small (2-s access) rewards with either 100% or 50% probability across components. Preference for the larger reward was greater in the 100% component. In Experiment 2, the terminal links delivered reinforcement on 100% or 50% of terminal links and the rewards were large (4-s access to food) or small (2-s access) across components. Preference for the 100% alternative was greater when rewards were large. In both experiments, results indicate that the value of the larger reward decreased more when its probability was 50% than the value of the smaller reward, confirming the magnitude effect, and were similar regardless of whether the food/no-food outcomes for the 50% terminal links were differentially signalled. Results were predicted by an extension of the cumulative decision model (D. R. Christensen & Grace, 2010; Grace & McLean, 2006) which accounts for the effects of magnitude and probability on choice, and which can also explain the apparently contradictory results of prior research on the magnitude effect in delay discounting with pigeons. The model shows that a single process can account for delay and probability discounting in nonhumans, including the opposite effects of reward magnitude.