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I would really like chess as long as it can be against humans and not robots. I think we have most of the other games already.
Chess would be a great idea. Would be easy to make 1v1 matches and tournies. Only issue is that you would always have to wait for someone else to join the game to play and if person had to leave early there would have to be some penalties.
Unfortunately, those wouldn't be the only problems with chess, and other similar games - particularly as money would be involved. As sherbyspark alluded to, bots would be a bigger issue, as they provide a huge advantage, and their use, in one form or another, is virtually impossible to prevent.