About Dots and Boxes

Dots and Boxes is a pencil-and-paper strategy game with surprisingly deep competitive theory: players take turns drawing lines between dots, and completing a box earns a point and an extra turn. The critical insight that separates beginners from experts is the chain theory: once a long chain of boxes is created, completing it hands your opponent a long run of extra turns. Expert play involves deliberately managing chain lengths to maintain control of the turn order, even if it means giving away boxes in the short term. The game is studied in combinatorial game theory and has been used to train strategic thinking in competitive mathematics programs.