Primrose Paddocks

What is dots and boxes?

Dots and boxes was first published in 1889 by the French mathematician Edouard Lucas, who called it la pipopipette. It has been drawn in the margins of exercise books ever since, under plenty of names: boxes, squares, paddocks, dots and dashes, the dot game and, our favourite, pigs in a pen.

The rules take ten seconds to learn. The strategy took mathematicians most of the last century to work out, and the late Elwyn Berlekamp wrote a whole book about it. We built Primrose Paddocks so you can enjoy both: a quick, friendly game with the drawing feel of real ink, and house players and hints that quietly teach the ideas strong players use. It's free, it runs in your browser and there's nothing to download.

How to play dots and boxes

1. The board. A grid of dots. We play 4 by 4 boxes (5 by 5 dots) by default, and you can pick anything from 3 by 3 to 8 by 8.
2. Draw a line. On your turn, join two dots that sit next to each other, across or down. Diagonals don't count.
3. Close a box. If your line is the fourth side of a box, the box is yours. We fence it in, wash it in your color and pop your critter inside.
4. Go again. Closing a box means you must draw another line. One line can even close two boxes at once.
5. The end. When every line is drawn, whoever owns the most boxes wins. On boards with an even number of boxes a tie is possible.

We also offer two classic starts from Scandinavia. On a Swedish board the outside border is already drawn, which makes every box on the edge more dangerous. On an Icelandic board the left and bottom edges are drawn.

Chains, loops and the double-cross

Early in the game nobody wants to draw the third side of a box, because the next player simply takes it. These harmless moves are safe lines. As they run out, the board turns into chains (corridors of boxes where opening one end lets the other player take them all) and loops (closed rings of boxes).

Sooner or later someone has to open a chain. Here's the trick that separates beginners from strong players. When you are handed a long chain, take every box except the last two, then draw the line at the far end instead. That hands two boxes back as a little gift. Your opponent takes them, and now they have to open the next chain for you. This is the double-cross, and the player doing it has control. With a loop you hand back four boxes instead of two.

Giving away two boxes per chain to collect all the rest is usually a bargain. But not always: when the chains left are short, or there are lots of loops, keeping control costs more than it earns, and the right play is to take everything. Our hints and our game review tell you which is which.

The long chain rule

Whoever has to open the first long chain (three boxes or more) usually loses. You can steer that from the middle of the game. The rule, from Berlekamp: count the dots on the board and the long chains you expect. The first player wants dots plus long chains to be an even number; the second player wants it odd. On our 4 by 4 board there are 25 dots, so the first player is hoping for an odd number of long chains.

You change the count by joining two short chains into a long one, or by cutting a long one in two. Sometimes it's worth sacrificing a box or two early just to change who will run out of safe lines first.

Playing Primrose Paddocks

• On a phone or tablet: touch near the line you want. We pick the nearest open line anywhere on the board, so you never have to hit a thin line exactly. Slide to change it, lift your finger to draw it. If a line would give boxes away, the boxes at risk light up and a little label says how many. Turn on Tap twice to draw in Settings if you like to be sure.
• With a mouse: point at a line to see it, click to draw it.
• With a keyboard: Tab to the board, walk the lines with the arrow keys and press Enter to draw. H shows a hint, U takes a line back and Esc opens the menu. Screen readers hear every line by its dots, like B2 to B3, and what drawing it would do.
• Undo, hints and the review: take lines back against house players and in pass and play. The light bulb shows our pick and says why. After a game, the review marks the lines that cost you, with notes like gave away a 4-chain while a safe line was left, or you should have double-crossed here.

High contrast mode gives every player a pattern as well as a color, and there's a less motion setting, pencil guides on the open lines and optional dot names round the board.

The house players

Five critters from the meadow, each a clear step up from the last. We measured every one against the one below it over hundreds of games.

Our engine is our own. Once the safe lines are gone and the board is only chains and loops, it knows the exact result straight away, the way Berlekamp's theory says it should.

Daily Paddocks and the ladder

Every day brings three new endings, the same for everyone. Each is a take the most boxes you can round against Sage, who defends perfectly. Short chains is a 3 by 3 board with every safe line gone. In Keep control, a 4 by 4 board, Sage has just opened a chain for you: take it all, or double-cross? Fight for control is a 3 by 4 board with a few safe lines left. Each round is worth 100 points if you take the most boxes there were, and 25 less for each box short. Your first go of the day goes on the daily leaderboard, out of 300, and you can share a spoiler free card.

The ladder is a rating that starts at 1200 and moves after every game against a house player. Beating a stronger player moves it more. Sign in to keep your ladder, streak, awards and unlocked paper and critters on every device.

Play with friends

Dots and boxes is a great game for more than two. In pass and play, 2, 3 or 4 players share one device, each with their own color and critter, and who goes first moves round the table every game. To play someone far away, open Play a friend, host a game and share the four letter room code or link. The host picks the board, and either of you can ask for a rematch. Online games use preset reactions only, with no typed chat.

Tips and strategy

• Before you draw a line, count its box's sides. A third side is a gift to the other player.
• When you must give something away, give the smallest thing: a single box, or a chain of two opened in the middle (that one can't be double-crossed).
• Opening a chain of two at the end lets the other player choose. Opening it in the middle doesn't.
• When you are handed a long chain, stop and count what is left before taking the last two boxes. If more long chains are coming, the double-cross usually wins.
• Loops cost twice as much to keep control of. With several loops on the board, taking everything can be better.
• Count dots plus long chains. If the count is wrong for you, try to make or break a chain, or sacrifice a box early to swap who runs out of safe lines first.
• On a 3 by 3 board the second player wins with perfect play, six boxes to three. Moving first, you need your opponent to slip.

Questions