Suji




Read the numbers across.

Suji 「筋」 is the use of the "mahjong intervals" to determine safe tiles from an opponent's discard pile. It applies to the numbered suits: souzu, pinzu, and manzu. There are three main intervals, as seen to the right: 1-4-7, 2-5-8, and 3-6-9. Numbers within each interval can be paired, such as 1-4 or 2-5.

Basic Theory

The most common type of wait is an open wait (i.e. a ryanmen wait). An open wait is a wait that wins off two sides of a sequence, e.g. a hand containing {23}, or a hand containing {34}.
Sequences are comprised of three sequential tiles. Therefore, an open wait will win off two tiles that are 3-apart. For example, {23} can win off either a 1 or 4 of the same suit. {34} can win off 2 or 5 of the same suit. This continues until you get the intervals of: 1-4, 4-7, 2-5, 2-8, 3-6, and 3-9.
Due to the furiten rule, if a player has previously discarded any tile they could have won off of, they cannot win from other players.
This makes suji helpful. For example, if an opponent discards a 4, then the 1 of the same suit becomes safer against them. If they had a wait that wins off the 1-4 interval (such as {23}), then it would be subject to furiten. Thus, in this case, they couldn't win off your 1 discard. Similarly, the 7 also becomes safer when a 4 is discarded, due to the 4-7 interval.

Note: suji also applies to the other forms of furiten. After an opponent declares riichi, then any non-winning tile discarded by anyone becomes safe. Therefore, suji can be applied to these tiles as well. If an opponent declares riichi, and the next opponent discards a 4, then 1 and 7 are still considered suji.

Intervals

The intervals for suji apply to any of the numbered suits. Nine types of intervals are available. For these examples, only 1 suit is used per interval, but all intervals apply to every suit.

Middle tiles	Interval name	Completion
Two-sided, or Ryanmen
	1-4, or Iisuu 「イースー」	or
	2-5, or Ryanuu 「リャンウー」	or
	3-6, or Saburou 「サブロー」	or
	4-7, or Suuchii 「スーチー」	or
	5-8, or Uuppaa 「ウッパー」	or
	6-9, or Roukyuu 「ローキュー」	or
Three-sided, or Ryanmenten
	1-4-7, or Iisuuchii 「イースーチー」	and OR and OR and
	2-5-8, or Ryanuuppaa 「リャンウッパー」	and OR and OR and
	3-6-9, or Saburoukyuu 「サブローキュー」	and OR and OR and

The left column shows tiles that may appear in a player's hand, while the middle tiles show the tiles needed in order to complete a needed tile group. The recognition makes it helpful to identify waiting tiles by association. In the case of these waiting patterns, if a hand is waiting for one tile, it is likely waiting for another tile in the interval. Even if these take on Japanese names, they are simply the numbers. Finally, the end result shows the the waiting tiles as the completed tile grouping(s).

Nakasuji

Nakasuji 「中筋」 is literally the "middle suji". In other words, given the three different intervals, they are the middle numbers of 4, 5, and 6.

Defense

Suji implies that a player is using a ryanmen wait, or a related wait like ryanmenten, nobetan, or sanmentan. Ryanmen itself appears in around ~50% of winning hands, which is common, but not even close to guaranteed. Hands like toitoi and chitoitsu are immune to suji.

Note that the middle tiles (4,5,6) have two different suji intervals to account for. For example, 4 is part of the intervals 1-4 and 4-7. If an opponent discards a 7, the 4 isn't much safer, because the ryanmen of 1-4 is still present. In order to make 4 safer, both 1 and 7 must be safe. If both 1 and 7 are safe, then 4 is considered a nakasuji. The same applies to the other intervals.

Not all suji are equally safe. This is because some tiles can be targeted by penchan or kanchan.

Suji terminals (1 and 9) are the safest, as they can only be targeted by a tanki or shanpon.
Suji 2 and 8, as well as a completed nakasuji (4,5,6), are the next safest. They can be targeted by a tanki, shanpon, or kanchan.
Suji 3 and 7 are the most dangerous, though still reasonably safe. They can be targeted by a tanki, shanpon, kanchan, or penchan.

"Half suji" tiles, e.g. a 4 after only a 7 has been discarded, are not much safer than a regular tile.

Suji based off the riichi declaration tile is considered to be more dangerous than normal. This is due to the strength of a ryankan shape. See the Offense section for more information.

28 Suji vs 456 Nakasuji Safety

There are a few considerations about the relative safety of 28 suji and 456 nakasuji tiles.

