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Perhaps this is either a nurtured/innate difference in level of competitive/cooperative tendencies in the individual. Girls are frequently taught by well-meaning parents, extended family, and other caregivers from a rather young age that being "competitive" is not very feminine, at the very least. Those messages are pretty insidious and difficult to avoid. Girls learn quite young that being a cutthroat competitive personality is a route to social misery, at least within one's own gender. Some of that seems to be biologically driven.

There is no way to play chess "collaboratively" so that nobody loses. KWIM?

Mmm hmm. Indeed.

I was blown away, and not in a good way, when a friend laughingly told me how my DD and hers "always just make up rules and play silly chess" during chess instruction in school. Keep in mind that while DS is no doubt more talented than DD (he is, after all, 4 years younger), she certainly does beat him sometimes and he must concentrate for sure when they play. "I guess she's not like [DS], huh?" she said.

The child is my DD's best friend. I asked DD about it. "She's not any good," she told me, "so I don't want to really play her because I would win and she would be embarrassed."