How to play dots and boxes: Box Grab rules and strategy

Dots and boxes is the notebook classic: you take turns drawing lines between dots, and whoever draws the fourth side of a box claims it and goes again. It looks simple, but the ending is decided by chains. This guide covers the rules, how to play without handing out boxes and the double-cross trick strong players rely on. On Stockboi the game is called Box Grab.

Play Box Grab

What is dots and boxes and how is the board set up?

The board is a grid of evenly spaced dots. Lines are drawn between two neighboring dots, and every square closed in by four lines is a box.

Box Grab has three boards: 3x3 boxes (16 dots, 24 lines), 4x4 boxes (25 dots, 40 lines) and 5x5 boxes (36 dots, 60 lines). We count boxes, not dots, so the game you’d play on a 5x5 grid of dots on paper is our 4x4 board.

Dots and boxes rules

Players take turns drawing one horizontal or vertical line between two neighboring dots. There are no diagonal lines, and a line can’t be drawn twice.
Draw the 4th side of a box and it’s yours, plus you go again. If your next line closes a box too, you keep going; that’s how you collect a whole chain.
A single line can close two boxes at once if it’s their shared side. That’s a double box, and it also earns you another move.
Closing a box is never required. You can draw a different line even when a box is up for grabs, and the double-cross trick below depends on exactly that.
The game ends when every line is drawn, and the player with more boxes wins. The 3x3 and 5x5 boards have an odd number of boxes, so there are no draws; on 4x4, 8-8 is a draw.
Some people play without the extra turn. Stockboi uses the classic rule: close a box and you go again.

A round, step by step

The game starts on an empty board. In the first moves, both players draw lines without giving any box its 3rd side.
As safe lines run out, boxes with two sides drawn form corridors across the board. These are chains.
At some point there are no safe lines left, and the player to move has to give a box its 3rd side. They pick the spot that gives away the fewest boxes.
The opponent takes the opened box or chain; when their line at the end closes nothing, the turn passes and now they have to open the next chain.
When the last line is drawn, the boxes are counted and the higher total wins.

Opening and middle game: never give the 3rd side

The most basic rule: don’t draw a box’s 3rd side. If you do, your opponent draws the 4th, takes the box and moves again.

Early on almost every line is safe, so the opening goes quickly. The real question is who will be on move when the safe lines run out. Counting the safe lines lets you see it coming.

While you prepare for the moment you’ll have to give boxes away, create small pieces. Pieces of one or two boxes give little away; chains of three or more decide the game.

Chains and the double-cross: keeping control

A chain is a corridor of boxes linked by open sides: once one gets its 3rd side, they can all be taken in a row. A chain of three or more boxes is a long chain. A chain whose ends join up is a loop.

Near the end, usually only chains remain and the player to move has to open one. The player who doesn’t have to open chains, the one in control, usually wins.

The way to keep control is the double-cross trick. When your opponent opens a long chain for you, don’t take it all: take every box except the last two, then draw the line at the far end of the chain. That leaves two boxes with 3 sides each and their shared side open. Your opponent takes both with one line, but then it’s still their turn and they have to open the next chain for you.

Giving up two boxes to take the whole next long chain is usually a great deal. In a loop the same trick means leaving the last four boxes, so loops are more expensive to keep control through.

If you’re forced to hand over a two-box chain, draw the line in the middle. The two boxes then open separately and your opponent can’t pull the double-cross on you. Drawing an end line instead gives them the chance to keep control.

The long chain rule

The shortcut for working out who will end up in control is the long chain rule, found in the classic books on the game: the first player wants the number of dots plus the number of long chains to be even; the second player wants it odd.

Applied to Box Grab: the 3x3 and 5x5 boards have an even number of dots (16 and 36), so the first player wants an even number of long chains and the second player an odd number. The 4x4 board has 25 dots, so there the first player wants an odd number of long chains and the second player an even number.

If the count isn’t going your way, you can sacrifice a box or two in the middle game to split a chain or join two pieces into one. Loops complicate the count; the rule is a compass, not a guaranteed win.

Common dots and boxes mistakes

Grabbing every box right away. Taking all of a long chain near the end can hand over control and cost you the even longer chain that follows.
Opening the long chain. When you have to open something, give your opponent the shortest chain.
Handing over a two-box chain from the end. Unless you draw the middle line, your opponent can double-cross and keep control.
Not counting safe lines. If you don’t know who will be on move when they run out, you’ll be too late to shape the chains.

A short history of dots and boxes

The game was first written down in 1889 by French mathematician Édouard Lucas, and it has lived on the back pages of school notebooks ever since.

Ideas like chains, the double-cross and the long chain rule were put into a system much later, when mathematicians studied the game with combinatorial game theory. Box Grab plays by the same classic rules.

How to play Box Grab on Stockboi

Vs computer: pick the board size (3x3, 4x4, 5x5) and the difficulty from Settings at the bottom. You start the first round, then the first move switches sides every round. Your results are kept separately for each difficulty and size.
Easy sometimes misses a free box and sometimes hands you a 3rd side for nothing. Medium always takes boxes and tries not to give away a 3rd side. Hard knows how to leave you two boxes at the end of a chain and keep control.
Play with a friend: create a room, then send the link or tell them the room code. Random opponent: you get matched with someone who wants to play right now; if nobody is around, we say so clearly and you can play the computer.
Online games are always on the 4x4 board. You have 60 seconds per move; run out and you lose. If you disconnect, you have 60 seconds to come back. A rematch needs both of you to ask, and the first move switches sides.
Controls: press near a line, slide your finger to pick the right one and let go to draw it.

Frequently asked questions

Do you go again after completing a box in dots and boxes?

Yes. In Box Grab, drawing the 4th side of a box gives you the box and another move. Closing two boxes with one line also earns one more move.

Do you have to complete a box if you can?

No. You can draw a different line even when a box is available. That’s what makes it possible to leave the last two boxes and keep control.

What is the best strategy for dots and boxes?

Never give a box its 3rd side unless you must, and open the shortest chain when you have to. When your opponent opens a long chain, leave the last two boxes to keep control.

What is a double-cross in dots and boxes?

It’s a single line that completes two boxes at once. Leave your opponent a double-cross on purpose and you give up two boxes, but they have to open the next chain.

Can dots and boxes end in a tie?

Only on a board with an even number of boxes. In Box Grab, 8-8 on the 4x4 board is a draw; 3x3 and 5x5 always have a winner.

How many players can play dots and boxes?

Two. On Stockboi you can play a friend by link, a random opponent or the computer at three difficulty levels.