Dots and Boxes terminology

Dots and Boxes Glossary

What makes a chain long? Who is in control? Find the terms used in the rules, strategy and history of Dots and Boxes, grouped by when you’ll encounter them.

The board

Dot: One of the points on the grid. The LarkSpark board has 36 dots in six rows of six.
Line: What you draw on your turn. A line joins two neighboring dots across or up and down, never diagonally, and can be drawn only once.
Edge: A line between two neighboring dots, drawn or not. An inside edge is a side of two boxes, and an edge on the border is a side of one. The LarkSpark board has 60 edges.
Rail: A drawn line as it appears on the LarkSpark board. Blue’s rails are blue and Red’s are red, though the color of a rail has no effect on who claims a box.
Box: A square closed on all four sides. It belongs to the player who drew the fourth side, and the LarkSpark board has room for 25.

Scoring and turns

Turn: Everything you draw before play passes to your opponent. A turn is one line if it claims nothing, and it keeps going for as long as each line claims a box.
Extra move: The line you draw after claiming a box. It is required whenever any lines remain, even if every one of them gives something away.
Double box: Two boxes claimed with one line, which happens when the line sits between two boxes that each have three sides. It scores two points and earns one extra move.
Third side: The line that leaves a box one side short of finished. Drawing it without scoring lets your opponent claim that box on the next move.
Safe move: A line that doesn’t give any box its third side. Once the safe moves run out, every line gives something away.
Endgame: The last phase of play, after the safe moves are gone. The board has settled into chains and loops, and each turn decides who must open the next one.

Chains and loops

Chain: A run of boxes where claiming one opens up the next. Follow the undrawn edges from box to box, including around corners, to see how far a chain goes.
Short chain: A chain of one or two boxes. Opening one costs little. A two-box chain opened as a hard-hearted handout gives your opponent no chance to keep control with it.
Long chain: A chain of three or more boxes. Whoever takes it can always stop two boxes short with a double-dealing move.
Loop: A chain that connects back to itself, so it has no ends. The smallest is a 2×2 block of four boxes, and keeping control of a loop costs four boxes where a chain costs two.
Opening a chain: Drawing the first line in a chain or loop, which gives a box its third side. Your opponent can then take boxes from it one after another.
Handout: Boxes you give up because you have to move somewhere. The term is most often used for opening a short chain.
Half-hearted handout: Opening a two-box chain with a line at one end. Your opponent can take both boxes, or answer with a double-dealing move and hand the pair back to you along with the next move.
Hard-hearted handout: Opening a two-box chain by drawing the line between the two boxes. Each box now needs its own line, so your opponent has no way to decline them and must take both and then move again.
Double-dealing move: The all-but-two move. With two boxes left in a chain, you draw the far end line and leave the middle edge open. You score nothing, and your opponent can take the pair with one line.
Double-cross: The trade set up by a double-dealing move. Your opponent takes the two boxes you left with a single line, then has to open the next chain for you. In Berlekamp’s counting, a doublecross is that one line taking two boxes.

Control and counting

Control: The position of the player who has just finished a turn when every move left opens a long chain or a loop. That player can take most of each one and still make the opponent open the next.
Sacrifice: Giving up boxes on purpose. You might hand over a box or two early to change the number of long chains, or leave two at the end of a chain to keep control.
Loony move: Berlekamp’s name for a move that lets your opponent choose between taking everything on offer and keeping control. Opening a long chain or a loop is loony, and so is a half-hearted handout.
Parity: Whether a count is odd or even. In Dots and Boxes the count that matters is the number of turns, because it decides who is left to open the first long chain.
Long-chain rule: Berlekamp’s counting rule. Dots plus doublecrosses equals turns, so the first player should try to make the dots plus the long chains an even number and the second player an odd one. On LarkSpark’s 36-dot board, Blue wants an even number of long chains and Red wants an odd number. Loops don’t count as long chains, and sacrifices can upset the count.

The mathematics

Strings and Coins: The same game drawn another way. Each box is a coin, each undrawn edge is a string tied to the coins on either side or to the ground, and a move cuts one string. You pocket a coin when you cut its last string, then cut again.
Nimstring: A game with the same moves as Strings and Coins and no score. The player who completes the last box loses, because that player must move again and can’t. Winning it often shows who gets control in Dots and Boxes.
La pipopipette: The name Édouard Lucas gave the game in 1889, when it was sold as a set of thirty-six pegs and sixty bars. The history chapter tells the story.
Solved game: A game whose result under perfect play has been worked out. A board of 4×5 boxes is a tie. The 5×5 board LarkSpark uses has no published solution that we know of.