Dots and Boxes

You and the computer take turns drawing one line between two adjacent dots, and whoever completes the fourth side of a box claims it and goes again. It's the same pencil-and-paper game people have doodled in notebook margins forever, just with color added to the boxes you win. The real strategy shows up late in the game, when finishing a box for yourself can also hand your opponent a whole chain of easy boxes on the next turn.