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Created page with "'''Home * Games * Nine Men’s Morris''' FILE:Nine Men's Morris board with coordinates.svg|border|right|thumb|Game of Nine Men's Morris <ref>[https://en.w..."
'''[[Main Page|Home]] * [[Games]] * Nine Men’s Morris'''
[[FILE:Nine Men's Morris board with coordinates.svg|border|right|thumb|Game of Nine Men's Morris <ref>[https://en.wikipedia.org/wiki/Nine_Men%27s_Morris Nine Men's Morris from Wikipedia]</ref> ]]
'''Nine Men’s Morris''',<br/>
a [https://en.wikipedia.org/wiki/Two-player_game two-player] [https://en.wikipedia.org/wiki/Zero-sum_%28game_theory%29 zero-sum] and [https://en.wikipedia.org/wiki/Perfect_information perfect information] [https://en.wikipedia.org/wiki/Abstract_strategy abstract strategy] [https://en.wikipedia.org/wiki/Board_game 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|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 <ref>[http://www.ics.uci.edu/~eppstein/cgt/morris.html Nine Men's Morris is a DRAW] by [[Ralph Gasser]], [[Computer Chess Forums|rec.games.chess, rec.games.go, rec.games.abstract]], November 23, 1993</ref> <ref>[[Ralph Gasser]] ('''1993'''). ''Nine Men's Morris is a DRAW'' Dept. Informatik, Swiss Federal Institute of Technology (ETH)</ref> .
=Photos=
[[FILE:Burg Teufelsstein Muehle.jpg|none|border|text-bottom|640px]]
Nine Men’s Morris field from the [https://en.wikipedia.org/wiki/Middle_Ages Middle Ages] <ref>Not the [https://en.wikipedia.org/wiki/Stone_Age Stone Age]!</ref>, [https://de.wikipedia.org/wiki/Teufelsstein_%28Ha%C3%9Fberge%29 Teufelsstein], [https://en.wikipedia.org/wiki/Ha%C3%9Fberge_Hills Haßberge Hills], [https://en.wikipedia.org/wiki/Germany Germany] <ref>[https://de.wikipedia.org/wiki/M%C3%BChle_%28Spiel%29 Mühle (Spiel) from Wikipedia.de] (German)</ref>
=Publications=
* [[Ralph Gasser]] ('''1991'''). ''Applying Retrograde Analysis to Nine Men’s Morris.'' [[2nd Computer Olympiad#Workshop|Heuristic Programming in AI 2]]
* [[Martin Riedmiller]], [[Heinrich Braun]] ('''1993'''). ''A direct adaptive method for faster backpropagation learning: The RPROP algorithm''. [http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=1059 IEEE International Conference On Neural Networks], [http://paginas.fe.up.pt/~ee02162/dissertacao/RPROP%20paper.pdf 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]], [ftp://ftp.inf.ethz.ch/pub/org/ti/jn/paper/da_lincke.ps.gz ps]
* [[Ralph Gasser]] ('''1996'''). ''Solving Nine Men’s Morris''. [http://library.msri.org/books/Book29/index.html Games of No Chance] edited by [[Richard J. Nowakowski]], [http://www.msri.org/publications/books/Book29/files/gasser.pdf pdf]
* Friedrich Berger ('''2004'''). ''From circle and square to the image of the world: a possible interpretation for some petroglyphs of merels boards''. [https://en.wikipedia.org/wiki/Rock_Art_Research Rock Art Research] 21 (1), [http://mc2.vicnet.net.au/home/aura/shared_files/Berger1.pdf pdf 1], [http://history.chess.free.fr/papers/Berger%202004-2.pdf pdf 2]
