About Dots and Boxes
Dots and Boxes has been played on scraps of paper for well over a century. The rules take a moment to learn. The strategy underneath is deep enough to have had whole books written about it.
How a match works
The board is a grid of twenty-five dots, making sixteen possible squares. Players take turns to join two neighbouring dots with a line, across or down. Whoever draws the fourth side of a square owns it, and the square fills with their colour.
Completing a square earns another turn, and you have to take it. That rule is what makes the game. A player can sometimes take a whole run of squares one after another. With sixteen squares, the match can end eight all.
The stages of a game
The opening is quiet. For the first dozen or so moves there are plenty of safe lines to draw. The danger is drawing the third side of a square, because that hands your opponent the fourth.
Then the safe moves run out. Somebody has to give something away, and the board has usually formed into chains: corridors of squares that can be taken in one go.
How to win
Count before you draw. Never add the third side to a square unless you have no choice.
When you must give something away, give the smallest chain. Opening a chain of two costs you two squares. Opening a chain of six costs six.
Learn the sacrifice. When you are taking a chain, you do not have to take all of it. Stop with two squares left, and draw the line that leaves both for your opponent. They collect two, and are then forced to open the next chain for you. Giving up two to gain five or six is the move that separates strong players from everyone else.
For thoughtful two-player HTML5 games, this is the place to start.