About Chain
Chain is the daily boxes endgame. Everyone knows the game from the back of a school exercise book: join two dots, close a box, go again. Almost nobody plays the ending, which is where the whole thing is actually decided.
Once the safe edges run out, every move opens a chain for the other player, so the game turns into a question of who runs out of quiet moves first. That is why taking every box on offer can lose: handing the last two back keeps your opponent on move, and the move is often worth more than the boxes. Some days that is right and some days it is exactly wrong, which is the read the puzzle asks for.
Every board is a real position reached by a real game, checked so that exactly one edge still wins it. More dailies: Four, Mate, Check.