Should men play against women in some sports?

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Obviously not football, or any contact or collision sport. Men are physically superior, although I read that this could be at least partially attributed to the fact women weren't encouraged to do anything physical (be it work or sport) until recently, and that since the push for equality they've caught up in leaps and bounds. Even so, it's a given that the average man is bigger and stronger than the average woman, and I'm not suggesting that women boxers should step up to the plate. But what about non-contact sports? Power is still a big part of some of these sports, like tennis or golf, and you could argue that the average woman would still be disadvantaged. (I hear you but Serena Williams is NOT average.) And what about sports that are much less reliant on physical attributes? Sports like darts, motor racing, horse riding, snooker or even chess? Should gender segregation be abandoned in some of these sports? Where do you draw the line? Note: I'm aware that some women have already entered the world of men's sport, but generally these were one-off exhibitions. I'm talking more about a widespread breakdown of the barriers, and where and when you think it's a viable option. Also, I'm aware that the definition of sport varies and some people will dispute some examples like chess or card games. Just go with it and humour me.