In most cultures, extramarital sex is highly restricted for women. In most of those cultures, men transfer wealth to their own sons. In some cultures extramarital sex is not highly restricted for women, and in most of those cultures, men transfer wealth to their sisters' sons. Inheritance to sisters' sons ensures a man's biological relatedness to his heirs, and matrilineal inheritance has been posited as a male accommodation to cuckoldry—a paternity strategy—at least since the 15th century. However, longitudinal analysis of (...) the cumulative effect of female extramarital sex indicates that matrilineal inheritance is most advantageous for women and would be more accurately considered a grandmaternity strategy. That is, if the probability that men's putative children are their biological children is less than 1, the probabilistic degree of relatedness between a female and her matrilineal heirs is higher than her corresponding relatedness to her patrilineal heirs. The same holds true for men only if ρ is very low. The upshot is that for moderate levels of female extramarital sex, matrilineal inheritance, relative to patrilineal inheritance, is highly advantageous for women and disadvantageous for men. Consideration of female variance in reproductive success beyond the first generation, and of a man's network of obligation to the inclusive fitness of his relatives, suggests that although the establishment of matrilineal inheritance may require extremely high levels of female extramarital sex, once established, it is likely to be maintained at levels of ρ that reasonably characterize many societies in the ethnographic record. New analysis of previously published data shows a strong association between matrilineal inheritance and moderate to low probability of paternity, and an even stronger relationship between patrilineal inheritance and high probability of paternity. (shrink)