Landsburg's solution is somewhat head-scratching. It works fine if you're sampling families. But the problem as stated doesn't sample individual families. It asks about the overall population.

This washes out his effect pretty strongly, to the point that the expected excess in the case of an infinite-sized country is the same absolute excess as in the case of one family: <strikethrough>You expect 0.3 more boys than girls.</strikethrough> zero.

In total. Across the whole country. And it wasn't asking about the families, it was asking about the country. So the ratio is a teeny tiny deviation from 50%, not 30.6%. This is very much an ends in 'gry' situation.

(Note: what I was trying to say above, about the 0.3 more boys than girls, and then got confused:

This is all about the stopping condition. The stopping condition produces a bias by the disproportionate effect of the denominators on either side of 1/2. But this stopping condition only steps in once to the country and to the single family all the same: there's effectively only one stopping condition, that being when N boys have been born. Increasing N from 1 to a million just washes out the effect by adding more unbiased random babies on what for clarity you can imagine as the beginning of the sequence. So you have this biased ratio, and then you weighted-average it with 1/2 with a huge weight on the 1/2)