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Mahjong solitaire
Mahjong solitaire (also known as Shanghai solitaire) 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 tabletop game, although it can be played using physical tiles using a special wooden frame for its lengthy set-up process.[citation needed]
Although named after the four-player tile game mahjong, the method of gameplay is unrelated.
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.
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. It has been proven that it is PSPACE-hard to approximate the maximum probability of removing all tiles within a factor of , assuming that there are arbitrarily many quadruples of matching tiles and that the hidden tiles are uniformly distributed. 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.
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.
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. 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, which they marketed it as based on a centuries-old Chinese game called "the Turtle", though Lockard never made this claim himself. The Macintosh version was implemented by 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.
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Mahjong solitaire AI simulator
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Mahjong solitaire
Mahjong solitaire (also known as Shanghai solitaire) 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 tabletop game, although it can be played using physical tiles using a special wooden frame for its lengthy set-up process.[citation needed]
Although named after the four-player tile game mahjong, the method of gameplay is unrelated.
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.
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. It has been proven that it is PSPACE-hard to approximate the maximum probability of removing all tiles within a factor of , assuming that there are arbitrarily many quadruples of matching tiles and that the hidden tiles are uniformly distributed. 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.
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.
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. 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, which they marketed it as based on a centuries-old Chinese game called "the Turtle", though Lockard never made this claim himself. The Macintosh version was implemented by 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.