How to play Dots and Boxes

Dots and Boxes is played on a rectangular lattice of dots. This version offers four, five and six boxes to a side, which means a five-by-five game starts as six rows of six dots with sixty lines waiting to be drawn and twenty-five boxes waiting to be claimed.

Setup and the order of play

Nothing is placed at the start; the grid is empty. The first player draws a single horizontal or vertical line joining two dots that are next to each other. Diagonals are never legal, and a line already drawn cannot be drawn over. Play then alternates, one line per turn, until every line on the grid has been drawn. Nobody may pass, and nobody may draw two lines in a turn unless the first one earned it.

Claiming a box

A box belongs to whoever draws its fourth side. The claim is automatic and cannot be declined: if your line closes a square, that square is yours whether you wanted it or not. Claiming also grants an extra turn, and that extra turn is the engine of the whole game.

The detail people most often get wrong is a line that closes two boxes at once. A single line sitting between two squares that each already have three sides will complete both. You claim both, and you still receive exactly one extra turn, not two. That asymmetry is what makes the double-cross below work.

The extra turn is granted for closing a box, not for trying. A line that leaves a square on three sides earns nothing and ends your turn.

The vocabulary

A chain is a run of boxes joined end to end, each of which is one line away from being handed over as a group. Open a chain and your opponent can walk the whole thing, claiming every box in it, because each capture grants another turn.

A loop is a chain that closes on itself, and it is worth four boxes more than it looks, for reasons the double-cross explains.

A position is loony when every remaining line opens something. From that point on, nobody can move without giving boxes away, and the game becomes a question of who is forced to move first.

The double-cross, sometimes called the all-but-two, is the answer to a long chain. Instead of eating every box, you take all but the last two and then play the line that hands those two over in a single move. Your opponent claims two boxes, gets one extra turn, and finds nothing left to take — so they must open the next chain for you. Two boxes bought control of everything that follows.

Control is the name for holding that position: being the player who is eating chains rather than opening them.

Scoring and the end

There is no scoring beyond the boxes themselves. Each box is one point to whoever closed it, and the totals are shown live at the top of the board.

The game ends the moment the last line is drawn — there is no resignation and no other stopping condition, and because every turn draws exactly one line, a grid of sixty lines is always over inside sixty turns. On an odd number of boxes, such as the twenty-five of a five-by-five grid, a draw is impossible. On sixteen or thirty-six boxes an even split is a draw.

The computer

Easy claims every box on offer and otherwise plays a line that gives nothing away. It never double-crosses, so it wins the boxes in front of it and loses the endgame.

Medium looks a few moves ahead and will double-cross when it can see the payoff.

Hard counts the chains and loops left on the board, works out who ends up on opening duty, and will refuse boxes to stay in control. Beating it means taking control away from it, which usually means thinking about chain lengths long before the first box is closed.