We present a Monte Carlo method for determining the distribution of founders' genetic contributions to descendant cohorts. The simulation of genes through known pedigrees generates the probability distributions of contributed genes in recent cohorts of descendants, their means, and their variances. Genealogical data from three populations are analyzed: the Hutterite population of North America, the island population of Sottunga from the Aland archipelago, and the large Utah Mormon population. Two applications of the Monte Carlo method are presented. First we investigate the relative opportunity for founder effect in the three populations, which have dissimilar pedigree structures and dissimilar disease gene frequencies. Second, we measure the reproductive success of population founders in terms of the number of genes they contribute to a cohort some number of generations descendant and compare the effects of polygyny versus monogamy on reproductive success. The distribution of Hutterite founder contributions describes the context for a classic founder effect. Hutterite founders have a higher probability of leaving no genes in the population (72%) than Sottunga (48%) and Mormon (48%) founders. However, founder genes that survive among Hutterite descendants do so in larger numbers on average than founder genes in the other two populations. Greater variation among monogamous Hutterite founders compared with Mormon polygynous founders demonstrates that polygyny alone does not maximize the variance in reproductive success; other population characteristics are at least as important for determining variability among individuals in their genetic contributions to a gene pool. Our findings make it difficult to appreciate the reproductive advantage of polygyny in the Mormon population. Although the expected gene contributions and their variances were larger for polygynous founders compared with other Mormons, the main effect of polygyny was to increase the probability that any polygynist left a few genes among descendants. Furthermore, only 12% of the variation in the genetic contributions of Mormon founders is explained by their number of offspring. We conclude that shallow genealogical data (from one or a few generations) provide a poor measure of long-term reproductive success.