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What I don't like about scissors, rock, paper is that there's so much luck in it. I'd like the fights to be more strategical.
Maybe an ability can be added to each of the players: Block. They block the next attack but in turn they can't attack. (Is a little bit "tactical", isn't it?)
To sum it up: The most interesting fighting system would be one where stretegical, operational and then during the fight tactical choices would have to be made..?