Mill (game)

Game board

Mühle , also known as Nünistei (“nine stones”) in Switzerland , is a board game for two players. The game board consists of three squares one inside the other with connecting lines in the middle of the sides. The game pieces are usually nine black and nine white round, flat game pieces, which are usually made of wood or plastic. Other colors are also possible.

The game is won, (1) as soon as so many opposing stones have been captured by forming so-called mills (three of your own stones in a row) that the opponent only has two stones left, or (2) when the remaining stones are on the board opposing stones were blocked so that the opponent can no longer move.

General

Mill is a random free game with perfect information ; H. Both players always have the same information about the previous game.

The game always ends in a draw if neither player makes a mistake. The presence or second player to be making with respect to profit or loss any difference. In the course of the game, however, there is an advantage for those who follow suit: they place the last stone on the board and can calculate a possible forced move .

Compared to the game of chess , Mühle has significantly fewer variants. While the number of theoretically possible positions in chess is estimated at 2.28 · 10 ⁴⁶ , Mühle only has around 1.8 · 10 ¹⁰ different positions (which cannot be converted into one another by turning, mirroring or exchanging the inner and outer ring). There are 9 billion positions without repetitions and 128 billion positions with repetitions. The number of mill positions corresponds to the size of the mill database, in which one byte (256 states) is used for each position in order to store the number of moves until the win.

In contrast to many other combination games, it is feasible with the computing capacity available today to completely map the set of all possible positions (problem space) in a database.

The computer scientist Peter Stahlhacke completely calculated the game on his home computer. The 17  GB database with all positions was published on the game site Inetplay as the perfectly mill-playing program Mr. Data .

Mühle is not a trivial game: The position opposite corresponds to the position with the longest winning distance. Red on the move wins in 165 moves with a perfect play of both colors. Here red has a safe path through the problem area even if the opponent doesn't make a mistake. As a rule, however, players leave safe paths in order to return to them later or to find another path.

Red train. Win in 165 moves; with optimal play of both players, this is the longest winning distance of all positions

A wooden mill game

Game flow

The game has three phases:

• Placement phase: The players take turns placing one stone each, a total of nine, on intersections or corner points of the board
• Move phase: The pieces are drawn, that is, each player may move one piece to an adjacent, free point per round. If a player cannot move a piece, he has lost.
• End phase: As soon as a player only has three stones left, he can jump with his stones, that is, he can jump with one stone to any free point per round. As soon as another stone is taken from him, he has lost the game.

Three stones of one color lying next to each other in a straight line on fields are called a "mill". When a player closes a mill, he may remove any of his opponent's stones from play, provided that this stone is not also part of a mill. The official tournament rules have allowed a stone to be struck from a closed mill since 2010 if the opponent only has stones in closed mills. However, this is handled differently regionally and in some cases also in commercially marketed products.

strategy

Especially during the initial phase of the game, it is less important to set up mills at an early stage than to ensure that your stones can be moved easily. The four intersection points of the mill board are to be occupied preferentially, while the corner points are to be avoided. In addition, when hitting a stone, it is usually better to open an additional mill of your own than to prevent an opponent's mill.

"Dilemma"

The following situations are particularly desirable: The red stones form a so-called “double mill” (sometimes called a “ dilemma ”), which means that the red player can close a mill on each round. This allows him to quickly decimate the opponent's stones without the latter being able to take effective countermeasures.

A common strategy is the “center mill”. It consists in quickly aiming for a mill on the middle ring as an attractive player. White tries to occupy two of the central crossing points and then the corner between these crossing points. He is threatening two open mills at the same time. Experienced black players counter by also occupying intersections with the first two stones. If both opponents play optimally, this strategy leads to a draw. However, since such a game is difficult to understand and both players are therefore prone to errors, the game relatively often ends in practice with the victory of one of the players.

Play against programs

The actual game, which consists of the search for the shortest possible or original path through this problem area for each player , can be compared with objective data due to the availability of the optimal solution strategies. In this way, on the one hand, underperformance and logical errors can be recognized, but it is also possible to control programs which, within the framework of various parameters, perform an almost perfect style of play - measured against the (known) most effective solution for the respective situation. Since individual style, traditions, tricky traps or surprising creative solutions are also valued for enjoyment of the game, the quality of a program among gamers is not measured solely by its logical stringency.

A very strong Mühle24 program from the Mühlespielverein Bern is also widespread. It plays more offensively than Mr. Data, but is not infallible and has a graphic design that is currently (as of Oct. 2011) out of date. On the other hand, it is valued for its amazing and unexpected moves that get even experienced players into trouble.

