Interesting essay, especially the observation that
Imagine you’re playing a game of Catchup and you can see the players’ largest groups will likely end up the same size, so the game will be decided on a tie-break. So you start trying to ensure your second-largest group ends up bigger than your opponent’s second-largest group.
But when you do, you realize something more confounding: you don’t know how to ensure your second-largest group is larger than your opponent’s without simultaneously making your largest group smaller than your opponent’s – because a stone added to your second-largest group is a stone not added to your largest.
Each stone you place must somehow bring you closer to achieving both goals simultaneously, but they conflict.
PS: My mind also went off on a linguistic tangent, wondering if "recursive tie-break" would be a better / more accurate label than "fractal tie-break"...