I signed up just to post this comment because this is hilarious. EVEN IF this guy’s assumptions were correct in 100% of cases… it leads to an equal number of male and female children anyway.
To formalize the assumptions:
When a child is male, 50% chance to continue having children.
When a child is female, 100% chance to continue having children.
Stop having children after having two female children.
We’ll throw away the thing about stopping reproducing at economic capacity because that’s essentially random and uniformly affects the number of male and female children.
We’ll ignore trans and intersex children for now for the sake of easy math, and assume that every child has a 50⁄50 chance of being male or female.
Your first child can go three ways: male with sibling, male without sibling, and female with sibling, with probabilities 0.25, 0.25, and 0.5 respectively.
The expected value of having a first child is 0.5 male children, 0.5 female children, 0.25 siblings-with-all-brothers, and 0.5 siblings-with-one-sister.
The expected value of 1 sibling-with-all-brothers is the same as our expected value for a first child: 0.5 female, 0.5 male, 0.25 sibling-with-all-brothers, and 0.5 siblings-with-one-sister.
The expected value of 1 sibling-with-one-sister is 0.5 female, 0.5 male, and 0.25 sibling-with-one-sister.
These last two are defined recursively, with each one also being equal to 0.25 more of itself. This is equivalent to an infinite series which converges to a value of 4⁄3.
Thus, each yet-undefined sibling is expected to be equal to 4⁄6 female children, 4⁄6 male children. A sibling with all brothers is gives an additional 4⁄6 siblings-with-one-sister, and that value translates to an additional 16⁄64 = ¼ male child + ¼ female child.
Thus, a family based on these rules will have an expected size of 0.5 + 0.5(⅔) + 0.25(⅔ + ¼) boys, and 0.5 + 0.5(⅔) + 0.25(⅔ + ¼) girls. If we math that out, that’s 1.0625 boys and 1.0625 girls.
In fact, if you could devise some… parental algorithm for having more boys than girls other than “having a theoretically infinite number of kids and stopping when you have more boys than girls”, you could take that to vegas and win big at roulette!