Best play in Dots and Boxes endgames

Abstract

We give very simple algorithms for best play in the simplest kind of Dots and Boxes endgames: those that consist entirely of loops and long chains. In every such endgame we compute the margin of victory, assuming both players maximize the numbers of boxes they capture, and specify a move that leads to that result. We improve on results by Buzzard and Ciere on the same problem: our algorithms examine only the current position and do not need to consider the game tree at all.