Maker–Breaker · the Snaky hexomino · 728 proof cards
You play White, the Breaker. Black plays the strategy from “Snaky in 21 Maker moves” and is building the six-stone Snaky shape in any rotation or reflection. It always succeeds. The only question is how long you can make it take.
Copy this game, or paste an SGF and load it. Only White's moves are read; Black replays its own.
The paper proves the result with cards. A card is a promise of the form: if Black already owns the required cells A and White has no stone in the envelope T, Black wins within h more moves. Cards 0–5 are the six ways to be one stone from Snaky. Every later card plays one pivot stone and holds a hand of child cards whose envelopes have nothing in common except cells Black already owns. So whatever White replies, at least one child card survives, and its height is smaller.
The final card, 727, needs nothing (A = ∅), fits in a 17×17 square (|T| = 251), and has height 21. Its pivot is the paper's (8,8), which on this board is tengen, the centre point K10. In glass-box mode, every hot cell on the board is a reply that kills the fastest cards in Black's hand.
Black follows its plan to the letter. It only ever plays the next stone of its current card and never looks for other ways to finish, so it can leave a ready win on the board for many moves. A perfect defence exploits this; that is part of how 21 is reachable. A Black that also took every free win would never need more than 21 moves, and would often finish much sooner. In glass-box mode, a win Black has already passed over gets a green dashed ring.
An improved strategy that always wins within 20 moves is at Snaky in 20.
Card 727 is a hand of 32 placed cards in six groups (Table 1 of the paper). Step through them and watch their common envelope shrink until only the pivot is left. That is why Black needs nothing to start.
Open any of the 728 cards. Black stones are required cells, squares are the envelope, the red ring is the pivot. Click a child to follow it down.