Does anyone know of a board state that doesn't involve arbitrary actions, but a specific finite setup, which would nonetheless require the solution of an unsolved conjecture in order to resolve who wins?

I am thinking of an example like constructing two incredibly large numbers (of the same sort as grahams number) where it is not known which is larger, and then e.g. doing x damage to a creature with y health. Ideally this happens in a way that nobody would object to the construction if x and y, since they are simple to describe and construct.

I understand that you can construct a turing machine to perform an arbitrary computation, but that defeats the spirit of this question. The question is whether there is a simpler way to construct such a paradox where you might follow along happily until you get to the end.