$x$ Plays Pokemon, for Almost-Every $x$

Abstract

This paper provides a brief write-up showing that for any finite state game, a disjunctive number $x$ will eventually win that game. The proof techniques here are well known and this result follows immediately from folklore results in graph theory and cellular automata. This short paper primarily serves as an expositional piece to collect this proof with the fun context of $\pi$ Plays Pok\'emon serving as motivation.