=Forum Posts=
* [http://groups.google.com/group/rec.games.go/browse_frm/thread/eab894a7166e6df7 Nine Men’s Morris is a DRAW] by [[Ralph Gasser]], [[Computer Chess Forums|rec.games.chess, rec.games.go, rec.games.abstract]], November 23, 1993
* [http://www.ics.uci.edu/%7Eeppstein/cgt/morris.html Nine Men’s Morris is a DRAW] by [[Ralph Gasser]] and reply by [http://www.informatik.uni-trier.de/%7Eley/db/indices/a-tree/c/Colley:Paul.html Paul Colley] from [[Computer Chess Forums|rec.games.chess, rec.games.go, rec.games.abstract]], November 23, 1993
=External Links=
* [https://en.wikipedia.org/wiki/Nine_Men%27s_Morris Nine Men's Morris from Wikipedia]
* [http://www.gamesmuseum.uwaterloo.ca/VirtualExhibits/rowgames/mill.html Row Games: Mill - Morris - Mérelles - Morels - Mühle - Mølle] from [http://www.gamesmuseum.uwaterloo.ca/index.htm Elliott Avedon Virtual Museum of Games], [[University of Waterloo]]
* [http://gamescrafters.berkeley.edu/games.php?game=ninemensmorris nine men's morris] from [http://gamescrafters.berkeley.edu/ GamesCrafters]
* [https://www.game-ai-forum.org/icga-tournaments/game.php?id=34 Nine Men's Morris (ICGA Tournaments)]
* [http://merrelles.com/ Nine Mens Morris Web Game]
* [http://forwardcoding.com/projects/morris.html Nine Men's Morris AI Compo] by [[Gary Linscott]]
* [http://muehle-24.de/ Das uralte Mühlespiel ist gelöst - Mühle Datenbank] by Peter Stahlhacke <ref>[http://www.althofer.de/cebit-2007.html CeBIT 2007] by [[Ingo Althöfer]]</ref> (German)
* [https://de.wikipedia.org/wiki/Zwickm%C3%BChle_%28M%C3%BChlespiel%29 Zwickmühle (Mühlespiel) from Wikipedia.de] (German)
* [http://www.muehlespiel.eu/ WMD - Weltmühlespiel Dachverband] (German)
* [http://www.muehlespiel.ch/ Willkommen beim Mühlespielverein Bern] (German)
=References=
<references />
'''[[Games|Up one Level]]'''
[[FILE:Nine Men's Morris board with coordinates.svg|border|right|thumb|Game of Nine Men's Morris <ref>[https://en.wikipedia.org/wiki/Nine_Men%27s_Morris Nine Men's Morris from Wikipedia]</ref> ]]
'''Nine Men’s Morris''',<br/>
a [https://en.wikipedia.org/wiki/Two-player_game two-player] [https://en.wikipedia.org/wiki/Zero-sum_%28game_theory%29 zero-sum] and [https://en.wikipedia.org/wiki/Perfect_information perfect information] [https://en.wikipedia.org/wiki/Abstract_strategy abstract strategy] [https://en.wikipedia.org/wiki/Board_game 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|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 <ref>[http://www.ics.uci.edu/~eppstein/cgt/morris.html Nine Men's Morris is a DRAW] by [[Ralph Gasser]], [[Computer Chess Forums|rec.games.chess, rec.games.go, rec.games.abstract]], November 23, 1993</ref> <ref>[[Ralph Gasser]] ('''1993'''). ''Nine Men's Morris is a DRAW'' Dept. Informatik, Swiss Federal Institute of Technology (ETH)</ref> .
