Dots and Boxes · Rules guide
Dots and Boxes rules: how to play
Draw a line, close a box, go again. The rules take fifteen seconds — and then the endgame turns into one of the most surprising strategy problems in any paper-and-pencil game.
The short answer
- Players alternate drawing one line between adjacent dots.
- Completing the fourth side of a box claims it and gives you another turn immediately.
- Never give a box its third side — your opponent will take it and keep going.
- The game ends when every line is drawn; most boxes wins.
- Who is forced to open the first chain decides almost every game.
The rules
Dots and Boxes starts as a grid of dots. On your turn you draw one line joining two adjacent dots, horizontally or vertically. Whoever draws the fourth side of a square claims that box, writes their initial in it — and takes another turn immediately.
- One line per turn, except after claiming a box, when you go again.
- Claiming is compulsory in effect — if you can close a box you almost always should, and the extra turn keeps coming as long as you keep closing.
- The game ends when every line is drawn. Most boxes wins; an equal split is a draw.
Why it is not a doodle
The whole game turns on one thing: giving a box a third side lets your opponent take it. So most of the game consists of drawing lines that do not complete a third side — and eventually there are none left.
At that point somebody has to open a region, and whoever does hands their opponent a chain of boxes. The game is decided by who is forced to open first, and how big the regions are. That is the entire strategic content, and it is far richer than it sounds.
| Phase | What is happening |
|---|---|
| Opening | Both players draw safe lines; almost nothing is at stake. |
| Filling up | Safe lines run out; the board divides into chains and loops. |
| Endgame | Someone must open a chain. The other takes it — then must open the next. |
| Sacrifice play | Strong players decline the last two boxes of a chain to stay in control. |
Board sizes, and the first-player question
Boards are described by the number of boxes: a 5×5 board has 6×6 dots and 25 boxes.
- 2×2 — a minute long, good for teaching.
- 3×3 and 5×5 — an odd number of boxes, so a draw is impossible.
- 4×4 and 6×6 — an even number of boxes, so draws are possible.
Whether the first player has an advantage depends on the board, and it is not a simple pattern. Small boards have been solved exhaustively; the general game is hard, which is why the theory below matters.
Common questions
Do you have to take a box if you can?
Not by the rules — and declining is sometimes the winning move. Taking all but the last two boxes of a chain, then giving the last two away, keeps your opponent on the move.
Do you get another turn after claiming a box?
Yes, and you keep going as long as each line you draw completes another box. A long chain can be taken entirely in one turn.
What size should the board be?
5×5 boxes is the standard serious size: long enough for real chain play and short enough to finish in ten minutes. 3×3 and 5×5 have an odd number of boxes, so draws are impossible.
Can Dots and Boxes be a draw?
Only on boards with an even number of boxes, such as 4×4 or 6×6. With an odd number someone must come out ahead.
Does the first player win?
It depends on the board size, and not in an obvious pattern. Small boards have been solved by computer; on ordinary boards the result depends on chain parity, which good players control.
What is a chain in Dots and Boxes?
A run of boxes connected so that opening one lets your opponent take them all in a single turn. Counting chains — and their parity — is the core of the game.
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