Great job here! The scoring method is simultaneously brilliant (fits the theme perfectly) and user friendly (where can I go to hit as many tokens on the right). It makes me want to go on my own Buzz Tour and see how things shake out!
"Stingy" is a fascinating idea that seemed overly punishing at first, but I can see why it needs to be there. Just curious why you would ever choose to battle, since it mostly seems detrimental to you (unless you were picking off some defenseless cardboard)?