Dots and Boxes — the free browser version of the classic pencil game

Thirty-six dots in a six-by-six square, sixty lines waiting to be drawn, and twenty-five boxes to fight over. You and the computer take turns joining two neighbouring dots. Draw the fourth side of a box and it is yours — and you move again, immediately, which is why a good position can suddenly pour ten boxes into one player's lap in a single turn.

You always go first, in green. Your score is simply how many of the 25 boxes you end up holding, so 13 is a win and 25 is a perfect game. There are no draws: an odd number of boxes makes sure of that. The computer is not a random line-drawer — it counts chains, keeps safe moves in reserve, and will refuse two free boxes at the end of a chain in order to hand the next one to you.

How to play

• Tap anywhere near a gap between two dots to draw the line there. You do not need to hit the line itself — the nearest free line to your finger is the one you get.
• Completing a box claims it and gives you another turn. Keep going as long as you keep closing boxes.
• A turn passes the moment you draw a line that closes nothing.
• The game ends when all 60 lines are drawn. Your score is your boxes, out of 25.
• On a keyboard, tab to a line and press Enter or Space.

The whole game is the endgame: chains, safe moves and the double-cross

Here is the uncomfortable truth about Dots and Boxes: the opening barely matters. For the first thirty-odd moves both players are just drawing lines that give nothing away, and almost any of them will do. The game is decided later, in a phase most beginners never notice is happening.

Call a line safe if drawing it leaves no box with three sides. Safe lines are the whole early game — you play them, your opponent plays them, and neither of you scores a thing. But safe lines run out. When they do, whoever is on move must draw a line that gives a box its third side, and their opponent takes that box, and then the box next to it, and the box next to that. Boxes link up into chains, and because closing a box grants another turn, a chain is eaten whole in one long turn. The player forced to open the first long chain hands over every box in it. That is the game. Everything before it is manoeuvring for who runs out of safe moves first.

Which sets up the one move that separates a decent player from a beginner: the double-cross. Suppose you have just been handed a chain of six. The greedy line is to take all six — and then you have no safe moves left, so you must open the next chain and hand it straight back. Instead, take four and stop. With two boxes left in the chain, draw the line that closes the chain off rather than the one that scores: it completes nothing, so your turn ends, and your opponent is left staring at two free boxes that they must take, after which they are the one with no safe move and they open the next chain. You gave up two boxes to buy every chain that follows. On a long chain that is a bargain, and the computer here plays it against you — if it takes some of a chain and then stops short, that is what just happened. (Against a closed loop the price is four rather than two, because a loop has to be cut into two dominoes; the same idea, one size larger.)

Finally, the counting. Since control passes back and forth with every double-cross, you can work out who ought to end up in control before a single chain is opened, just from how many chains the position will break into. The rule of thumb: with an even number of dots along each side — six here, so it applies — the first player wants an odd number of chains, and the second player wants an even number. You are first, so while you are still playing safe lines, look at how the board is dividing up and steer the count towards odd: join two would-be chains into one, or split one into two, whichever gets you there. Beginners spend the early game trying not to give anything away. Good players spend it deciding what the endgame will look like.

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