Post your ideas for unconventional games here.
One that I was just thinking of was a musical chairs type game designed to encourage casual play. Maybe each player would only stick with one nation for a set number of turns, after which they rotate. That way you don't get too stuck on a particular position and have some room to experiment. And of course everyone else has the same problem and advantage. Of course, I'm not sure how workable this is. Maybe it would be more feasible to rotate between teammates in a team game. Anyway, there are probably other ways of encouraging casual plays, this is just one that came to me right now.