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.