Black and White take turns claiming cells. Black wins by owning all six cells of a Snaky, the hexomino on the left, in any rotation or reflection. White wins by stopping that until the board is full; White's own shapes don't count. Black moves first. You are White.
Black can't lose. It is not searching: every Black move comes from a fixed set of 8,671
cards. A card says "Black owns these cells, White has nothing in this region, Black
plays here, and Black wins within h moves". Each White reply sends Black to a card of
lower height, under a rotation, reflection or shift. A Lean proof,
Snaky.snaky_wins_15x15, checks the whole card set in the kernel, and this page
plays the same file. The "promise" counter is the current card's height. The
certificate, the Lean proof and the full write-up are in
gotrevor/snaky-15x15
(the note).
Frank Harary asked which polyominoes the first player can force; Snaky was the one hexomino left open, and Harary conjectured a first-player win on 15 × 15. Halupczok and Schlage-Puchta showed Snaky loses on 8 × 8 and wins on the plane with a one-stone handicap (2007). In 2026 OpenAI gave a 21-move win on the infinite board, proved in Lean, and derived a win on 17 × 17.