Playing simple loony dots and boxes endgames optimally

TL;DR

This paper presents a simple, efficient algorithm for playing certain dots and boxes endgames optimally, enabling human players to improve their over-the-board game performance.

Contribution

It introduces a highly efficient and simple algorithm for optimal play in specific dots and boxes endgames, suitable for human learning and practical use.

Findings

Algorithm achieves optimal play in simple dots and boxes endgames.

The method is simple enough for humans to learn and apply during games.

The approach improves over-the-board gameplay in practice.

Abstract

We explain a highly efficient algorithm for playing the simplest type of dots and boxes endgame optimally (by which we mean "in such a way so as to maximise the number of boxes that you take"). The algorithm is sufficiently simple that it can be learnt and used in over-the-board games by humans. The types of endgames we solve come up commonly in practice in well-played games on a 5x5 board and were in fact developed by the authors in order to improve their over-the-board play.