Dots and Boxes

Dots and boxes rules

The game starts with a square grid of dots. Players take turns, and each turn draws one line between two dots that are next to each other, across or down, never diagonally. When a line closes the fourth side of a box, the player who drew it claims the box, writes an initial in it and must draw another line. One line can close two boxes at once, and both count. A line that closes nothing ends the turn. When every box is claimed, the player with the most boxes wins.

The grid size is counted in boxes here. A 4 × 4 grid has 16 boxes, so 5 dots on each side and 40 lines in total. With 16 boxes two players can tie at 8 each; on the 3 × 3 and 5 × 5 grids an odd number of boxes rules out a tie between two players.

Strategy: safe lines, chains and control

Early in the game most lines are safe: they do not give any box its third side. Drawing the third side is a gift, because the next player closes the box and moves again. So the first part of the game is a race of safe lines, and the player who runs out of them first has to give something away.

By then the board has split into chains, rows of boxes with two sides each where taking one box opens the next, and loops, chains that close on themselves. The player who has to move opens the shortest one they can. The other player takes the boxes, but has to move again afterwards, and so must open the next chain.

Elwyn Berlekamp's book The Dots and Boxes Game: Sophisticated Child's Play (A K Peters, 2000) describes the key trick. When you are handed a long chain, take all of its boxes except the last two, then draw the line at the far end so that those two boxes form a pair closed by one line. Your opponent takes the pair, and has to open the next chain for you. Berlekamp calls this a double-dealing move, and the single line that then takes both boxes a double-cross. Giving up two boxes each time keeps you in control, which pays off when the chains left are long. In a loop the same idea costs four boxes. His long chain rule ties the number of long chains each player should aim for to the number of dots on the board, so the fight in the middle of the game is about how many long chains there will be.

A chain of two is the exception: open it with the middle line, so each box has three sides on its own. Then the other player cannot hand the pair back to you.

The computer levels

• Easy takes any box it can close. Otherwise it draws a random line, so it often draws third sides and gives you boxes.
• Medium takes every box it can and never draws a third side while a safe line is left. When none is left, it opens the chain that gives you the fewest boxes.
• Hard does all that. When twelve or fewer safe lines are left, it plays every order of them out to see who will have to open the first chain, and picks the line that leaves you that job. In the end game it counts the chains and loops, decides whether to take a whole chain or leave you the last two boxes, and opens chains of two with the middle line.

Pen-and-paper play

The PDF under the game prints an empty dot grid from 5 × 5 to 10 × 12 boxes on US Letter or A4, with a score table for 2 to 4 players. Each player uses their own pen color or writes an initial in each box they close. Larger grids make longer games: a 10 × 12 grid has 120 boxes.

How to play dots and boxes online

1. 1Choose Against the computer or Friends on one device, then the grid size, the level or the number of players.
2. 2Type names if you like. Their first letters mark the boxes each player claims.
3. 3Tap the gap between two dots to draw a line, or use the arrow keys and Enter. Close a box to claim it and move again.
4. 4Undo takes back the last line (against the computer, your last line and the computer's answer). New game starts over.

Related guides

• How to Play Solitaire: Klondike Rules Step by Step
• Tic-Tac-Toe Strategy: How to Never Lose
• Single vs Double Elimination: Games, Byes and Seeding

Built by Tobias. Updated November 11, 2026.

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