[Terr_]

I think the "paradox" comes from how people implicitly assume "any number of sons" is somehow distributed or weighted in a way that favors towards numbers of 1 or above.

In contrast, "0 sons" is going to describe a full half of all marriages.

[jon_richards]

Same situation with the bus.

[pwagland]

Not really. In the son/daughter case, the calculations are: expected daughters: 1 expected sons: 1/20 + 1/41 + 1/82 + 1/163 + 1/324 + …

So number of expected daughters = 1, number of expected sons = 1. In practice since women can't have an infinite number of children, then this wouldn't be an infinite series, so the real number of expected boys would be lower than one, but there you go…

Now, for the bus case, you get +1 if your bus turns up first, and -1 for every other bus that turns up first. Assume that it is completely random, then: expected + score is: 1/2 1 expected - score is: 1/2 * -1 + 1/4 * -2 + …

Expected + is 0.5, expected - is -1.

[repsilat]

I guess it would be balanced if the rule was,

> 1 when your bus turns up, -1 for every bus going the other way.

[selestify]

Isn't that the same as what the OP's rules were?

[pwagland]

Correct.