You simulated the limiting case, where you don't stop having babies until you get a boy. That's (obviously) not realistic as we have a finite lifespan and ferti

You simulated the limiting case, where you don't stop having babies until you get a boy. That's (obviously) not realistic as we have a finite lifespan and fertility, but note that the expectation still holds. In this process you will always get 1 boy, obviously. But you have a (1/2)^k * (1/2) chance of getting k girls before your first boy. Thus the expected number of girls is Sum[k * (1/2)^k * (1/2), k, 0, inf] which is 1: https://www.wolframalpha.com/input/?i=Sum%5Bk+*+%281%2F2%29%5Ek+*+%281%2F2%29%2C+k%2C+0%2C+inf%5D https://www.wolframalpha.com/input/?i=Sum%5Bk+*+%281%2F2%29%... .