Nine Men’s Morris

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Nine Men’s Morris, a two-player zero-sum and perfect information abstract strategy board game.

=Rules= Nine Men’s Morris is played on a board with 24 spots where men may be placed. The game begins with an empty board and both players, White and Black start with nine men each. The object of the game is to leave the opposing player with fewer than three pieces or, as in checkers, with no legal moves. During the opening phase Players alternately place men on an empty spot. After all men are placed, players slide stones to adjacent vacant point. When closing a mill (three-in-a-row), any opponent's piece which is not part of a mill may be removed. If all the opponent's men are part of mills, any may be removed. Removed pieces may not be placed again. Closing two mills simultaneously during the opening phase only allows one of the opponent's men to be removed. With only three men left, a player may jump a piece to any vacant point.

=Solved= In 1993, Ralph Gasser at ETH Zurich solved the Game by Retrograde Analysis for all mid- and endgame positions, and an 18 Ply deep Alpha-Beta Search for the opening phase then found the value of the initial position.

=Photos= Nine Men’s Morris field from the Middle Ages, Teufelsstein, Haßberge Hills, Germany

=Publications=
 * Ralph Gasser (1991). Applying Retrograde Analysis to Nine Men’s Morris. Heuristic Programming in AI 2
 * Martin Riedmiller, Heinrich Braun (1993). A direct adaptive method for faster backpropagation learning: The RPROP algorithm. IEEE International Conference On Neural Networks, pdf
 * Ralph Gasser (1993). Nine Men’s Morris is a DRAW Dept. Informatik, Swiss Federal Institute of Technology (ETH)
 * Ralph Gasser, Jürg Nievergelt (1994). Es ist entschieden: Das Mühlespiel ist unentschieden. Overflow. Informatik Spektrum, Vol. 17, No. 5 (German)
 * Thomas Lincke (1994). Perfect Play using Nine Men’s Morris as an example. (Diploma thesis) ETH Zurich, ps
 * Ralph Gasser (1996). Solving Nine Men’s Morris. Games of No Chance edited by Richard J. Nowakowski, pdf
 * Friedrich Berger (2004). From circle and square to the image of the world: a possible interpretation for some petroglyphs of merels boards. Rock Art Research 21 (1), pdf 1, pdf 2

=Forum Posts=
 * Nine Men’s Morris is a DRAW by Ralph Gasser, rec.games.chess, rec.games.go, rec.games.abstract, November 23, 1993
 * Nine Men’s Morris is a DRAW by Ralph Gasser and reply by Paul Colley from rec.games.chess, rec.games.go, rec.games.abstract, November 23, 1993

=External Links=
 * Nine Men's Morris from Wikipedia
 * Row Games: Mill - Morris - Mérelles - Morels - Mühle - Mølle from Elliott Avedon Virtual Museum of Games, University of Waterloo
 * nine men's morris from GamesCrafters
 * Nine Men's Morris (ICGA Tournaments)
 * Nine Mens Morris Web Game
 * Nine Men's Morris AI Compo by Gary Linscott
 * Das uralte Mühlespiel ist gelöst - Mühle Datenbank by Peter Stahlhacke (German)
 * Zwickmühle (Mühlespiel) from Wikipedia.de (German)
 * WMD - Weltmühlespiel Dachverband (German)
 * Willkommen beim Mühlespielverein Bern (German)

=References=

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