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Mahjong solitaire (also known as Shanghai solitaire, electronic or computerized mahjong, solitaire mahjong or simply mahjong) is a single-player matching game that uses a set of mahjong tiles rather than cards. It is more commonly played on a computer than as a physical tabletop game.

Its name comes from the four-player game mahjong, but it is played entirely differently.

Play[edit]

The 144 tiles are arranged in a four-layer pattern with their faces upwards. A tile is said to be open or exposed if it can be moved either left or right without disturbing other tiles. The goal is to match open pairs of identical tiles and remove them from the board, exposing the tiles under them for play. The game is won when all pairs of tiles have been removed from the board, and lost if the remaining tiles contain no exposed pairs.

Mathematical analysis[edit]

Playing Mahjong solitaire optimally in the sense to maximize the probability of removing all tiles is PSPACE-complete, and the game is NP-complete if looking below tiles is allowed.^[1] It has been proven that it is PSPACE-hard to approximate the maximum probability of removing all tiles within a factor of $n^{\epsilon }$ , assuming that there are arbitrarily many quadruples of matching tiles and that the hidden tiles are uniformly distributed.^[2] The perfect-information version of this puzzle is where the player knows, before the game starts, the position of every tile. In this case, however, it is NP-complete to decide whether all tiles can be removed.^[1]

An analysis of ten million games with the default layout, "the turtle", found that about 3 percent of the turtles cannot be solved even when looking below tiles is allowed.^[3]

Variations[edit]

Mahjong solitaire can be played using genuine tiles and a special wooden frame for set-up. Usually though, it is played in an electronic form as a computer game. This removes the tedium of set-up and the temptation to cheat. Some electronic Mahjong solitaire games offer extra options, such as:

Shuffling the tiles;
Changing the tile set and patterns from the traditional tiles to flowers, jewels or other items that may be easier to match up at a glance;
Playing a series of different layouts with varying levels of difficulty (usually given Chinese-looking names such as 'the ox' or 'the snake');
Adding "wildcard tiles" and other tiles that have special functions.

Mahjong solitaire can be played either solo or with a partner, in which case the aim is to accumulate the most pairs, to be the last one to match a pair, or to score the most points. Points are gained for each pair removed, with bonus points for removing matched pairs in sequence or removing pairs in sequence that are parts of sets. Using traditional mahjong tiles, the sets include the dragons, the flowers, the seasons, and the winds.

Some implementations offer to shuffle the tiles when there are no exposed pairs remaining, making it almost always possible for the player to complete the game.

Computer game history[edit]

The computer game was originally created by Brodie Lockard in 1981 on the PLATO system and named Mah-Jongg after the game that uses the same tiles for play. Lockard claimed that it was based on a centuries-old Chinese game called "the Turtle".^[4] The computer game was released for free and was played using a CDC-721 touch screen terminal.

Activision released Shanghai in 1986 for the IBM Personal Computer, Commodore Amiga, Macintosh, Atari ST and Apple IIgs. The Macintosh version was created by Brodie Lockard, and the Apple IIGS version was ported from the Macintosh by Ivan Manley with Brad Fregger as the producer. Around 10 million copies were sold. The game has since been ported to many different platforms. The name "Shanghai" was trademarked by Activision.

As the game is based on mahjong tiles, some confusion arose with the 4-player mahjong game. Although the name mahjong solitaire is widely used, other names include The Turtle, Shanghai Solitaire, Taipei, and Kyodai.

