Dots and Boxesडट्स एन्ड बक्सेस

The page

The game is played on a square grid of dots. The usual page has 5 dots across and 5 down, which makes 16 boxes in four rows of four (a 4 × 4 grid). Before the game you can choose 3 × 3, 5 × 5 or 6 × 6 boxes instead.

A box is the square between four neighbouring dots. Each box has four sides, and a side between two boxes belongs to both of them.

Two, three or four people can play. Each player has their own ink: blue, red, green or violet.

Drawing lines

Player one draws first, then the turn goes round the table in order.

• A line joins two dots that sit next to each other, across or down. Lines never run diagonally, and never jump over a dot.
• Each gap between two dots can be drawn only once, by whoever gets there first.
• Lines belong to nobody: it does not matter who drew the other sides of a box, only who draws the last one.
• You may not pass. If it is your turn, you draw a line.

Claiming boxes

• When your line draws the fourth side of a box, you claim it: the box is washed in your ink and your initial is written in it.
• Closing a box earns you another line, and you must draw it, even if every line left gives something away.
• Keep going for as long as each line closes a box. Your turn ends with the first line that closes nothing.
• One line can close two boxes at once, when it is the last side of both. You claim both, and you still get just one more line.
• You never have to close a box you could close. Leaving one on purpose is sometimes the best move (see the double-cross below).

How the game ends

The game ends when the last box is claimed. Every box counts one point, and the player with the most boxes wins.

• With two players a 4 × 4 or 6 × 6 page can end level (8 boxes each, or 18 each), which is a draw. A 3 × 3 or 5 × 5 page always has a winner.
• With three or four players, players level on the highest score share first place. If everyone has the same number of boxes, the game is a draw.

Online games with a turn timer

If the host turns on a turn timer and a player runs out of time, a line is drawn for them: one that closes a box if there is one, otherwise one that gives nothing away, otherwise the line that gives away the fewest boxes.

Where these rules come from

Dots and Boxes has no rulebook body or federation. The French mathematician Édouard Lucas first described it in the 19th century as la pipopipette, and the rules have hardly changed since. This table plays the standard game:

• One line per turn between neighbouring dots, the fourth side claims the box, and the player who closes a box draws again: Wikipedia's Dots and Boxes article and Ivars Peterson's Science News column on Elwyn Berlekamp's book.
• Closing a box is never compulsory. Strategy guides such as Thomas Ferguson's notes at UCLA rest on a player being free to leave the last two boxes of a chain.
• The extra line after a box is compulsory, and a line that closes two boxes earns one extra line, not two, as in every source.
• The default page is 4 × 4 boxes, a game of about five minutes. Wikipedia suggests a small board for learning and a 5 × 5 board for experts, so 3 × 3, 5 × 5 and 6 × 6 are offered too.
• Who draws first is player one. With three or four players the turn simply goes round the table, as people play it on paper.

Grid size

Choose 3 × 3 boxes for a quick game, 4 × 4 (the default) for about five minutes, or 5 × 5 and 6 × 6 for a long game with more chains to fight over.