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Dots & Boxes
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Draw a line, close a box, go again. Dots and Boxes is the game every schoolbook margin has seen — and one of the few pencil games where the endgame hides real mathematics.

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How to play
  1. Players take turns drawing one line between two neighbouring dots on a grid of 5×5 boxes.
  2. If your line completes the fourth side of a box, you claim it — and you immediately take another turn.
  3. One move can close two boxes at once, and a well-set-up chain can close many in a row.
  4. When every line has been drawn, whoever owns the most boxes wins. Draws are possible.

Strategy & tips
  • The opening barely matters — until it does. Early on, just don't hand out boxes: never draw the third side of a box unless you have no choice.
  • The endgame is all about chains. Eventually every safe move runs out and someone must open a chain of boxes for the opponent. Whoever is forced to open the first long chain usually loses.
  • Count the long chains. Chains of three boxes or more decide the game, and it's a parity problem: the number of them determines who runs out of safe moves first. Experienced players are counting from the middle of the game onwards.
  • Learn the double-cross. When your opponent opens a chain, don't greedily take every box. Leave the last two — this forces them to open the next chain instead of you. Giving up 2 boxes to win 8 is the single most valuable trick in the game.

Where it comes from

The game was described by the French mathematician Édouard Lucas in 1889 under the name la pipopipette. Despite its simple rules, it's the subject of serious mathematical study — Elwyn Berlekamp wrote an entire book on its theory. Beginners think it's about grabbing boxes; the real game is about controlling who's forced to move.