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International Chess Federation (FIDE) to ban and punish transgender players
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They do. There are two types of chess competition: open and women only. Women don't do well in the open competition which is why they added the women only competition.
But it's not because men on average have an advantage. It's because men have a greater spread of chess ability so the very top men tend to do better than the top women.
Something to keep in mind with studies are outside social factors such as less women playing chess and less women being exposed to chess at a young age. There are fewer women in chess and fewer girls learning chess, for probably centuries. This will have a factor when comparing two demographics.