## Mostly Misaligned Mirrors

Recently my stochastic professor introduced me to a problem he has been pondering for over two decades: on the two-dimensional integer lattice $\mathbb{Z}^2$ one shall flip a three-sided coin for each point and uniformly place one of three mirrors, $\{\diagup,\,\cdot\,,\diagdown\}$, where $\,\cdot\,$ denotes not placing a mirror. After having populated the world, one picks their favorite integer tuple and points a beam of light in one of the four cardinal directions. With what probability does the light fall into a loop, never fully escaping?