Dots and boxes

Usually two players take turns adding a single horizontal or vertical line between two unjoined adjacent dots.

A 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.

[9] For most novice players, the game begins with a phase of more-or-less randomly connecting dots, where the only strategy is to avoid adding the third side to any box.

The next level of strategic complexity, between experts who would both use the double-cross strategy (if they were allowed to), is a battle for control: an expert player tries to force their opponent to open the first long chain, because the player who first opens a long chain usually loses.

However, Dots and Boxes lacks the normal play convention of most impartial games (where the last player to move wins), which complicates the analysis considerably.

An intermediate version with only the left and bottom sides starting with drawn lines is called an Icelandic board.

A game of dots and boxes
Example game of Dots and Boxes on a 2×2 square board. The second player ("B") plays a rotated mirror image of the first player's moves, 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 so B connects the center dot to the center-right dot, causing the remaining unscored boxes to be joined in a chain (shown at the end of move 8). With A's next move, A gets all three of them and ends the game, winning 3–1.
The "double-cross" strategy: faced with position 1, a novice player would create position 2 and lose. An experienced player would create position 3 and win.