Dominect: A Simple yet Deep 2-Player Board Game Oswin Aichholzer1, Maarten Löffler2, Jayson Lynch3, Zuzana Masárová4, Joachim Orthaber1, Irene Parada5, Rosna Paul1, Daniel Perz1, Birgit Vogtenhuber1, and Alexandra Weinberger1 1Graz University of Technology, Austria; {oaich, ropaul, daperz, bvogt, aweinber}@ist.tugraz.at,
[email protected] 2Utrecht University, the Netherlands; m.loffl
[email protected] 3University of Waterloo, Canada;
[email protected] 4IST Austria;
[email protected] 5TU Eindhoven, the Netherlands;
[email protected] Abstract In this work we introduce the perfect information 2-player game Dominect, which has recently been invented by two of the authors. Despite being a game with quite simple rules, Dominect reveals a surprisingly high depth of complexity. Next to the rules, this work comes with a webpage containing a print-cut-glue-and-play version of the game and further information. Moreover, we report on first results concerning the development of winning strategies, as well as a PSPACE-hardness result for deciding whether a given game position is a winning position. Introduction and Game Description Dominect is a finite, deterministic perfect information 2-player game developed by Oswin Aichholzer and Maarten Löffler during the 33rd Bellairs Winter Workshop on Computational Geometry in 2018. It belongs to the class of connection games, where a typical goal is to form a path connecting two opposite sides of the game board; see for example [1, 8]. Prominent members of this class are Hex (aka Con-tac-tix), TwixT, and Tak. But many others like Havannah, Connect, Gale (aka Bridg-It), or the Shannon switching game are also rather popular, as games or mathematical puzzles or both.