A version of this game was also included in the Microsoft Entertainment Pack for Windows 3.x in 1990 under the name Taipei. It was subsequently included in the Best of Windows Entertainment Pack. Premium editions of the Windows Vista operating system and Windows 7 include a version of the game known as Mahjong Titans.^[5]

Mahjong Solitaire was added to Clubhouse Games: 51 Worldwide Classics for Nintendo Switch.^[6]^[7]

References[edit]

^ ^a ^b "Computational Complexity of Games and Puzzles". ics.uci.edu. Retrieved 2024-02-23.
^ Condon, Anne; Feigenbaum, Joan; Lund, Carsten; Shor, Peter (1997). "Random debaters and the hardness of approximating stochastic functions". SIAM Journal on Computing. 26 (2): 369–400. CiteSeerX 10.1.1.57.936. doi:10.1137/S0097539793260738.
^ http://www.math.ru.nl/~debondt/mjsolver.html Solitaire Mahjongg solver.
^ Fregger, Brad (1998). Lucky that way. pp. 69–70. ISBN 1-887472-56-8.
^ Paul Thurrott (2010-10-06). "Microsoft Windows Vista Build 5219 (Community Technical Preview 1) Review | Product Review content from Paul Thurrott's SuperSite for Windows". Winsupersite.com. Archived from the original on 2013-10-04. Retrieved 2013-06-29.
^ "Nintendo Shares A Handy Infographic Featuring All 51 Worldwide Classic Clubhouse Games". Nintendo Life. 25 May 2020. Retrieved 2020-07-21.
^ "Nintendo Reveals The Most Popular Games In Clubhouse Games: 51 Worldwide Classics". Nintendo Life. 13 July 2020. Retrieved 2020-07-21.

[eppstein-1] "Computational Complexity of Games and Puzzles". ics.uci.edu. Retrieved 2024-02-23.

[2] Condon, Anne; Feigenbaum, Joan; Lund, Carsten; Shor, Peter (1997). "Random debaters and the hardness of approximating stochastic functions". SIAM Journal on Computing. 26 (2): 369–400. CiteSeerX 10.1.1.57.936. doi:10.1137/S0097539793260738.

[3] ttp://www.math.ru.nl/~debondt/mjsolver.html Solitaire Mahjongg solver.

[4] Fregger, Brad (1998). Lucky that way. pp. 69–70. ISBN 1-887472-56-8.

[5] Paul Thurrott (2010-10-06). "Microsoft Windows Vista Build 5219 (Community Technical Preview 1) Review | Product Review content from Paul Thurrott's SuperSite for Windows". Winsupersite.com. Archived from the original on 2013-10-04. Retrieved 2013-06-29.

[6] "Nintendo Shares A Handy Infographic Featuring All 51 Worldwide Classic Clubhouse Games". Nintendo Life. 25 May 2020. Retrieved 2020-07-21.

[7] "Nintendo Reveals The Most Popular Games In Clubhouse Games: 51 Worldwide Classics". Nintendo Life. 13 July 2020. Retrieved 2020-07-21.

