Chess is like, the only example that can work with "doesn't matter who plays", since it's ****ing Chess.
Everything else that's meant for fun and is not supposed to be competitive on a worldwide level depends on the people.
Anyway, A2A + Alcohol is godly. Especially when playing with an exchange student from Puerto Rico who didn't understand 1/4 of the words and made the game incredibly funny.
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http://28.media.tumblr.com/tumblr_lcb35gGx0t1qailr4o1_500.gif
http://www.megavideo.com/?v=57N0YAEJ