The Lasker variant with the strong solution The Morabaraba variant with the strong solution The standard variant with the ultra-strong solution For more details on the algorithm, see our paper, which appeared in IEEE Transactions on Computational Intelligence and AI in Games. You can play with the computed databases, or even recompute them, with our program, Malom. ( You can read the rules here, or in our paper.) Here we provide resources (databases, executables, sources, and theoretic background) about solving these games. Pieces can be moved and mills made along these extra lines in the usual way.Nine Men’s Morris (Mills, Mühle), and its variants, Morabaraba, and Lasker Morris are popular board games. One common pattern adds four extra diagonal lines to the basic board outlined above, the lines being drawn from the corners of the inner square to the corners of the outer square. In this case, any player with only three pieces remaining is allowed to move from any point to any other point on the board regardless of lines or whether the destination point is adjacent.Īlternative Merels board layouts have been used over the centuries. Sometimes a 'wild' rule is played for when a player is reduced to only three pieces.

The game is finished when a player loses either by being reduced to two pieces or by being unable to move. It is only upon the formation of a mill that a piece is captured but a player will often break a mill by moving a piece out of it and then, in a subsequent turn, play the piece back again, thus forming a new mill and capturing another piece.Ĭaptured pieces are never replayed onto the board and remain captured for the remainder of the game. If all the opponents pieces form mills then an exception is made and the player is allowed to remove any piece. After that, play continues alternately but each turn consists of a player moving one piece along a line to an adjacent point.ĭuring both of these phases, whenever a player achieves a mill, that player immediately removes from the board one piece belonging to the opponent that does not form part of a mill. To begin with, players take turns to play a piece of their own colour on any unoccupied point until all eighteen pieces have been played.

Player's toss a coin to decide who will play white - white moves first and has a slight advantage as a result. Every time this is achieved, an opponent's piece is removed, the overall objective being to reduce the number of opponent's pieces to less than three or to render the opponent unable to play. The basic aim of Nine Mens Morris is to make 'mills' - vertical or horizontal lines of three in a row. Accompanying the board, there should be 9 black pieces and 9 white pieces usually in the form of round counters. Pieces are played on the corner points and on the points where lines intersect so there are 24 playable points.

The game of Nine Mens Morris (also called Merels or Mill) is played on a board consisting of three concentric squares connected by lines from the middle of each of the inner square's sides to the middle of the corresponding outer square's side.

Two mills in nine mens morris