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@@ Line 1: / Line 1: @@
+{{Short description|Single-player game played with mahjong tiles}}
-<div style="float:right;width:315px;">
+{{About|the tile-matching solitaire game|the Chinese tile-based game|Mahjong|other uses|Mahjong (disambiguation)}}
-  [[image:Mahjong-01.jpg|thumb|right|A Shanghai solitaire in "Dragon formation".]]
-  [[image:Mahjong-02.jpg|thumb|right|The same solitaire, with "free tiles" highlighted]]
+[[File:Gnome Mahjong.jpg|thumb|A Mahjong solitaire video game with the tiles arranged in "turtle formation"]]
+'''Mahjong solitaire''' (also known as '''Shanghai solitaire''', '''electronic''' or '''computerized mahjong''', '''solitaire mahjong''' or simply '''mahjong''') is a [[Single-player video game|single-player]] [[matching game]] that uses a set of [[mahjong tiles]] rather than [[playing cards|cards]]. It is more commonly played on a computer than as a physical tabletop game.
-  </div>
+Its name comes from the four-player game [[mahjong]], but it is played entirely differently.
-'''Mahjong solitaire''', also known as '''Shanghai solitaire''', '''electronic''' or '''computerized mahjong''', '''MahJong solitaire''', '''solitaire Mahjong''' and, erroneously, as '''[[mahjong]]''', is a [[solitaire]] matching game that uses a set of [[Mahjong tiles]] rather than cards. The 144 tiles are arranged in a special four-layer grid with their faces upwards.
-A tile that can be moved left or right without disturbing other tiles is said to be exposed.  Exposed pairs of identical tiles (Flower tiles in the same group being considered identical) are removed from the grid one at a time, gradually exposing the lower layers to play. The aim of the game is to clear the grid by pairing up all the tiles. The game is finished when either the grid is empty, or there are no exposed pairs remaining.
+==Play==
-While Shanghai solitaire can be played using genuine tiles and a special wooden frame for set-up, it is usually played in an electronic form as a [[computer game]]. This removes the tedium of the set-up process and the temptation to cheat. Some electronic Mahjong solitaire games offer extra options, such as the ability to change the tile set and patterns from the traditional tiles to flowers, jewels or some other item that may be easier to match up at a glance, to play a series of different layouts with increasing levels of difficulty (usually given Chinese names such as 'the ox' or 'the snake'), or "wildcard tiles" and other tiles that have special functions. These games also have an optional time limit, and offer hints/cheat options such as the ability to have a match found for you, or to backtrack and undo already made moves. Additionally, most implementations of the game arrange the tiles in such a way that the game is solvable in at least one way.
+[[Image:Mahjong solitaire-02.jpg|thumb|right|An untouched turtle formation, with exposed "free" tiles highlighted in blue]]
+The 144 tiles are arranged in a four-layer pattern with their faces upwards. A tile is said to be open or exposed if it can be moved either left or right without disturbing other tiles. The goal is to match open pairs of identical tiles and remove them from the board, exposing the tiles under them for play. The game is won when all pairs of tiles have been removed from the board, and lost if the remaining tiles contain no exposed pairs.
-Mahjong solitaire can be played either solo, or with a partner in which case the aim is either to accumulate the most pairs, or to be the last one to match a pair.
+===Mathematical analysis===
-Players should open up new tiles with every pair they eliminate. Haphazardly choosing obvious pairs, such as those from the top levels, will often end the game prematurely (i.e. lose) by leaving essential tiles under cover.
