In the movie Ice Storm, the middle class people in the suburbs of New York did something like: they put their car keys in a bowl when they went to a house party. At the end, the ladies would randomly pick up a key. The male owner of the key would go with her.
Personally I think the game sucks. I mean I am not morally any better, I may have an affair with a woman I like/love. But having sex with a woman I draw randomly? Not really my cup of tea