  Hex is a well known connection game in which two players attempt to connect
opposite sides of the board by colored stones. In 2022, Hamkins and Leonessi
introduced an infinite version, in which the goal is to construct a certain
kind of two-way infinite path of adjacent stones. It was explicitly left open
whether the winning condition is Borel. We prove that it is arithmetic, with
complexity between $\Sigma^0_4$ and $\Delta^0_5$.
