Analyzing a variant of Clobber: The game of San Jego

Article type: Research Article

Authors: Thiele, Raphael | Althöfer, Ingo^{; *}

Affiliations: Institute of Mathematics, Friedrich Schiller University, 07740 Jena, Germany

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: San Jego is a two-player game with perfect information. It is a variation of the games Clobber (2001) and Cannibal Clobber. Given is a rectangular board with black and white pieces on the cells. Multiple pieces which are stacked on each other are called towers. The piece on top of a tower indicates her owner. A move consists of picking an own tower and placing it completely on top of an adjacent tower. If both players can not move anymore, the game ends. Winner is the player with the highest tower. An upper bound for the state-space complexity of San Jego is determined. Furthermore, the game-tree complexity is approximated theoretically and numerically. For small board sizes, the optimal game-theoretic values are calculated and the advantage of the first move is determined.

Keywords: Board game, Clobber variant, state-space complexity, game-tree complexity, game-theoretic value

DOI: 10.3233/ICG-200164

Journal: ICGA Journal, vol. 42, no. 4, pp. 257-271, 2020