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While this would definitely change the game dramatically, it would not be impossible.
Consider any sport where your standing is based on judged's scores rather than a definite team sport (gymanstics, figure skating, etc.). The game could have a vauge goal for each robot to accomplish, then your robot could be judged based on how well and to what degree your robot accomplished the goal and also the way in which you achieved it.
I'm not sure how well a game like this would go over, but if it were done right we would definitely see a lot more creativity and originality amoung the robots than we have in the past.
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