In a game without red fives, the 456 tiles could be seen as safer. This is because to have a kanchan on a middle tile, for example, a 4, they would have had a 135 shape in their hand. It's generally seen as better to wait with the 13 shape, since the 4 is more useful and less likely to be discarded, so a middle tile kanchan suji trap is slightly less likely for this reason.

However, in a game with red fives, the player has an incentive to keep the red five. If they have a 135 shape, and the 5 is red, they would likely discard the 1 in order to keep the dora. Or, with a 246 shape, they could take the 46 shape and hope to win on the red five. 456 could be viewed as more dangerous in this ruleset, especially if you can't see the red five in the suit of your 2 or 8. As a side note, this is why the suji of a discarded red five is seen as especially safe.

The dora itself can also change things. If the 1 or 2 is dora, the player would generally want to keep the 13 shape for the value, while if the 4 or 5 is dora, they would want to keep the 35 shape. This applies to the other suji shapes as well.

Checklist

For defense, eighteen different suji are in consideration as listed above. Six basic suji multiplied by the three suits produces the count of eighteen suji. By counting the number of visible suji, players can determine roughly how risky it is to discard a dangerous tile.

Manzu (1 - 4) (4 - 7)	Pinzu (1 - 4) (4 - 7)	Souzu (1 - 4) (4 - 7)
Manzu (2 - 5) (5 - 8)	Pinzu (2 - 5) (5 - 8)	Souzu (2 - 5) (5 - 8)
Manzu (3 - 6) (6 - 9)	Pinzu (3 - 6) (6 - 9)	Souzu (3 - 6) (6 - 9)

Say an opponent declares riichi on turn 1, discarding an honor tile, and your turn is next. If we assume the opponent has a ryanmen wait, there is only a 1/18 chance that any one of the untested suji intervals deals in.

If an opponent declares riichi after discarding 4-man, 2-pin, 6-pin, and 5-sou, then the following suji are safe: 1-4 man, 1-7 man, 2-5 pin, 3-6 pin, 6-9 pin, 2-5 sou, and 5-8 sou. This "eliminates" 8 suji intervals, leaving 10 intervals unaccounted for. Therefore, if we assume the opponent has a ryanmen wait, an untested suji has a 1/10 chance to deal in. As more tiles become safe

Offense

The strategy of suji may be used offensively. By utilizing suji in reverse, a player may use a tile within an interval to lure out a winning tile along the same interval. A defending player may presume a certain tile to be safe by suji, when it is actually not. This is commonly known as the "suji trap".

A common way for this to occur is when a player has a ryankan shape, such as 468. They can discard the 4 to wait on 7, which is suji of the 4. Other players who know about suji may see this and be more likely to discard the 7. This is part of the reason why the suji of the riichi tile is considered dangerous.

Other suji

Matagi suji

Main article: Matagi suji

Matagi suji is a concept that considers suji based on middle tiles discarded from potential sequences. Given the discard timing, the individual tile may indicate suji intervals surrounding the tile. However, this read can be difficult given other information on the board.

Musuji

Musuji 「無スジ」 is a tile that is not 100% safe and not suji.

If an opponent discards multiple musuji tiles in a dangerous situation (e.g. after a riichi), then it's likely that they are in tenpai as well.

Ura suji

Ura suji is a theory which suggests that: when a middle tile is discarded relatively early, unsafe suji intervals that are nearby become more dangerous. For example, say an opponent had a 35 kanchan in their hand. If a 2 is drawn, then 5 would be discarded from the "235", leaving just a 23 shape. The 23 waits on a 1 or 4, so if a 5 is discarded relatively early, then 1-4 becomes more dangerous.

According to ura suji:

Discarded makes more dangerous.
Discarded makes more dangerous.
Discarded makes and more dangerous.

In the modern day, ura suji is often disregarded. If an opponent discards 5-pin early, then declares riichi, then non-suji 4-pin would be a dangerous tile. However, a non-suji 4-man, 5-man, 4-sou, etc. would also be dangerous tiles. Therefore, knowing about ura suji would not change your behavior.

If you were folding, you wouldn't discard any musuji unless you had to.
If you were attacking, you would discard ura suji anyways, because an ura suji is not that much more dangerous than a regular non-suji tile.

In addition, it assumes your opponent is going for maximum tile efficiency, and it also assumes that the 35 kanchan had existed in the first place.

External links

筋_(麻雀)

Suji in Japanese Wikipedia

Identifying Dangerous Suji

Osamuko strategy article on suji