# Official International Mahjong: A New Playground for AI Research
## 3 Official International Mahjong  
As the official variant of Mahjong rules widely used in Mahjong competitions, Official International Mahjong is a better playground for AI research than other Mahjong variants for two reasons. First, unlike most of the regional variants such as SBR where luck dominates the result of the game, Official International Mahjong involves a moderate amount of luck, but mostly strategies and skills. Second, Official International Mahjong has a complex scoring rule with 81 different scoring patterns, many more than in other variants, including RCR. In fact, Official International Mahjong integrates most of the scoring patterns among various regional variants, requiring more sophisticated strategies for human players and indicating higher complexity for AI algorithms. This section introduces the rules of Official International Mahjong in detail. Official International Mahjong is played with a full set of 144 Mahjong tiles split into 3 categories: suited tiles, honored tiles, and flower tiles, as shown in Table 1. Suited tiles are divided into three suits: Characters, Bamboos, and Dots, each numbered from one to nine. There are 4 identical copies of each tile, totaling 108 suited tiles. Honor tiles are divided into two sets: wind tiles of four directions and dragon tiles of three colors. Like suited tiles, each tile has 4 identical copies, totaling 28 honor tiles. The remaining eight tiles are special flower tiles, each with an artistic rendering of one plant or season, which play a unique role in the mechanics of the game. When playing the game, four players sit down at their respective positions around the table in the shape of an inverted compass: east is the dealer, the right of the dealer is south, across is west, and the left is north. The position of each player is called their \"seat wind\". A full match usually consists of four rounds, each representing a \"prevailing wind\", starting with east. Four games are played each round, with players shifting their seat winds. The seat wind and prevailing wind are important because they affect the scoring of the game, which is further discussed in Appendix A. When a game starts, all of the tiles are randomly shuffled and stacked as two layers before each player to form a square wall. Tiles are drawn from a specific breaking position of the wall so that the tile wall decreases clockwise, and that position is usually decided by dice rolling. At the start of each game, 13 initial tiles are drawn by each player in a specific order, as shown in Figure 2. Then, players draw and discard one tile in turn in counterclockwise order until some player declares a winning hand, or no one wins before the tile wall runs out, ending in a tie. This regular order of play can be interrupted in four cases. In the first case, whenever a player draws a flower tile, it should be exposed and put aside. The player has to draw  
Figure 1: The number and average size of information sets of some imperfect-information games. the last tile of the wall as a replacement so that they still have 14 tiles before they discard any tile. This also happens when dealing the initial 13 tiles, and can happen successively in a player's turn if they draw another flower tile as the replacement. In the second case, when a player discards a tile, any other player may steal the tile to complete a meld. Melds are groups of tiles within players' hands, which are essential components to form a winning hand. There are three kinds of melds: pumps, kongs, and chows. A pung is three identical tiles, either suited tiles or honor tiles. A kong is four identical tiles, but only counts as a set of three tiles. A chow is three suited tiles of the same suit in a consecutive numerical sequence. When a meld is formed by stealing another player's discard, it is put aside and exposed to all players; otherwise, it remains concealed. A player can only steal a tile from the player left to them to form a chow, but from any player to form a pung or a kong.