place a stone, link your two edges.
every finished board holds exactly one chain — so nobody ever draws.
your move
Take turns placing stones on empty cells. You win by building an unbroken chain from the left edge to the right; the machine links top to bottom. Every filled board contains exactly one such chain, which is why draws are impossible — a fact equivalent to the Brouwer fixed-point theorem.
Solid threads join stones that touch. Dashed threads mark bridges: two stones a step apart sharing two empty cells. A bridge is as good as a connection, because if your opponent takes one of the two cells you simply take the other. Learning to see bridges is most of learning Hex, so the board draws them for you.
Same board, inverted goal: whoever completes a chain loses. Every instinct you build in the normal game turns against you, and the endgames get strange.
Moving first is a real advantage, so after your opening stone the machine may mirror it across the diagonal and claim it. That one option is enough to make the game fair, and it means your first move wants to be good but not obviously best.
No opening book, no evaluation function. Before each move it plays thousands of games out from the current position, filling the board at random and seeing who ends up connected, then picks whatever won most often. Deep buys it more time to think, not more knowledge.