Dots and Boxes Strategy: Chains, Loops and the Double-Cross

Most players learn Dots and Boxes as a game of not drawing the third side of a box. That is where it starts, but games are decided in the endgame. There, every move gives something away, and the winner is usually the player who controls the long chains. These seven ideas take you from beginner to a player who beats the normal computer. Some of them are also how the hard computer thinks. If you're new to the game, read the rules first.

1. Never draw the third side of a box

A box with three sides is a free box for your opponent. They take it, and because completing a box earns another move, they keep the initiative too. In the opening and middle game, only draw safe lines: lines that don't give any box its third side.

The top-middle box already has two sides. Drawing the dashed line would give it a third, and your opponent would take it.

2. The middle game is a race to run out of safe lines

Safe lines get used up. When none are left, the player to move must give something away. So the whole middle game is a fight over who has to move first once the safe lines are gone. Count the safe lines that remain as the board fills up. You want the other player to draw the last one.

3. Learn to see chains and loops

Late in the game the board breaks into regions. Every box in a region has two sides drawn:

A chain is a row of boxes linked through their open sides, with two ends. Once any line in it is drawn, someone can take the whole chain one box after another.
A loop is a chain that closes on itself, a ring of boxes with no ends.

Chains of three or more boxes are long chains. They decide most games.

A loop of four boxes (L) and a chain of five (1–5). Every box has two sides, so whoever moves next must open one of them.

4. When you must give something away, give the least

With no safe lines left, give away the shortest chain first. Single boxes and chains of two cost little, and they keep the turn moving while the long chains wait.

Loops are a special case. Your opponent can keep control of a loop, but it costs them four boxes instead of two. So it can be right to open a loop before a slightly shorter chain. In the diagram above, the player to move should open the loop, not the chain of five.

5. Open a chain of two in the middle

A two-box chain can be opened two ways:

Hard-hearted handout: the middle line. Two separate boxes, and no way to decline them cheaply.

Half-hearted handout: an end line. Your opponent can now take both boxes or decline them with a double-cross.

Use the middle line. After an end line, your opponent has a choice: take both boxes, or decline them and keep control. After the middle line they have no good way to decline. They take the two boxes and must move again.

6. The double-cross: give two boxes, keep the game

When your opponent opens a long chain for you, it looks natural to take every box. But then you must move next and open the next chain. Instead, take every box except the last two. Then draw the line at the far end of the chain. That leaves a two-box domino.

Player A took three boxes of the chain, then drew the dashed line instead of taking the last two. B takes the two boxes, then has to open the loop.

Your opponent takes the two boxes with one line, which is the double-cross. They now have to move, and the next chain is yours too. The player who keeps doing this is in control. They give up two boxes per chain (four per loop) and collect everything else.

Control isn't always worth it. If what's left on the board is smaller than the boxes you'd give back, just take everything. A quick check: keep control when at least one more long chain, or a big loop, is still to come.

Watch for the double-cross from the other side too. If your opponent leaves you a domino, take it. That's free. Then remember that you have to move next.

7. The long chain rule

Who ends up in control is decided earlier, by how many long chains the board breaks into. Elwyn Berlekamp's long chain rule says: on a rectangular board, the first player wants dots + long chains to be even, and the second player wants it odd. Loops don't count for this rule.

kawu's boards have 16, 36 and 64 dots, all even. So:

If you moved first, steer towards an even number of long chains: 0, 2, 4…
If you moved second, steer towards an odd number: 1, 3…

In the middle game you can split one long region into two chains, or join two regions into one. Do it while safe lines remain, to fix the count in your favour. This takes practice, so start by counting chains on the 5×5 board in each game.

Practising on kawu

Start on 3×3 against Normal. It's small enough to see every chain, and the computer will double-cross you if you open chains carelessly.
On 5×5, use Hint when the safe lines run out. It shows the line the computer would draw.
Hard plays the whole endgame exactly. If you beat it on 7×7, you understand chains.

Frequently asked questions

What is the best strategy in Dots and Boxes?

Avoid drawing the third side of any box for as long as possible. Then aim to be the player who takes control of the long chains at the end, using the double-cross: take all but the last two boxes of a chain and hand those two back, so your opponent has to open the next chain.

What is a double-cross in Dots and Boxes?

When you are given a chain, you take every box except the last two. Then you draw the line at the far end instead of taking them, which leaves a two-box domino for your opponent. They take the two boxes, but then they must move and open the next chain for you. In a loop you leave the last four boxes instead, as two dominoes.

What is the long chain rule?

On a rectangular board, the first player wants the number of dots plus the number of long chains (three or more boxes) to be even; the second player wants it odd. All of kawu's boards have an even number of dots, so the first player is aiming for an even number of long chains.

Is it ever right to take every box?

Yes. If the boxes you would give back are worth more than what is left on the board, just take them all. Keeping control only pays when long chains or loops are still to come.

Last updated 2026-10-17