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Dots and Boxes

The classic pencil-and-paper game. Take turns drawing a line between two dots; close the fourth side of a box to claim it and move again. Play a computer with three levels (the hardest one knows chain strategy) or pass the device to a friend.

You0
Your turn
Computer0
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How to use the Dots and Boxes

  1. Choose a mode: vs Computer (pick Easy, Medium or Hard) or 2 Players on the same device. Pick a board size.
  2. Draw a line by clicking or tapping the gap between two neighboring dots. With a keyboard, Tab to a line and press Enter.
  3. Close a box by drawing its fourth side: the box gets your color and you must move again.
  4. Avoid drawing the third side of a box, because your opponent can then take it. Late in the game, try to make your opponent open the long chains.
  5. When every box is taken, the player with more boxes wins. Press New game to play again or Undo to take back a move.

Dots and Boxes strategy, step by step

  1. Opening: play safe lines. At the start almost every line is safe. A line is safe if it does not become the third side of any box.
  2. Never give the third side away unless every remaining line does. One careless line hands your opponent a box and an extra move.
  3. Count the chains. When the safe lines run out, the board breaks into chains (boxes in a row that are linked through their open sides) and loops (chains that close on themselves). Whoever has to move then must open one of them.
  4. Give away the smallest chain first. Hand over 1-box and 2-box chains before long ones. For a 2-box chain, draw the line between the two boxes so your opponent can't use a double-cross.
  5. Keep control with a double-cross. When you take a long chain and more long chains are still waiting, take all but the last two boxes and draw the far end line instead. Your opponent gets 2 boxes, but must open the next long chain for you. In a loop you leave four boxes instead.

How many boxes does each board have?

Board (boxes)DotsLinesBoxes to win
3 × 316245 of 9
4 × 425409 of 16 (8–8 is a draw)
5 × 5366013 of 25
6 × 6498419 of 36
7 × 76411225 of 49
8 × 88114433 of 64

A board of n × n boxes has (n+1)² dots and 2n(n+1) lines. Because every line is drawn exactly once, the total number of moves in a game is always the same; only who draws them changes.

Controls

ActionMouse / touchKeyboard
Draw a lineClick or tap between two dotsTab to the line, then Enter or Space
UndoUndo buttonCtrl + Z
Get a hintHint button (the suggested line blinks)Tab to Hint, then Enter

Frequently asked questions

What are the rules of Dots and Boxes?

Players take turns drawing one horizontal or vertical line between two adjacent dots. A player who completes the fourth side of a box claims it and must draw another line. The game ends when all boxes are claimed, and the player with the most boxes wins.

Who invented Dots and Boxes?

The game was first described in 1889 by the French mathematician Édouard Lucas, who called it la pipopipette. It has been a favorite pencil-and-paper game ever since and was analyzed in depth by Elwyn Berlekamp in his book The Dots and Boxes Game.

What is a chain in Dots and Boxes?

A chain is a row of boxes that each already have two sides drawn, connected so that taking one box lets you take the next. Once someone draws a line inside a chain, the opponent can capture the whole chain. Long chains (3 or more boxes) decide most games between good players.

What is a double-cross (double-dealing move)?

When you are capturing a long chain, you can stop two boxes before the end and draw the line at the far end instead, giving those last two boxes away. Your opponent takes them but must then open the next chain for you. Sacrificing 2 boxes to keep control often wins many more later. The Hard computer does this.

How strong is the computer?

Easy makes random moves and often misses free boxes. Medium never misses a box and avoids giving boxes away until it has to, then hands over the smallest chain. Hard also counts chains in the endgame and uses double-crosses to keep control, so it is tough to beat on small and medium boards.

What is the best strategy for beginners?

Never draw the third side of a box unless you have no other choice. When safe moves run out, give away the shortest chain first, and give a 2-box chain by drawing its middle line so your opponent can't double-cross. Advanced players use Berlekamp's long chain rule: on a board of m × n dots, the first player wants the number of dots plus the number of long chains to be even, and the second player wants it to be odd.

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