Order versus Chaos

IEEE Conference on Games (CoG), vol. 529, pp. 391–398

Abstract

The positional game of Order versus Chaos can be considered a maker-breaker variant. The players Order and Chaos take turns placing circles or crosses on a board, in which the goal of Order is to create a consecutive line of identical symbols of a certain length, while Chaos aims to prevent this. In this paper, we provide some theoretical results on winning strategies for both players on finite boards of varying sizes, as well as on infinite boards. The composition of these strategies was aided by the use of Monte-Carlo Tree Search (MCTS) players, as well as a SAT solver. In addition to these theoretical results, we provide some more experimental results obtained using MCTS.

Authors 3

1. Mark J. H. van den Bergh Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch instituut, Leiden University, Leiden, The Netherlands

2. Sipke T. Castelein Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch instituut, Leiden University, Leiden, The Netherlands

3. Daniël van Gent Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch instituut, Leiden University, Leiden, The Netherlands