Why a farm?

The squares in this game were always pens. One of the old names for dots and boxes is pigs in a pen, and once you’re drawing fences between posts, a farm is the obvious picture. So every square you close becomes a little pen, and an animal walks in: a sheep, a pig, a hen, a cow, a duck or a rabbit.

On paper, you write your initial in a closed box and that’s it. We wanted pens you could keep, so the animals you pen against the computer go home to your barn, even in a game you lose.

A bit of real dots and boxes history

The French mathematician Édouard Lucas described the game in 1889 and called it la pipopipette. He credited the idea to his students at the École polytechnique, whose nickname in student slang was pipo.

Elwyn Berlekamp, a mathematician at Berkeley, learned the game in first grade in 1946 and kept playing and studying it from then on. He wrote it up with John Conway and Richard Guy in a chapter of Winning Ways for your Mathematical Plays in 1982. In 2000 he gave it a whole book, The Dots and Boxes Game, with the subtitle Sophisticated Child’s Play.

Computers have solved some small boards. In 2012, Joseph Barker and Richard Korf showed that a board of 4 by 5 boxes ends in a tie when both players play perfectly. At the time, it was the largest board anyone had solved.

The three farmers

• 🐤 Chick: usually closes a pen when it can and usually avoids giving you a third side. Not always.
• 🐐 Goat: always closes a pen when it can and never gives you a third side if it has a choice. When it has to give something away, it gives as little as it can.
• 🐂 Farmer Ox: plays the chain game. It uses the leave-two trick, and near the end it works through every way the game can finish.

How to play

• Tap or click between two posts to put up a fence.
• If your fence closes the fourth side of a square, that square is your pen. An animal walks in and you put up another fence.
• When all the fences are up, the farmer with more pens wins.
• Play the computer or 2 players on one device, on a Small (3×3), Middle (4×4) or Big (5×5) field.
• Stars for a win against the computer: 1 for any win, 2 for winning by 3 or more pens, 3 for winning by 5 or more. Goat opens after you beat Chick once, and Farmer Ox after you beat Goat once.
• On a keyboard, Tab to the field, move with the arrow keys and press Enter to build.
• Sound is on to start. Tap 🔊 to mute, or 🎵 for music.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips

Don’t add a third side. A square with three fences is a free pen for the other player. Early on, pick fences that leave every square with two sides or fewer.

Count the long chains. Late in the game the open squares join up into chains. A chain is long if it has 3 or more squares, and the player who has to open the first long chain usually loses. On a 3×3 or 5×5 field, the player who goes first wants an even number of long chains. On a 4×4 field, the first player wants an odd number.

Leave two. When someone opens a long chain for you, take every pen except the last two. Then put your fence on the far end of those two. The other player gets two pens with one fence and has to open the next chain for you.

Give away short chains first. If you have to open something, open a chain of 1 or 2 squares before a long one. When you give away two squares side by side, put your fence on the line between them, so the other player can’t leave them for you.

Your turn

The posts are in and the animals are waiting. Pick a farmer and a field, and play.