+Playing Mahjong solitaire optimally in the sense to maximize the probability of removing all tiles is [[PSPACE-complete]], and the game is [[NP-complete]] if looking below tiles is allowed.<ref name="eppstein">{{Cite web |title=Computational Complexity of Games and Puzzles |url=https://ics.uci.edu/~eppstein/cgt/hard.html |access-date=2024-02-23 |website=ics.uci.edu}}</ref> It has been proven that it is PSPACE-hard to [[Hardness of approximation|approximate]] the maximum probability of removing all tiles within a factor of <math>n^\epsilon</math>, assuming that there are arbitrarily many quadruples of matching tiles and that the hidden tiles are uniformly distributed.<ref>{{cite journal|last1=Condon|first1=Anne|last2=Feigenbaum|first2=Joan|last3=Lund|first3=Carsten|last4=Shor|first4=Peter|title=Random debaters and the hardness of approximating stochastic functions|journal=SIAM Journal on Computing|date=1997|volume=26|issue=2|pages=369–400|doi=10.1137/S0097539793260738|url=https://www.researchgate.net/publication/3560142|citeseerx=10.1.1.57.936}}</ref> The perfect-information version of this puzzle is where the player knows, before the game starts, the position of every tile. In this case, however, it is NP-complete to decide whether all tiles can be removed.<ref name="eppstein" />
-==History==
+An analysis of ten million games with the default layout, "the [[Turtle (Shanghai solitaire)|turtle]]", found that about 3 percent of the turtles cannot be solved even when looking below tiles is allowed.<ref>http://www.math.ru.nl/~debondt/mjsolver.html Solitaire Mahjongg solver.</ref>
-The computer game was originally created by [[Brodie Lockard]] in [[1981]] on the [[PLATO]] [[computer]] and named ''Mah-Jongg''. It was released for free and was played using a CDC-721 touch screen terminal. [[Control Data Corporation]] released a new version as a paid [[online game]] in [[1983]]. The first version remained available for free.
+==Variations==
-However, it was not until [[Activision]] released ''Shanghai'' in [[1986]] for the [[Apple Macintosh|Macintosh]] the game gathered momentum. Again created by Brodie Lockard (programming and graphics) while [[Brad Fregger]] was the producer. The game became very successful and around 10 million copies were sold. It has been [[port]]ed to many different platforms.
+Mahjong solitaire can be played using genuine tiles and a special wooden frame for set-up. Usually though, it is played in an electronic form as a [[computer game]]. This removes the tedium of set-up and the temptation to [[cheating|cheat]]. Some electronic Mahjong solitaire games offer extra options, such as:
-[[Image:Mahjongg.png|thumb|right|Mahjongg on [[Ubuntu Linux]] ([[GNOME]].)]]The name "Shanghai" was [[trademark]]ed by Activision. As the game is based on mahjong tiles some confusion arose with the 4 player [[mahjong]] game on the search for a new name. Although '''mahjong solitaire''' is generally accepted, other names include ''The Turtle'' and ''Shanghai Solitaire''. Other known brandnames of mahjong solitaire include ''Taipei'', ''Kyodai'', and ''Moraff's''.
+# Shuffling the tiles;
+# Changing the tile set and patterns from the traditional tiles to flowers, jewels or other items that may be easier to match up at a glance;
+# Playing a series of different layouts with varying levels of difficulty (usually given [[Culture of China|Chinese]]-looking names such as 'the [[ox]]' or 'the [[snake]]');
+# Adding "wildcard tiles" and other tiles that have special functions.
+Mahjong solitaire can be played either solo or with a partner, in which case the aim is to accumulate the most pairs, to be the last one to match a pair, or to score the most points. Points are gained for each pair removed, with bonus points for removing matched pairs in sequence or removing pairs in sequence that are parts of sets. Using traditional mahjong tiles, the sets include the dragons, the flowers, the seasons, and the winds.
-Some have suggested that "Shanghai" may be based on 'The Turtle', a Chinese game several centuries old. According to Brad Fregger's book ''Lucky That Way'', this story rests upon no less an authority than Brodie Lockard, the original programmer; discussion on the question, however, continues to this day.
+Some implementations offer to shuffle the tiles when there are no exposed pairs remaining, making it almost always possible for the player to complete the game.
-A game called ''Ac Chen'' was released for the [[NeXTStep]] system, which was basically mahjong solitaire with pop culture symbols on the pieces instead of traditional Chinese pictures.
+==Computer game history==
-A version of this game was also included in [[Microsoft]]'s Entertainment Pack for [[Microsoft Windows|Windows]] 3.x in [[1990]] and went by the name ''Taipei''. A significantly upgraded version of this game, retitled ''Shanghai Solitaire'', is set to be included in Microsoft's [[Windows Vista]] for a [[2007]] release.
