There is an inherent relationship between the process of pairwise sequence alignment and the estimation of evolutionary distance. This relationship is explored and made explicit. Assuming an evolutionary model and given a specific pattern of observed base mismatches, the relative probabilities of evolution at each evolutionary distance are computed using a Bayesian framework. The mean or the median of this probability distribution provides a robust estimate of the central value. The evolutionary distance has traditionally been computed as zero for an observed homology of 20 bases with no mismatches; we prove that it is highly probable that the distance is greater than 0.01. The mean of the distribution is 0.047, which is a better estimate of the evolutionary distance. Bayesian estimates of the evolutionary distance incorporate arbitrary prior information about variable mutation rates both over time and along sequence position, thus requiring only a weak form of the molecular-clock hypothesis. The endpoints of the similarity between genomic DNA sequences are often ambiguous. The probability of evolution at each evolutionary distance can be estimated over the entire set of alignments by choosing the best alignment at each distance and the corresponding probability of duplication at that evolutionary distance. A central value of this distribution provides a robust evolutionary distance estimate. We provide an efficient algorithm for computing the parametric alignment, considering evolutionary distance as the only parameter. These techniques and estimates are used to infer the duplication history of the genomic sequence in C. elegans and in S. cerevisiae. Our results indicate that repeats discovered using a single scoring matrix show a considerable bias in subsequent evolutionary distance estimates.