Championship-Level Play of Dots-and-Boxes
Julian West · 1997
A single-elimination Dots-and-Boxes tournament was held during the MSRI meeting, with a $500 purse. This is an analysis of the finals, in which Daniel Allcock defeated Martin Weber, playing both first and second player. A systematic notation is developed for the analysis. Dots-and-Boxes, described in Chapter 16 of Winning Ways [Berlekamp et al. 1982], is a game played on a finite rectangular unit lattice of dots (or, in dualized form, on an arbitrary graph). A move consists of joining two adjacent dots, that is, dots at distance one; if this completes one or more squares, a point (“box“) is awarded for each and the player retains her turn. A move after which turn does not pass to the opponent is known as a complimenting move and, under socalled normal win conditions—last player to move wins—leads to so-called loony values (explained below). However, Dots-and-Boxes does not have a normal win condition; indeed, analysis is complicated considerably by the unusual who-dieswith- the-most-wins condition. Under various names, this game is popular with children in many countries. As played by most practitioners, it is a fairly uninteresting game, consisting of a phase of randomly segmenting the board followed by a phase of greedily dividing up the spoils. So it would seem an odd choice for a tournament between serious game theory researchers. But Dots-and-Boxes is a classic example of a game that is Harder Than You Think. Winning Ways (p. 535) gives an account of all the stages you will go through in becoming a Dots-and-Boxes expert.