I find it doubtful that baboon females are quite so non-competitive as all that. They just channel it more productively :)
When I think of polite sports with cut-throat hidden competition, I can't help but think of croquet. Sure, the balls are a stretch for baboons, but rounded rocks would work. and they could weild short mallets easily enough. The social complexities that can be shown in a game of croquet, without a word being said, would no doubt be amazing.
--Bryan
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