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Nine Men's Morris Good Moves Dataset

Brief History of this dataset

This data set has been created by Andrea Galassi, as part of his master thesis in Computer Science Engineering ("Ingegneria Informatica", in italian). Please feel free to contact him (a.galassi *at* unibo.it) or his thesis supervisors (Paola Mello, paola.mello *at* unibo.it, Federico Chesani federico.chesani *at* unibo.it) for further questions.

For further information, the thesis is available here: Symbolic versus sub-symbolic approaches: a case study on training Deep Networks to play Nine Men’s Morris game.

 

Good Moves Dataset

The dataset consist of 100,154 game states and as many good moves elaborated by an Artificial Intelligence for the game of Nine Men's Morris.

None of the states in the dataset is symmetric to any other, therefore anyone can handle the symmetries as he prefers.
If all the symmetric states are explored, the dataset can reach 1,628,673 pairs.

The dataset contains states both reachable and unreachable during a normal match, decreasing the probability of reaching a training state during a testing match. The moves contained in it could be different from the optimal one, however, it constitutes a good knowledge base, from which other AI system can learn to play the game.

All the data have been generated making play an Artificial Intelligence called Deep Mill against other artificial intelligence and gathering the choices made by Deep Mill during the games.

Three version of the dataset are available:

  • The COMPLETE DATASET contains all the data, without the symmetric pairs.
  • The GAMING DATASET do not contains data coming from a regular match starting with an empty board. Therefore it contains states which are more unlikely to be reached during a match.
  • The EXPANDED DATASET contains all the data and the symmetric pairs.

 

Data format

The dataset does not distinction between black and white checkers but only between player checkers and enemy ones. An entry of the dataset consist of a string of 31 to 35 characters: 

  • The first 24 characters describe the board state with a letter representing the state of each position: O if the position is empty, M (Mine) if there is a checker of the player and E (Enemy) if there is an opponent one. The position are represented in order as they appear from left to right and from top to bottom
  • A sequence of 4 numbers completes the state representation, where the first two numbers represent, respectively, the number of checkers that the player has in its hands and the ones that his adversary has; the last two represent, in the same order, the number of checker that the players have on the board.
  • An hyphen divides the game state from the move description, which is written as pairs of coordinates letter-number; the meaning of each coordinate depends on the game phase: the parts of the move are written (if present) in the order FROM, TO and REMOVE.

 

Reachable States Dataset

The dataset consist of 2,085,613 states which are reachable through a finite sequence of legal moves starting from the initial empty board configurations.
None of the states contained in this dataset is present in the Good Moves Dataset.

 

 

NNMM: Neural Nine Men's Morris

This dataset has been used to train a neural networks system called Neural Nine Men's Morris to play the game, without inserting symbolic knowledge about the game rules.
After training the system has been tested on the whole expanded dataset (therefore considering any symmetric state) and the outcome is:

  • The system has learnt the rules (99.55% of cases the chosen move is legal)
  • The system has an accuracy of the whole move of 39.54%

 

For more information about neural networks, NNMM and its testing, see Symbolic versus sub-symbolic approaches: a case study on training Deep Networks to play Nine Men’s Morris game.

 

Useful resurces