+The computer game was originally created by [[Brodie Lockard]] in 1981 on the [[PLATO (computer system)|PLATO system]] and named ''Mah-Jongg'' after the game that uses the same tiles for play. Lockard claimed that it was based on a centuries-old Chinese game called "the Turtle".<ref>{{cite book|last=Fregger|first=Brad|title=Lucky that way|year=1998|isbn=1-887472-56-8|pages=69–70}}</ref> The computer game was released for free and was played using a CDC-721 touch screen terminal.
+[[File:Shisen-Sho.png|thumb|right|The [[KDE]] game ''Shisen-Sho'']]
-== External link ==
+[[Activision]] released ''[[Shanghai (video game)|Shanghai]]'' in 1986 for the [[IBM Personal Computer]], [[Amiga|Commodore Amiga]], [[Macintosh]], [[Atari ST]] and [[Apple IIgs]]. The Macintosh version was created by Brodie Lockard, and the Apple IIGS version was ported from the Macintosh by Ivan Manley with Brad Fregger as the producer. Around 10 million copies were sold. The game has since been [[porting|ported]] to many different platforms. The name "Shanghai" was [[trademark]]ed by Activision.
-<!-- Please do not add links to individual Mahjong products here. Please see WP:EL and WP:SPAM to understand why. -->
-*[http://home.halden.net/vkp/vkp/ Mahjong Solitaire] History, rules, and links to over 200 computer implementations of Mahjongg solitaire.
-*[http://www.mahjongescape.com/mahjong_strategy.html Mahjong Solitaire] Mahjongg solitaire strategy and tips.
+As the game is based on mahjong tiles, some confusion arose with the 4-player [[mahjong]] game. Although the name ''mahjong solitaire'' is widely used, other names include ''The Turtle'', ''Shanghai Solitaire,'' ''Taipei'', and ''Kyodai''.
+A version of this game was also included in the [[Microsoft Entertainment Pack]] for [[Windows 3.x]] in 1990 under the name ''Taipei''. It was subsequently included in the ''[[Best of Windows Entertainment Pack]]''. Premium editions of the [[Windows Vista]] [[operating system]] and [[Windows 7]] include a version of the game known as ''[[Mahjong Titans]]''.<ref>{{cite web |author=Paul Thurrott |url=http://winsupersite.com/product-review/microsoft-windows-vista-build-5219-community-technical-preview-1-review |title=Microsoft Windows Vista Build 5219 (Community Technical Preview 1) Review &#124; Product Review content from Paul Thurrott's SuperSite for Windows |publisher=Winsupersite.com |date=2010-10-06 |accessdate=2013-06-29 |archive-url=https://web.archive.org/web/20131004234639/http://winsupersite.com/product-review/microsoft-windows-vista-build-5219-community-technical-preview-1-review |archive-date=2013-10-04 |url-status=dead }}</ref>
+Mahjong Solitaire was added to [[Clubhouse Games: 51 Worldwide Classics]] for [[Nintendo Switch]].<ref>{{Cite web|url=https://www.nintendolife.com/news/2020/05/nintendo_shares_a_handy_infographic_featuring_all_51_worldwide_classic_clubhouse_games|title=Nintendo Shares A Handy Infographic Featuring All 51 Worldwide Classic Clubhouse Games|website=Nintendo Life|date=25 May 2020 |accessdate=2020-07-21}}</ref><ref>{{Cite web|url=https://www.nintendolife.com/news/2020/07/nintendo_reveals_the_most_popular_games_in_clubhouse_games_51_worldwide_classics|title=Nintendo Reveals The Most Popular Games In Clubhouse Games: 51 Worldwide Classics|website=Nintendo Life|date=13 July 2020 |accessdate=2020-07-21}}</ref>
+==See also==
+{{Portal|Video games}}
+* [[Mahjong]]
+* [[Shisen-Sho]], another solitaire game with Mahjong tiles
+* [[Crazy Quilt (solitaire)]], a solitaire card game where cards are removed from the edges of a grid
+* Other [[Solitaire (game)|Solitaire]] games, especially [[Patience (game)|Patience]], or solitaire with cards
+* [[Tile-matching video game]]
+* [[Solitaire (game)|Solitaire]]
+* [[Klondike (solitaire)]]
+==References==
+{{reflist}}
+<!--== External links ==
+Please do not add links to individual Mahjong products here. Please see WP:EL and WP:SPAM to understand why. -->
+[[Category:Activision games]]
 [[Category:Mahjong]]
-[[Category:Computer board games]]
+[[Category:Mahjong video games| ]]
-[[Category:Activision games]]
+[[Category:Microsoft Entertainment Pack]]
-[[Category:Puzzle computer and video games]]
+[[Category:Microsoft games]]
+[[Category:Puzzle video games]]
-[[ja:&#19978;&#28023; (&#12466;&#12540;&#12512;)]]
+[[Category:Solitaire Mahjong tile games| ]]
+[[Category:Tabletop tile games]]
+[[Category:Double-deck patience card games]]