Tournaments

A big mill game at Twedter Plack in Flensburg - Mürwik

World Mühlespiel umbrella organization (WMD)

The tournament system is regulated by the World Mühlespiel umbrella organization , WMD for short. He not only sets the exact rules of the game, but also regulates the course of the tournament. As with chess, if there are a large number of participants, the game is played according to the Swiss system and if there are small numbers, full rounds (everyone against everyone). In order to keep the number of undecided games to a minimum, time limits are generally used. Depending on the number of rounds, the game is played with 5, 7 or 10 minutes per player and round, with chess clocks being used for control . The aim of the WMD is to promote the mill game worldwide. Active centers exist in Switzerland , Germany , Austria , Great Britain , the Czech Republic , Italy and Poland (as of February 2008).

title

Similar to chess, the WMD awards two different titles: the grandmaster title (GM) and the master title (MM). Twenty tournament victories or 20 standard points according to the WMD regulations are required for the grandmaster title. 15 podium places are required for the championship title. Tournaments are only counted if they have been announced to the WMD beforehand and if certain requirements regarding the number of participants and rounds are met. As of February 2008 there are four grandmasters and 20 masters. The grandmasters are Markus Schaub as the dominant personality from 1982 to 1992, Alain Flury , Manfred Nüscheler and Adrian Wenger .

Championships

The WMD has organized a European championship since 1996. Until 2004 this took place at Lenk in Switzerland, from 2005 to 2008 and 2017 in Passau , 2009 in Seeon near Seebruck am Chiemsee, from 2010 to 2016 in Munich , 2018 in Budapest and 2019 in Augsburg. With eleven titles, GM Alain Flury (CH) is the most successful player at European championships. Other European champions are GM Adrian Wenger (Switzerland, two titles), GM Markus Schaub (Switzerland, one title), Jakub Borlik (Poland, one title), Matthias Lorenz (Germany, one title), Karl-Heinz Andraschko (Germany, two titles ) and György Bándy (Hungary, five titles). As of May 2019.

From 1987 to 1997 a world championship took place in Hutton-Le-Hole, England . The leader with four titles is MM Andy Fawbert (Great Britain). Each has one title: MM Mike Sunley (Great Britain), MM Anthony Eddon (Great Britain), MM Raymond Thompson (Great Britain), MM Eric Weldon (Great Britain), GM Markus Schaub (Switzerland), GM Adrian Wenger (Switzerland) and MM Franz Beyeler (Switzerland).

Association

There are two Mühlespielvereine in Switzerland: In 1974 the Club de Charret de Granges-Marnand was founded in French-speaking Switzerland. In addition to club tournaments, this club also organized tours through western Switzerland, with MM Angelo Fuschetto largely dominating the scene in western Switzerland to this day. In 1978 the Mühlespielverein Bern was founded. With Hans Schürmann, Markus Schaub, Manfred Nüscheler, Alain Flury and Adrian Wenger, this club produced such strong mill players that almost all internationally important tournaments from 1996 onwards could be won by this club.

Various attempts to establish a club with regular meetings in Germany failed, so that the best players each duel over the Internet.

Internet platforms

The mill game has profited from the Internet boom in recent years. There are innumerable internet platforms on which the mill can be played.

variants

• Lasker mill with two rule changes: (1) The two phases are not separated from one another, i.e. H. the players are free to move or place a stone. (2) It is played with ten stones each.
• The African Mill consists of nine fields that are connected to each other and the players only have stones. The game is thus similar to the well-known tic-tac-toe
• Another African variant of the game of mills , called Morabaraba , uses 12 stones and mills can also be formed on the diagonals. The stones are cows ( cows called). Even if more than one mill is formed in one move, only one stone may be removed from the opponent.

Playing field for Morabaraba

• There are also game variants in which the three squares on the board are replaced by regular pentagons or hexagons. The number of pieces per player then increases to 11 or 13, otherwise the rules remain the same.
• The wheel mill (also known as round mill) shown below is a Roman variant that was played with just three stones per player. Whoever owned a mill first won.
• There are also two variants that shift the game of the mill into the third dimension: With the space mill , you try to get a row of four balls on 4 × 4 bars. The rules are similar to four in a row . The " cube mill " variant consists of three nested cubes, which are connected with rods so that each side of the largest cube forms a mill board . Now the game is played on six mill boards at the same time. The rules are similar to those of the classic game of the mill. However, the number of game pieces is increased to 18 and you can jump from seven remaining pieces.
• In the variant of the Somali Shax or Jar, mills formed during the placement phase do not immediately result in the removal of an opposing piece.
• A pentagonal mill game called DAS KANN JEDER for 2–5 people was published in 1966 by Otto Maier Verlag Ravensburg.

history

• Historic mill boards
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  Reconstructed circle mill game from antiquity.

