This study examined how pigeons discriminate the relative frequencies of events when the events occur serially. In a discrete-trials procedure, 6 pigeons were shown one light nf times and then another nl times. Next, they received food for choosing the light that had occurred the least number of times during the sample. At issue were (a) how the discrimination was related to two variables, the difference between the frequencies of the two lights, D = nf - nl, and the total number of lights in the sample, T = nf + nl; and (b) whether a simple mathematical model of the discrimination process could account for the data. In contrast with models that assume that pigeons count the stimulus lights, engage in mental arithmetic on numerons, or remember the number of stimuli, the present model assumed only that the influence of a sample stimulus on choice increases linearly when the stimulus is presented, but decays exponentially when the stimulus is absent. The results showed that, overall, the pigeons discriminated the relative frequencies well. Their accuracy always increased with the absolute value of the difference D and, for D > 0, it decreased with T. Performance also showed clear recency, primacy, and contextual effects. The model accounted well for the major trends in the data.