=Photos=
[[FILE:Burg Teufelsstein Muehle.jpg|none|border|text-bottom|640px]]
Nine Men’s Morris field from the [https://en.wikipedia.org/wiki/Middle_Ages Middle Ages] <ref>Not the [https://en.wikipedia.org/wiki/Stone_Age Stone Age]!</ref>, [https://de.wikipedia.org/wiki/Teufelsstein_%28Ha%C3%9Fberge%29 Teufelsstein], [https://en.wikipedia.org/wiki/Ha%C3%9Fberge_Hills Haßberge Hills], [https://en.wikipedia.org/wiki/Germany Germany] <ref>[https://de.wikipedia.org/wiki/M%C3%BChle_%28Spiel%29 Mühle (Spiel) from Wikipedia.de] (German)</ref>
=Publications=
* [[Ralph Gasser]] ('''1991'''). ''Applying Retrograde Analysis to Nine Men’s Morris.'' [[2nd Computer Olympiad#Workshop|Heuristic Programming in AI 2]]
* [[Martin Riedmiller]], [[Heinrich Braun]] ('''1993'''). ''A direct adaptive method for faster backpropagation learning: The RPROP algorithm''. [http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=1059 IEEE International Conference On Neural Networks], [http://paginas.fe.up.pt/~ee02162/dissertacao/RPROP%20paper.pdf 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]], [ftp://ftp.inf.ethz.ch/pub/org/ti/jn/paper/da_lincke.ps.gz ps]
* [[Ralph Gasser]] ('''1996'''). ''Solving Nine Men’s Morris''. [http://library.msri.org/books/Book29/index.html Games of No Chance] edited by [[Richard J. Nowakowski]], [http://www.msri.org/publications/books/Book29/files/gasser.pdf pdf]
* Friedrich Berger ('''2004'''). ''From circle and square to the image of the world: a possible interpretation for some petroglyphs of merels boards''. [https://en.wikipedia.org/wiki/Rock_Art_Research Rock Art Research] 21 (1), [http://mc2.vicnet.net.au/home/aura/shared_files/Berger1.pdf pdf 1], [http://history.chess.free.fr/papers/Berger%202004-2.pdf pdf 2]
=Forum Posts=
* [http://groups.google.com/group/rec.games.go/browse_frm/thread/eab894a7166e6df7 Nine Men’s Morris is a DRAW] by [[Ralph Gasser]], [[Computer Chess Forums|rec.games.chess, rec.games.go, rec.games.abstract]], November 23, 1993
* [http://www.ics.uci.edu/%7Eeppstein/cgt/morris.html Nine Men’s Morris is a DRAW] by [[Ralph Gasser]] and reply by [http://www.informatik.uni-trier.de/%7Eley/db/indices/a-tree/c/Colley:Paul.html Paul Colley] from [[Computer Chess Forums|rec.games.chess, rec.games.go, rec.games.abstract]], November 23, 1993
=External Links=
* [https://en.wikipedia.org/wiki/Nine_Men%27s_Morris Nine Men's Morris from Wikipedia]
* [http://www.gamesmuseum.uwaterloo.ca/VirtualExhibits/rowgames/mill.html Row Games: Mill - Morris - Mérelles - Morels - Mühle - Mølle] from [http://www.gamesmuseum.uwaterloo.ca/index.htm Elliott Avedon Virtual Museum of Games], [[University of Waterloo]]
* [http://gamescrafters.berkeley.edu/games.php?game=ninemensmorris nine men's morris] from [http://gamescrafters.berkeley.edu/ GamesCrafters]
* [https://www.game-ai-forum.org/icga-tournaments/game.php?id=34 Nine Men's Morris (ICGA Tournaments)]
* [http://merrelles.com/ Nine Mens Morris Web Game]
* [http://forwardcoding.com/projects/morris.html Nine Men's Morris AI Compo] by [[Gary Linscott]]
* [http://muehle-24.de/ Das uralte Mühlespiel ist gelöst - Mühle Datenbank] by Peter Stahlhacke <ref>[http://www.althofer.de/cebit-2007.html CeBIT 2007] by [[Ingo Althöfer]]</ref> (German)
* [https://de.wikipedia.org/wiki/Zwickm%C3%BChle_%28M%C3%BChlespiel%29 Zwickmühle (Mühlespiel) from Wikipedia.de] (German)
* [http://www.muehlespiel.eu/ WMD - Weltmühlespiel Dachverband] (German)
* [http://www.muehlespiel.ch/ Willkommen beim Mühlespielverein Bern] (German)
=References=
<references />
'''[[Games|Up one Level]]'''
