Proposal and generation of endgame puzzles for an imperfect information game Geister

Abstract

Geister is a two-player imperfect information game played with two kinds of pieces, blue and red, where each player cannot observe the colors of the opponent’s pieces on the board. In this paper, we propose Geister endgame puzzles for players to enjoy the game in another form or to practice figuring out moves that are proven to win, similar to chess mating problems. In Geister endgame puzzles, the goal is to find the shortest winning moves under the assumption of the worst cases. We propose not-revealed and partly-revealed puzzles according to how the opponent’s piece colors are revealed to the player. We also propose two kinds of special puzzles, capture-win and red-wall, that utilize specific victory conditions of Geister. We generate Geister endgame puzzles by randomly placing pieces on the board and then using a solver to check whether winning moves exist. The generation success rates for not-revealed and partly-revealed puzzles are approximately 20% to 30%. The experiments also show that puzzles with more moves to win are less frequently generated. In addition, we conduct preliminary experiments that invite beginners to evaluate generated puzzles, which shows that longer-win and special puzzles tend to be more difficult and interesting, respectively.