Abstract
This paper presents a statistical approach for the decomposition of games in the General Game Playing framework. General game players can drastically decrease game search cost if they hold a decomposed version of the game. Previous works on decomposition rely on syntactical structures, which can be missing from the game description, or on the disjunctive normal form of the rules, which is very costly to compute. We offer an approach to decompose single or multi-player games which can handle the different classes of compound games described in Game Description Language (parallel games, serial games, multiple games). Our method is based on a statistical analysis of relations between actions and fluents. We tested our program on 597 games. Given a timeout of 1 h and few playouts (1k), our method successfully provides an expert-like decomposition for 521 of them. With a 1 min timeout and 5k playouts, it provides a decomposition for 434 of them.
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Notes
- 1.
In Asteroids the player must drive a small spaceship (in up to 50 steps) to an asteroid and stop on it. If the ship stops before reaching the destination, the game ends with the score 0.
- 2.
Chinook is composed of two games of Checkers disputed on the white cells and the black cells of the same board.
- 3.
At each turn a player chooses a Tictactoe grid from two to place one of his marks. The goal is to win in both grids.
- 4.
The goal of Snake is to move, for 50 steps, a snake that grows steadily without biting its tail.
- 5.
Factoring Turtle Brain is a series of LightsOn games where the player has to turn on 4 lights: each lamp goes out gradually while he lights up the others.
- 6.
Sukoshi is about creating a path by aligning ordered integers. In the multiple version only one grid counts for the score, the others are useless.
- 7.
In Nim each player takes in turn any number of matches in one of 4 stacks. Whoever no longer has a match to pick loses.
- 8.
Positive fluent
and negative fluent 
are represented by the same node in the dependency graph. - 9.
In Connect Four players drop colored tokens from the top into a seven-column, six-row vertically suspended grid. The goal is to align 4 tokens.
- 10.
Rainbow is a puzzle that consists in coloring a map such that no adjacent regions have the same color.
- 11.
Four game of LightsOn are played in parallel by a single player who chooses in which subgame he wishes to act on each turn. The player gets 100 points if he wins any of the 4 subgames.
- 12.
We excluded GDL-II descriptions using the sees predicate.
- 13.
These data are available upon request to the main author.
- 14.
Note that an expert-like decomposition may not equal a correct decomposition. For example, a human expert would like to decompose Nine Board Tictactoe. However such a decomposed game would be difficult to solve.
- 15.
The goal of Queens or Max-Knights is to place a given number of queens or knights on a chessboard so that no chessman threatens another.
- 16.
Point Grab is played in 30 steps. At each step, 2 players have the choice between different useless actions or grab a point a or a point b. If both player choose the same point, nobody wins.
- 17.
Smallest is a game played in a maximum of 25 steps. At each step, four player choose simultaneously a number. The player with the strictly smallest one wins 5 points.
- 18.
Roshambo consists of 10 rounds of rock/paper/scissors/well.
- 19.
Beat Mania is a 2 player game. The first player loose blocks from 3 different positions and the other must catch them. Each missed or caught block earns points to the corresponding player.
- 20.
We do not test Double Crisscross 2 which is not available in repositories.
and negative fluent 
are represented by the same node in the dependency graph.References
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Hufschmitt, A., Vittaut, JN., Jouandeau, N. (2019). Statistical GGP Game Decomposition. In: Cazenave, T., Saffidine, A., Sturtevant, N. (eds) Computer Games. CGW 2018. Communications in Computer and Information Science, vol 1017. Springer, Cham. https://doi.org/10.1007/978-3-030-24337-1_4
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