Dots and Boxes strategy: how to win with chains and the double-cross

Dots and Boxes rules

In Dots & Boxes, players take turns drawing one line between two neighbouring dots, across or down, never diagonally.

• If your line completes the fourth side of a box, the box is yours, and it fills with your colour and shape.
• Closing a box gives you another turn straight away, so you can take several boxes in a row. Your turn only ends when you draw a line that doesn't close a box.
• You never have to close a box. You can always draw a different line instead (this matters later).
• When every line has been drawn, the player with the most boxes wins. Players tied for the most boxes share the win.

On PlayTrova you can choose a 3×3 board (9 boxes, quick and great for younger kids), 4×4 (16 boxes) or 5×5 (25 boxes, a long strategic battle). Two, three or four players can share one device, each with their own colour and shape. Games against the computer and online games with an invite link are for two players.

Beginner strategy: never draw the third side

A box with three sides drawn is a free gift: the next player closes it and goes again. So the first rules of Dots and Boxes strategy are simple:

• Take free boxes. If a box has three sides, close it (with one clever exception, coming up below).
• Don't draw the third side of a box if you can avoid it.
• Play safe lines early. A safe line is one that doesn't give any box its third side.

At the start almost every line is safe. As the board fills up, the safe lines run out, and eventually someone has to give boxes away. That moment decides the game, and the rest of this guide is about winning it.

Chains: where Dots and Boxes is really won

When the safe lines run out, the open boxes have usually joined up into chains: corridors of boxes where any line you draw lets your opponent take the whole corridor, one box after another.

• A short chain has one or two boxes.
• A long chain has three or more boxes.
• A loop is a chain that joins back onto itself in a ring.

With no safe lines left, the player to move must open something. Open the smallest thing first: single boxes, then pairs, and a long chain only when there's nothing else.

The double-cross: a worked example

This is the move that separates beginners from strong players. Imagine the safe lines have run out, and the only boxes left are two long chains: one of 3 boxes and one of 6 boxes. It's your opponent's turn, so they must open one. They open the 3-chain.

Option 1: take everything. You close all 3 boxes. But after closing a box you must draw again, and every line left opens the 6-chain. Your opponent takes all 6. Score from these chains: you 3, them 6.

Option 2: the double-cross. You take only 1 box, all but the last two. Then, instead of closing the next box, you draw the line at the far end of the chain. That line doesn't close anything, so your turn ends, and the last two boxes are left waiting to be closed together by one line.

Your opponent closes both boxes with that single line. But closing boxes means they must draw again, and the only lines left open the 6-chain. You take all 6. Score: you 7, them 2.

Giving away two boxes to win six is a great trade. The player who can keep doing this is in control: the opponent keeps having to open chains, and the controller keeps taking all but two. Grandmaster Owl even teases you about it: "Two boxes for you, the rest for me."

• Double-cross when another long chain or loop is still to come.
• On the very last chain, never double-cross. Take every box.
• Keeping control of a loop costs four boxes instead of two, so it only pays when what's left is worth more.

The long chain rule: how to get control

So who ends up in control? Whoever makes the other player open the first long chain. Strong players fight over this long before the safe lines run out, using the long chain rule from the mathematics of Dots and Boxes:

Count the dots on the board and add the number of long chains there will be at the end. The first player wants that total to be even. The second player wants it odd.

On PlayTrova's boards, that works out like this:

• 3×3 board (16 dots): the first player wants an even number of long chains, such as 2. The second player wants an odd number, such as 1 or 3.
• 4×4 board (25 dots): it flips. The first player wants an odd number of long chains, and the second player wants an even number.
• 5×5 board (36 dots): like 3×3, the first player wants even and the second player wants odd.

Loops don't count as long chains for this rule. To use it, count the long chains that are forming in the middle of the game. If the number suits you, keep things calm with safe lines. If it doesn't, try to change it: split a big open area so it becomes two chains, or cut a growing chain into short pieces so it no longer counts.

For example, on the 3×3 board you went first and you can see a single long chain forming down one side. One is odd, which suits your opponent. Look for safe lines that will create a second long chain elsewhere, or cut the first one down to two boxes. The rule is for two-player games; with three or four players, play safe and give away as little as you can.

Common Dots and Boxes mistakes

• Drawing a third side early, just because it was the nearest line.
• Grabbing every box in the endgame without thinking. Taking a whole chain can hand your opponent the rest of the board.
• Double-crossing on the last chain, when there's nothing left to win back.
• Opening a long chain while a short chain or single box is still available to give away.
• Giving away a two-box chain by its end line instead of its middle line.
• Forgetting to count. Halfway through the game, stop and count the long chains.

Practise against the computer and daily box puzzles

The four computer characters make a perfect ladder for learning chains. Rookie Robo draws lines almost at random and grabs a box now and then. Clever Cat knows the beginner rules. Sly Fox understands chains and the double-cross, and Grandmaster Owl calculates the endgame exactly. You swap who goes first each game, so you get to practise both sides of the long chain rule.

In Solo mode there are three new box puzzles every day, the same for everyone. Each one is an endgame where you move first and must finish with more boxes than Grandmaster Owl. You get three hints, and you can retry or skip a puzzle. Most of them come down to knowing when to take everything and when to leave the last two boxes.

Like games where one move earns you another turn? Try Mancala, where landing your last seed in your store earns a free turn; our Mancala guide explains how. For more quiet strategy games, browse the puzzle games, or see our list of the best 2 player games for kids.

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