Good point about baseline.
It takes 33 bits to pick out one human from everyone alive
Is it basically just 2^33 > ~8 billion humans, therefore that's the minimum information context to identify a single individual? But then what counts as an information bit - any valid Yes/No question? And how do you calculate the bit value of a piece of info (i.e. 3 bits for the knowledge of playing chess)?
The way to think about the information content of a problem or of something you learn is exactly what you're suggesting. If you numbered every living person on earth, it'd take more than 32 bits and not quite fill the 33rd bit.
If you then learn a person's gender, you can eliminate all the people with the incorrect gender, which is going to leave you either 31.x bits (assuming binary gender) or 25-27 bits of remaining entropy (assuming some non-binary gender and, say, a 1-3% incidence rate).
When the parent you're responding to says you get 3 bits for knowing someone plays chess, they're guessing that 1/(2^3) = 1/8 of people, in an undifferentiated sense, play chess. Of course if we knew someone's age or gender or country of origin, the conditional information value in knowing they play chess could be greater or lesser. And realistically no one is ever trying to identify a human among all humans (partially because it seems highly unlikely that there are many questions that could equally implicate the president of the United States and a six year old on the Marshall Islands in their answer). Each bit of information represents a halving of the entropy of the target surface.
I think you got to within 1 bit of the answer from first principles ;)
I'd assume that they are estimate that 1/8 of the human population plays chess, which feels like an over-estimate to me (but not absurdly, depending on your threshold of "plays"; by a similar process I'd estimate that at least 1/8 of humans alive are under 10 years old).
That's why I said at least 3 bits. If chess players are rarer, then knowing someone is a chess player is a stronger filter. (By the same token, knowing that they're not is a weaker one; but that's not the case we're discussing.)