How to Play Dots and Boxes: Rules, Extra Turns and Who Wins

To play dots and boxes, two players take turns drawing one line between two neighboring dots, across or down. If your line draws the fourth side of a box, you claim the box and draw another line. When every line has been drawn, the player with more boxes wins.

That's the whole game. The rest of this guide covers the details: board sizes, the extra turn, one line that closes two boxes, ties, and the house rules you might meet. Every rule is described exactly as Poozee's Dots and Boxes plays it, every diagram was replayed with the game's own engine, and every number comes from games between copies of our computer player.

Dots and boxes rules at a glance

In this guide, A is the player who draws first and B the player who draws second.

The board: dots, lines and boxes

Board sizes are counted in boxes, which can be confusing, because what you draw on paper is dots. A board of 3 by 3 boxes needs a square of 4 by 4 dots:

Here's how the three sizes on Poozee compare:

Every game uses every line, so a 3x3 game always lasts exactly 24 lines, however the players split them. Poozee starts you on 4x4.

Playing on paper

You don't need a printed grid. Draw a square of dots with a pencil (on graph paper, use the points where the grid lines cross), pick a pen color each or just one pen, and take turns. When you close a box, write your initial inside it. At the end, count the initials.

For a board of R rows and C columns of boxes, there are (R + 1) x (C + 1) dots and R x (C + 1) + C x (R + 1) lines. A 3x3 board is a quick first game; 5x5 has room for the long chains that make the game interesting.

Taking a turn

On your turn, draw one line between two dots that are next to each other, across or down. You can't draw a diagonal, skip over a dot, or draw over a line that's already there, and you can't pass. On Poozee, tap or click near the line you want: every spot on the board belongs to the nearest line, so you don't have to hit it exactly.

Close a box and you go again

When your line draws the fourth side of a box, the box is yours, and you must draw another line. In this game, B has just drawn the bottom of the top-left box, giving it a third side:

A draws the highlighted line, and the box is A's:

If that extra line closes another box, A goes again, and so on. Your turn ends only when you draw a line that closes nothing. On Poozee the game tells you "You took a box: go again." when it's still your move.

This is why one turn can take a lot of boxes. When a row of boxes all have two sides drawn, closing the first one gives the next one its third side, and you can keep going down the line. In our 1,000 games between two Medium computers on the 5x5 board, the biggest single turn of each game averaged 11.4 boxes, and in one game a single turn took 24 of the 25 boxes.

The last line of a game always closes at least one box, so the game ends in the middle of somebody's turn.

One line can close two boxes

A line in the middle of the board is a side of two boxes. If both already have three sides, that one line closes both, and you claim two boxes at once:

You still get just one extra line, not two. Strong players call this a double-cross, and it matters more than it looks: the dots and boxes strategy guide explains why.

How the game ends and who wins

The game ends when every line is drawn, and the player with more boxes wins. On Poozee the game keeps going even when one player already has more than half the boxes. That can't change the winner, since boxes are never taken back, but every box still counts toward the final score.

Ties

A tie is only possible when the board has an even number of boxes. On 3x3 (9 boxes) and 5x5 (25 boxes), someone always wins. On 4x4 (16 boxes), 8‑8 is a tie, and on Poozee the game says "It's a draw, 8‑8." and adds one to the Draws count.

Ties are more common than you might expect. On 4x4, 40 of 1,000 Medium games, 109 of 1,000 Easy games and 44 of 200 Hard games ended 8‑8. And since the two scores always add up to 16, a 4x4 game can never be won by exactly one box: the closest result is 9‑7.

Does going first matter?

It depends on the board, and it changes with the skill of the players. We played two copies of each computer level against each other on each board: 1,000 games per board for Easy and Medium, and 200 for Hard, which thinks much longer. Every game had its own random seed, so the same games replay exactly.

On 3x3 the second player has a real edge, and with perfect play it's a sure thing: Poozee's solver checked every possible position, and the second player wins 6 boxes to 3 whatever the first player does. The 3x3 dots and boxes solution shows how. On the bigger boards the edge flips with the board size and the level, so take turns drawing first. Poozee does it for you. Why it flips, and what to aim for when you draw first, is in does going first matter in dots and boxes: it comes down to counting the dots.

Taking the first box doesn't mean you're winning

The first box usually goes to a player because the other one gave it away, and good players give boxes away on purpose. Between two Medium computers, the player who took the first box won 501 of 1,000 games on 3x3, 500 of 1,000 on 4x4 and 514 of 1,000 on 5x5: a coin flip. Between two Hard computers on 3x3, the player who took the first box lost 147 of 200 games.

House rules and variants

Dots and boxes is passed around on paper, so families and classrooms play it in slightly different ways. These are the differences you're most likely to meet:

If you're playing someone new, agree on the extra-turn rule before you start. It's the one that changes how you should play.

Playing on Poozee

• Board size: 3x3, 4x4 or 5x5 boxes. vs Computer or 2 Players, where Red and Blue share one screen.
• Who draws first: you (or Red) in the first game. Every Play again or New game switches who draws first. Changing the board size, level or opponent starts a new game with you drawing first.
• Computer levels: Easy takes every box it can, but otherwise 40% of the time it draws a line at random, which often gives boxes away. Medium takes every box and never draws a box's third side while it has another choice. Hard plays like Medium until 18 or fewer safe lines are left, then searches ahead, and once no safe lines are left (or 20 or fewer lines of any kind) it plays perfectly.
• Keyboard: Tab to the board, move between lines with the arrow keys and press Enter to draw.
• Hint shows the line the Hard computer would draw for you, and Undo takes back your last line along with the computer's reply. The lines of the latest turn are highlighted, so you can follow a long run of captures. Your game is saved in this browser.

First strategy tips

Once the rules feel natural, three ideas will win you a lot more games:

1. Don't draw a box's third side while you have any other choice. Whoever moves next just takes it.
2. Count the long chains. Late in the game, the boxes form chains, and the player who has to open the long ones usually loses.
3. Sometimes, give two boxes back. Taking every box isn't always right, because after your last capture you have to draw a line, and it may open a chain for your opponent.

Pro tip: Use Hint against the computer when you're not sure what to do. It shows you the line Hard would draw, which is a quick way to learn which lines are safe.

The dots and boxes strategy guide explains each of these with worked examples, and the 3x3 solution shows them deciding a whole game.

Keep playing

• Play Dots and Boxes against the computer or a friend
• Dots and boxes strategy: chains, control and double-dealing
• Dots and boxes 3x3 solution: who wins with perfect play, and why
• How to play Connect Four, another two-player classic, with its rules checked the same way