Machi 「待ち」 is the Japanese term for "wait patterns". Given any mahjong hand at any instance, players are waiting for specific tiles either to develop their hands or complete it. Wait patterns arise during hand development, when mahjong tiles in possession in the hand are in need of other tiles in order to complete mentsu (tile groups) or the entire hand. Wait patterns during tenpai are of particular interest. Players in tenpai must know their waiting tiles, or else end up missing a winning tile.
Five patterns here are classed as "basic wait patterns". These five patterns occur frequently; and they are not dependent on other patterns for formation. A combination of any of these five, including themselves, can form more complicated patterns.
Many different patterns arise during the course of hand development. Once a hand reaches tenpai, being able to interpret the hand's available winning tiles is a vital skill. If a player does not correctly read their winning tiles, they may miss a valid win, or they may commit a chombo with an illegal win call: either by calling a win on a tile that does not complete the hand, or calling ron while furiten due to a tile that they did not realize would complete the hand.
The most commonly occurring wait patterns have been given names, to make them more easily recognizable. More complex waits can arise involving a large number of potential configurations of the hand. This is especially true of hands with a large number of tiles in the same suit, most notably those aiming for chinitsu. Knowing the basic wait patterns also helps to combine them to interpret complex hands, which may have as many as 8 weights (not counting the special cases of chuuren poutou and kokushi musou, which are easily recognizable).
The waiting patterns can be analyzed using two numbers: n-sided waits and n-tiles available. This counts the number of tile types and the number of tiles themselves.
Patterns waiting for n-sided look for the number of tile types count as winning tiles. The largest number involves kokushi musou with a 13-sided wait pattern. The smallest number is 1.
As for counting the number of tiles available, this accounts every tile type having 4 copies each. Maximum possible counts exclude tiles required in the hand. Any tiles in other players' hands, the dead wall, or discarded tiles are not factored to this count. Of course, during the course of a hand, players must take into account the number of available tiles along with the maximum count.
During hand development, it is important to understand the hand's machi for two reasons. The first is that, when trying to bring a hand to tenpai, a player will want to maximize the number of available tiles to bring them closer. Doing this requires interpreting the patterns of potential groups in a similar manner to finding tile waits in a tenpai hand. The second is that furiten is best avoided, and so a player should avoid making discards that would leave them furiten once they reach tenpai. This can be a particular challenge when developing single-suited hands that may have a large number of different waits.
Basic wait patterns
These five are essentially the basic wait patterns. Upon tenpai, they only look to complete either the last tile group or the pair.
The basic patterns can be combined for more complex patterns; and the wait patterns listed here have taken on names.
Double yakuman patterns
These two unique patterns are linked to specific yakuman. Under all possible tile waits with these patterns, yakuman is ensured; under some scoring rules, winning a hand with these patterns is awarded double yakuman. There are no other wait patterns with more than 8 winning tiles (although it is possible for an 8-sided wait to include four of the same tile in such a way that a hypothetical fifth copy of the same tile would complete the hand).
Chuuren poutou kyuumen machi
Kokushi musou 13 machi
These combinations involve patterns that do not have specific names. Instead, they use combined forms of the other patterns. Furthermore, they mostly consist of consecutive, or closely consecutive, numbered tiles. Recognition of these patterns can produce some significantly powerful waits, which may be immune to suji and have large numbers of waiting tiles.
Hadaka tanki refers to when a player has made four tile calls (other than added kans), meaning that the hand is left with a single concealed tile for completion. The hand is necessarily tenpai with a tanki wait. Such a hand is very difficult to defend with, because the player will only have two tiles to choose from. Instead, the player opts for a complete attack posture.
Harabote refers to when a wait is embedded in the middle of a sequence, combining with a kanchan wait and eating up some of the available tiles. Usually this refers to a tanki wait (botetanki), but it can also refer to a shanpon (boteshanpon).
Jigoku 「地獄」 refers to when there is only one winning tile left to win with. If there is only one wait, this means that the other three copies of the winning tile are all in the player's hand, in a discard pool, in a called group, or visible as dora indicators. If there are multiple waits, this means that all but one of them must be completely used. In English, this is commonly known as the hell wait, a literal translation of the Japanese.
Karaten 「カラテン」, or empty tenpai, is the case where there are no tiles left to win with, due to all potential winning tiles already having been used in the player's hand, a discard pool, a called group, or visible as dora indicators. In some rulesets, a hand in this state is considered noten at an exhaustive draw.
Takame and yasume
Takame is a potential winning tile which is worth more points than another, called yasume.
- Machi in Japanese Wikipedia
- Forum list of various patterns
- Wait survey quiz in Tenhou.net