Actually it is notable that women and men have such similar intelligence. Women and men are quite easy to distinguish physically in a variety of ways, but there is probably way ( I don't believe one has been discovered) to reliably distinguish a woman from a man based purely on how their minds work. Minds are a lot more like livers, kidneys and eyeballs (effectively identical in each sex) than like body shape, genitals or hair distribution. I haven't heard this said before, but this would seem to suggest that minds are NOT primarily to get us laid, that they do not evolve from sexual selection, but rather arise from natural selection (survival of the fittest).

Of course, but "useful" is different from "increases reproductive fitness", and the basic assumption is that the selective pressure of intelligence came from competition inside the species. It is sort of difficult for me to imagine what kind of competition can happen between ancestral females to increase reproductive fitness (and not simply to have a better life, these two are different things). Let's assume for now it is not for higher quantity of children, nor for higher quality sperm thus the genetic quality of children (it does not really require much of a competition, it is cheap), what else is left? Largely the upbringing and life of those children. Am I on the right track there that it is more about what happens to the children once they are born? Are the get resources invested by the genetic father, by the tribe, by the chieftain, by the queen, by whoever, what status they get and so on? As this sounds vaguely possible for I just don't know to visualize it. (Sort of Cersei Lannister situation, push children into high status positions?)