Dots and Boxes

Dots and Boxes is a pencil-and-paper game for two players (sometimes more). It has gone by many other names, including the game of dots, boxes, dot to dot grid, and pigs in a pen.

Starting with an empty grid of dots, two players take turns adding a single horizontal or vertical line between two unjoined adjacent dots. The player who completes the fourth side of a 1×1 box earns one point and takes another turn. (A point is typically recorded by placing a mark that identifies the player in the box, such as an initial). The game ends when no more lines can be placed. The winner is the player with the most points. The board may be of any size. When short on time, a 2×2 board (a square of 9 dots) is good for beginners.[8] A 5×5 is good for experts.

The diagram on the right shows a game being played on the 2×2 board. The second player (B) plays the mirror image of the first player's move, hoping to divide the board into two pieces and tie the game. But the first player (A) makes a sacrifice at move 7 and B accepts the sacrifice, getting one box. However, B must now add another line, and connects the center dot to the center-right dot, causing the remaining boxes to be joined together in a chain (shown at the end of move 8). With A's next move, player A gets them all and wins 3–1.

In the game of "Dots and Boxes", the winner is generally the player who makes the last move. The reason for this is that at the end of the game, there are usually a few long corridors or chains of boxes left to be taken. If your opponent is forced to play in one of these chains, then you can take all but two of the boxes and, by sacrificing the last two boxes, make certain that it is his turn to play into the next long chain. You will thus win all but two boxes in each long chain, and of course you will win all boxes in the last chain. We say a chain is long if it contains at least three boxes.

The game is played starting with a rectangular array of dots.

The two players take turns to join two adjacent dots with a horizontal or vertical line. If a player completes the fourth side of a box they initial that box and must draw another line.

When all the boxes have been completed the winner is the player who has initialled the most boxes.

The game is more complex than it initially appears, and even on a 4x4 grid there is plenty of opportunity for skilful play.