About Dots and Boxes
Dots and Boxes starts with an empty grid of dots. Players take turns drawing lines, and whoever draws the fourth side of a box claims it and moves again. It looks like a simple game, but the endgame rewards careful counting.
How to play
- The grid has 6x6 dots, forming 25 boxes. You move first against the computer.
- On your turn, draw one horizontal or vertical line between two neighbouring dots that are not yet joined.
- If your line completes the fourth side of one or two boxes, you claim them and must draw another line. Otherwise the turn passes.
- The game ends when every line has been drawn. The player with more boxes wins. With 25 boxes, a draw is not possible.
- Your boxes are shaded indigo and the computer's are shaded rose. The number of boxes you claimed is submitted as your score, win or lose.
Controls
- Click or tap the gap between two dots to draw a line. Each gap has a wide invisible hit area to make tapping easier on phones.
- Press Play again at the end to start a new grid.
Tips and strategy
- Early on, avoid drawing the third side of any box. That simply hands the box to your opponent.
- Eventually every safe line runs out and someone must open a chain of boxes. Count the chains and try to make sure your opponent is the one forced to open them.
- When you are forced to give boxes away, give away the shortest chain available.
- The computer always takes every box it can. That means it never uses the double-cross sacrifice, so careful chain control lets you collect the long chains at the end.
- When you take a long chain, consider leaving the last two boxes for your opponent with a single line, so that they must open the next chain for you. This is the double-cross and it is the key advanced technique.
Background
Dots and Boxes was described in 1889 by the French mathematician Edouard Lucas, who called it la pipopipette. It has since become a favourite of recreational mathematicians because its endgames can be analysed with combinatorial game theory. Elwyn Berlekamp, one of the founders of that field, wrote a whole book on it, explaining how counting chains and using the double-cross let a strong player control who gets the long chains.
Questions
- How does the computer play?
- It follows three simple rules: complete a box if it can, otherwise pick a random line that does not create a third side on any box, and only when no safe line remains, pick any line at random. It is greedy and never sacrifices boxes on purpose.
- Why did I get another turn?
- Completing a box always earns an extra move. You keep going as long as each line you draw finishes a box.
- Can a game end in a tie?
- No. There are 25 boxes, an odd number, so someone always has more.