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Just because there's a separate world championship and title system for women doesn't mean there's a gender gap. Plenty of women play in and do quite well in open tournaments.

Hou Yifan, the top female player, is above 2600, which by any objective measurement is really fucking good. That's good enough for top 100 players in the world regardless of gender. Just because she isn't competitive againts Magnus doesn't mean there's a gender gap....because TBH nobody is truly competitive against him.

In the post I argue that the difference between the best male and the best female players can be partially explained by participation imbalance. This is, if in a race there are two teams, one with 100 people and the other with 3 people, it's very probable that the winner will be from the first group.
Presumably yes.

Better question: Even if a woman was magically guaranteed to both be in the 1% of chess talent, and to be unaffected by sexism...would "work at becoming a competitive chess player" be a rational life choice for her to make?