ICGA Journal - Volume 42, issue 4 - Journals

Editorial: Many games, many authors

Article Type: Editorial

DOI: 10.3233/ICG-200176

Citation: ICGA Journal, vol. 42, no. 4, pp. 243-243, 2020

Polygames: Improved zero learning

Article Type: Research Article

Abstract: Since DeepMind’s AlphaZero, Zero learning quickly became the state-of-the-art method for many board games. It can be improved using a fully convolutional structure (no fully connected layer). Using such an architecture plus global pooling, we can create bots independent of the board size. The training can be made more robust by keeping track of the best checkpoints during the training and by training against them. Using these features, we release Polygames, our framework for Zero learning, with its library of games and its checkpoints. We won against strong humans at the game of Hex in 19 × 19 …, including the human player with the best ELO rank on LittleGolem; we incidentally also won against another Zero implementation, which was weaker than humans: in a discussion on LittleGolem, Hex19 was said to be intractable for zero learning. We also won in Havannah with size 8: win against the strongest player, namely Eobllor, with excellent opening moves. We also won several first places at the TAAI 2019 competitions and had positive results against strong bots in various games. Show more

Keywords: Zero learning, board games

DOI: 10.3233/ICG-200157

Citation: ICGA Journal, vol. 42, no. 4, pp. 244-256, 2020

Price: EUR 27.50

Analyzing a variant of Clobber: The game of San Jego

Authors: Thiele, Raphael | Althöfer, Ingo

Article Type: Research Article

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. Show more

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

DOI: 10.3233/ICG-200164

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

Price: EUR 27.50

A polyomino puzzle for arithmetic practice

Authors: Foxcroft, Jeremy | Ashlock, Daniel

Article Type: Research Article

Abstract: Recent trends in mathematics education emphasize discovery learning over drill. This has proven to be a bad idea in some cases, for the simple reason that practice is required to learn basic arithmetic skills. Drills in arithmetic skills can be made interesting through gamification. This study proposes a family of puzzles that gamify arithmetic practice. The puzzles are designed with an evolutionary algorithm forming an instance of automatic content generation. Two methods of evolutionary puzzle design are presented and discussed. The first method used transformed the problem into an almost trivial optimization. The second algorithm was designed to avoid the …flaws of the first and produced a huge variety of puzzles. A hardness measure, based on the difficulty experienced by the evolutionary puzzle generator, is employed. The hardness measure is tested on a large collection of puzzles produced with the evolutionary automatic content generation system. An initial assumption, that all the pieces in the puzzle must be used to achieve a maximum score, was shown to be incorrect in puzzles located via automatic search. Two classes of puzzle are defined: those where the optimal solution uses all pieces and those where the optimal solution fails to use at least one piece. The latter sort of puzzle were found to be far more common in the search space. Show more

Keywords: Procedural content generation, gamification, evolutionary computation, puzzles

DOI: 10.3233/ICG-200170

Citation: ICGA Journal, vol. 42, no. 4, pp. 272-286, 2020

Price: EUR 27.50