I am a stupid dad. But maybe one solution to the RUNNING game is:
Let you daughter tell the other girl "Since you were the first last time we
ran, this time let me be the first. Let's play fair. let's take turns." In a
sense, this is akin to the notion that the voices from both sides/parties/
nations should be heard, and no one will be left behind due to his or her
apparent shortcoming or deficiency.
It's not totally fair (according to the definition of fair play), but it is
better than letting only one girl win all the time (simply due to her so-
called seniority).
Finally, LZ's daughter has great personality.