Characterize optimal play in Hex

Characterize what optimal play looks like in every state of Hex, or at least in its initial state, despite the game-theoretic result that Hex is a first-player win under optimal play (or a second-player win when the swap rule is used).

Background

Hex is a two-player connection game in which each player attempts to connect opposite sides of the board with their own colour. Although Hex has been proven to be a win for the first player under optimal play, or for the second player when the swap rule is applied, the paper notes that the actual optimal strategy has not been determined. In particular, the unresolved issue concerns identifying optimal play across all states, or even only from the initial position; the paper also notes that current machines are superhuman.

References

Hex can be proven to be a win for the first player under optimal play (or for the second player if the “swap rule” is used), but what optimal play looks like in every state (or even just the initial state) is not yet known.

— Local Updates, Global Learning (LUGL): Playing Games with non-incremental Learners  (2609.03660 - Milec et al., 3 Sep 2026) in Section II, subsection “Games,” subsubsection “Perfect information”