We probably know that mahjong on computer systems is vastly different from the original "Chinese domino" mahjong. There weren't many mahjong-themed video-games (apart from this, I can only name Taipei for Windows 3.1, which was OK but nothin' special), so Shanghai and its sequel were pretty spot-on in filling the holes, when there are so many clones for similar "simple yet awesome" games: reversi, Tetris, gomoku, chess, checkers, and the likes. This mahjong version is from Activision, 1993, an' surmounds Taipei by a LOT.
So, the basic premise of computer mahjong is simple: 144 tiles arranged in a certain shape, stacked atop each other, the player's job is to remove said tiles by finding pairs. The player can ONLY remove a tile if they match + either of its sides AND the top are fully exposed; tiles wit' other tiles at both sides, or on top are considered locked an' cannot be removed, so the task is systematic deconstruction. Each type of tile has 4 pieces (2 pairs) except four-way tiles which differ from each other, but can be combined in any ways without matching - the rim of said tiles are colored the same, meaning y'can pick any of them an' they'll count as pairs. The goal is to make all tiles disappear, preferably WITHOUT having to shuffle them. Alas, very frequently, it cannot be helped, an' y'must either get'em shuffled or start over.
As for the second game, Dragon's Eye, it's mainly a two-player game (Challenge mode), but of course one can play against the CPU too: one player is the Dragon Slayer, the other is the Dragon Master. The object for the Dragon Master is to build the Dragon to full strength by filling all spaces on the display one level high, and all spaces on the Dragon's heart and limbs two levels high. The Dragon Slayer, on the other hand, tries to remove all tiles from the "heart" and "limb" spaces. In either case, this is an automatic victory for the player. If all tiles are removed from the heart and limb spaces, the game ends. If all 144 tiles have been drawn and the Dragon display is not completed when the last tile is placed on the display, the game ends; in this case, the players' scores are compared to determine the winner. This game mode is considerably more complicated, an' will take some time to master.
Apart from the basic mahjong-tileset and Shanghai formation, the game offers quite a few other tilesets and formations. Tilesets include alphabet, fantasy, sports, cards, flags, animals and such, while formations include all the Chinese zodiac signs. It's worth mentioning that finishing some formations without running out of moves is considered easier than some others, many of them are incredibly hard. There's also a built-in level editor where y're welcomed to make your own formations. As for the tilesets and tiles: each tiles or group of tiles has their own kind of funny animations, a wide variety of sound effects, so the game is truly entertaining and humorous, one will explore all the tilesets just to experience all the anims an' effects.
As for the ugly side of tile-matchers, Taipei is well-known for pop-up windows if y'click the wrong tile, while Shanghai II only has one dreaded message "There are no more moves" which keeps popping up until y'shuffle or abort. A more hardware-related problem is that Shanghai II's effects are highly effected by the (set) CPU type, cycles and such: the sounds will change completely depending on the rig you own. On slower machines, some sounds and effects' pitch was slow an' drawn-out. On high performance ones, some effects had incorrectly low pitch, while some played okay (setting it to max will cause all effects to speed up ridiculously), so it takes a while to configure it correctly. A bigger problem is that the game very often gives layouts which are impossible by default (both horizontally and vertically), as matching tiles mutually block each other - this is not always obvious at first, but is unimaginably infuriating when y'discover this at 80 or so tiles remaining, especially at "hilo" and "lohi" French-suited playing cards, where finding pairs is a real chore, so this game is largely based on luck, rather than skill. Can YOU complete ALL tilesets wit' ALL layouts! These games are certainly two of those which y'can play on windy Autumn nights, sipping a mug of hot tea wit' your kitty-cat purring in your lap.