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  Römerstein (around 300) in St. Martin

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  carved mill game on the Aachen royal throne (around 800)

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  Medieval game plan on the Felsburgstall Teufelsstein in the Franconian Haßberge

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  An old table with two game boards: for mill and chess

The game of the mill is much older than the game of chess. The oldest mill board from 1400 BC BC was discovered on a roof slab of the temple in Kurna, Egypt.

The age of the mill game in Europe is not known. Although a game is said to have been found as a Bronze Age burial object in Cr Bri Chualann in Wicklow ( Ireland ), all records of the archaeological excavation have been lost, and this is why this claim is now considered unreliable by scientists.

A 13th century illustration of the game of the mill in the Libro de los juegos

Mill was also a very popular game in ancient Rome , the Romans knew it in two versions, the "Mola" (large mill) and the "Mola rotunda" (circular mill). The game boards were usually made of wood, ivory, marble or clay, but there is a lot of evidence still visible today that some Romans simply scratched their game board in the stone floor of a public square where they had just been standing. An example of this can be found on the steps of the Basilica Iulia . Another remarkable testimony in this regard can be found in the Aachen Palatine Chapel . There on the royal throne of Charlemagne you can still see the lines of an ancient mill game on one of the marble slabs that make up the throne (and which probably come from the Church of the Holy Sepulcher in Jerusalem ).

From the 11th to the 18th century , the mill game was one of the most popular board games in Europe . Only from the beginning of the 19th century was Mühle gradually ousted by the game of chess .

literature

• Katharina Uebel, Peter Buri: Roman games. Regionalia-Verlag, Euskirchen 2010, ISBN 978-3-939722-32-8 , p. 17, p. 37-38.
• Friedrich Berger: The mill board on a house in Goslar. In: Announcements from ANISA. 17, 1996, pp. 17-32.
• Friedrich Berger: The mill board between the Chinese fortune-telling device and the Carolingian computist diagram. In: Almogaren. 31, 2000, pp. 89-116.
• Thea Frank: Practical Guide to the Mühlespiel: An easy-to-understand introduction. Friedrich M. Hörhold-Verlag, Hildesheim 1951, DNB 451339312 .
• Ralph Gasser: Applying Retrograde Analysis to Nine Men's Morris. In: Artificial Intelligence. 2, 1990, pp. 161-173.
• Ralph Gasser: Solving Nine Men's Morris. In: Computational Intelligence. 12, 1996, pp. 24-41.
• Stefan Gräber: Strategies in the mill game. Thesis. Chair for Applied Mathematics and Computer Science, Saarbrücken 1973.
• Theo Hartogh: Mill, lady, Halma. Falken Verlag, Niedernhausen 1999, ISBN 3-8068-2050-3 .
• Jama Musse Jama: Shax: The preferred game of our Camel-herders and other traditional African Entertainments. Sun Moon Lake, Rome 2000, ISBN 88-87332-05-3 .
• Thomas Lincke: Perfect Play using Nine Men's Morris as an example (diploma thesis). Swiss Federal Institute of Technology, Zurich 1994.
• Franz Mandl: The mill representations on rock in the Northern Limestone Alps. In: Announcements from ANISA. 15, 1994, pp. 44-65.
• Reiner F. Müller: Mühle: Think outside the box and win. (= ECON advisor ). ECON Taschenbuch Verlag, Düsseldorf 1987, ISBN 3-612-20322-3 .
• Assia Popova: Analysis of formal et classification des jeux de calculs mongols. In: Études Mongoles. 5, 1974, pp. 7-60.
• Margarete Riemschneider: Glasberg and Mühlebrett. In: Yearbook for Symbol Research. 6, 1968, pp. 137-149.
• Hans Schürmann, Manfred Nüscheler: This is how you win a mill . Otto Maier Verlag Ravensburg, Ravensburg 1980, ISBN 3-473-43039-0 .

Web links

Commons : Mill  - collection of images, videos and audio files

Wiktionary: Mühlespiel  - explanations of meanings, word origins, synonyms, translations

• World Mühlespiel umbrella organization
• Instructions and thoughts on strategies
• Website for the mill game by Rainer Rosenberger with exercises, programs, sample games, reports and downloads

Individual evidence

1. ↑ Ralph Gasser, ETH Zurich 1993
2. ↑ Evidence from ETH Zurich from 1992 to 1994
3. ↑ WMD - World Mill Game umbrella organization. Retrieved May 7, 2019 . 
4. ↑ rules for Morabaraba on the website of Rainer Rosenberger [1]
5. ↑ Hans Schürmann, Manfred Nüscheler: This is how you win mill . Otto Maier Verlag, Ravensburg 1980, p. 4.