How a game really goes
Most games pass through three stages. First, both players draw safe lines that give nothing away. Then the safe lines run out, and the boxes have formed chains and loops. Finally someone has to open one, and the player in control takes most of what is left. Good players win the game at the change from the second stage to the third.
Stage one: don't draw the third side
A box with three sides drawn is a gift: your opponent closes it and draws again. While safe lines remain, never draw a box's third side, and take any box you are offered. A line is safe if neither box beside it ends up with three sides.
Keep an eye on how many safe lines are left. When only a handful remain, each one matters, because whoever draws the last safe line forces the other player to open something.
Chains and loops
- A chain is a run of boxes, each with two sides drawn, joined so that once your opponent draws a line in it, you can take the boxes one after another. Three or more boxes is a long chain; one or two is a short chain.
- A loop is a chain that joins up with itself, so it has no ends. The smallest is a 2×2 block of four boxes.
Short chains are small change. Long chains and loops decide the game.
The double-dealing move
Say your opponent opens a chain of five, and another long chain is still waiting. Taking all five looks obvious, but then you must draw again and open the next chain for them. The stronger play:
- Take the boxes one by one until two are left.
- Instead of taking the fourth box, draw the line at the far end of the chain. The last two boxes now form a closed pair with one undrawn line between them.
- Your opponent takes both with that one line (a double-cross) and then has to draw again, opening the next chain for you.
| You | This chain | Next chain |
|---|---|---|
| Take all five | 5–0 | You must open it |
| Take three, give two | 3–2 | They must open it |
Giving two boxes back keeps control. With a loop it costs four: take all but four, then draw the line between the middle two of them, leaving two pairs. On the last chain of the game, never decline: take everything. On Suvi you never have to take a box, so the double-dealing move is always open to you.
When you have to open something
If you are the one forced to give boxes away, give as little as you can, in this order:
- Single boxes and pairs. Open a pair by drawing the line between its two boxes. Opened at an end instead, it lets your opponent decline both boxes with a double-dealing move and keep control for the price of two.
- Loops, usually before long chains. To keep control on a loop your opponent must hand back four boxes rather than two.
- Long chains last, shortest first.
Counting chains: who gets control
Control usually goes to whoever does not have to open the first long chain, and there is a counting rule for it, known as the long chain rule. Add the number of dots on the board to the number of long chains there will be at the end. The first player wants that total to be even; the second player wants it odd. Loops don't count.
| Board | Dots | Boxes | First player wants |
|---|---|---|---|
| Small | 16 | 9 | An even number of long chains |
| Standard | 25 | 16 | An odd number |
| Large | 36 | 25 | An even number |
The second player wants the opposite on each board. In the middle game, while boxes still have only one or two sides, steer towards your number: break a growing chain into short pieces, or let two runs join into one long chain, whichever moves the count your way. A box or two given away early is a fair price if it changes who must open the first long chain. The small board has only a few chains, which makes it the best place to practise counting.
Playing Suvi's computer
- Medium takes every box it can and never draws a third side while it has a choice, but it never plays the double-dealing move, and it opens pairs from the end. When it has control, it takes a whole chain and hands control straight back. Use the double-cross yourself and you will win most endgames against it.
- Hard knows chains, loops and the double-cross, and once the safe lines run out it works out the rest of the game exactly. Beat it by winning the fight for control before then, which means getting the chain count right.
- Undo takes back your last line and whatever the computer drew after it, so you can replay an endgame and try another order. A hint shows the line Hard would draw.
If you only remember three things
- Never draw a third side while a safe line exists.
- When a long chain is opened for you and more are to come, take all but two and give the last two back.
- Count dots plus long chains, and fight for the total you need.
Try the double-cross on the small board against Medium, then take it to the standard board.
Questions
- What is a double-cross in dots and boxes?
- It is a single line that completes two boxes at once. You force your opponent into one with the double-dealing move: by leaving them a closed pair at the end of a chain, you make them take two boxes and then open the next chain for you.
- Should I always take a box when I can?
- Almost always. The exception is the end of a long chain or loop when more long chains are still to come: giving back the last two boxes, or four in a loop, keeps control and usually wins far more later.
- Do I have to take a box I can close?
- No. On Suvi you may draw any line on your turn. Closing a box simply gives you another line, which is why declining the last two boxes of a chain is allowed.
- Can dots and boxes end in a draw?
- Only on the standard board, which has 16 boxes and can finish 8 each. The small board has 9 boxes and the large board 25, so someone always wins.
- Which board size is best for learning?
- The small board. With 9 boxes the chains are short and few, so you can see exactly why giving two boxes back wins, and a game takes a couple of minutes.
Play it now
Dots and Boxes is free on Suvi, on your phone or computer, no download. Also: Dots and Boxes 4×4 dots · Dots and Boxes 6×6 dots · Dots and Boxes vs Computer · 2 Player Dots and Boxes · Dots and Boxes With a Friend Online.