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

In short: a tile becomes safer against an opponent if they've discarded every tile (of the same suit) that is an interval of 3 from that tile. For example, if an opponent had discarded a 4, then both 1 and 7 of the same suit are safer. If an opponent discarded both 1 and 7, then the 4 becomes safer. (If an opponent had only discarded a 1, the 4 is not much safer.)

The explanation is as follows:

• 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, a {23} ryanmen 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.
• Therefore, if every tile in a suji interval is discarded, then other tiles in that interval become safer against that player.
  • If an opponent discards a 4, it is impossible for an opponent to have an open wait on 1 (without being in furiten). There is only one interval for the 1, that being 1-4, which is eliminated. Therefore, the 1 is safer against that opponent. Likewise, the 7 becomes safer when a 4 is discarded, due to the 4-7 interval being impossible.
  • If an opponent discards a 1, it is not impossible for an opponent to have an open wait on 4. There are two different intervals for 4: 1-4 and 4-7. After discarding a 1, an opponent could still have an open wait on 4-7 interval. In order for the 4 to be a "full" suji, both 1 and 7 have to be discarded. The same logic applies to tiles numbered 5 and 6.

Note: suji also applies to the other forms of furiten. So long as a given tile is 100% safe (genbutsu) against an opponent, you can use the suji of that tile. After an opponent declares riichi, then any non-winning tile discarded by anyone becomes safe through furiten. Therefore, suji can be applied to those discarded tiles as well. So 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	Waiting for	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 relies on the fact that a player is likely to use 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 that do not use ryanmen, like toitoi and chiitoitsu, are immune to suji.

As mentioned above, the middle tiles (4,5,6) have two suji intervals to account for. A 4 has two suji intervals, 1-4 and 4-7. A discarded 1 does not make 4 much safer, because an opponent could still have a 4-7 ryanmen wait. In order for 4 to be a "full" suji, both 1 and 7 have to be safe.

Not all suji are equally safe. This is because some tiles can be targeted by kanchan (24) or penchan (12) waits.

• 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 1 has been discarded, are not much safer than a regular tile.

Suji based off the riichi declaration tile is more dangerous than normal. This is partly due to the strength of a ryankan shape. Ryankans are shapes like 135 or 468. These shapes are often kept for a long time for tile efficiency reasons. When reaching tenpai with a ryankan incomplete, a tile has to be discarded, e.g. 135 discarding 5 to wait on "suji" 2. Therefore, a player relying on suji may deal in. (Note that suji 1 and 9 are unaffected by this, as they cannot be part of a ryankan.)

28 Suji vs 456 Nakasuji Safety

Suji 28 and 456 nakasuji are about equal in terms of safety. There are a few considerations that make one more or less safe, though.

In a game without red fives, the 456 tiles could be seen as safer. To have a kanchan on a middle tile, for example, a 4, they could 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

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.

Suji counting

"Suji counting" is a strategy which is not directly related to suji. It basically states: as more types of tiles become safe, the more dangerous the non-safe tiles become.

In practice, this can be achieved by counting the number of visible suji. In other words, when more tiles are applicable for suji, the non-suji tiles become more dangerous. For suji counting, eighteen different suji are in consideration - six suji for each suit, and three suits total.

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. There are 18 "untested" suji intervals. So 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. (A given ryanmen could be any one out of the 18 different suji intervals, so 1/18.)

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, 4-7 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.

Offense

5-pin discarded to indicate 2-pin or 8-pin as potentially safe, when the 8 is not.

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. In this case, when reaching tenpai with a ryankan, the opponent can discard the 4, and wait on 7. This takes advantage of other player's knowledge of suji.

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 「無筋」 is a tile that is not 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, a nearby tile and its suji become more dangerous.

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 ryanmen shape. The 23 waits on a 1 or 4, so if a 5 is discarded relatively early, then 1-4 becomes more dangerous. Therefore, a discarded 5 makes 1 and 4 into ura suji. If a 4 is discarded later, then the "regular" suji takes priority over ura suji.

According to ura suji:

• Early discarded makes more dangerous.
• Early discarded makes more dangerous.
• Early discarded makes and more dangerous.

(Early discarded 1/2/8/9 tiles are not particularly noteworthy, since these tiles are often discarded early anyways.)

In the modern day, ura suji is often disregarded. It is true that, if an opponent discards a 5-pin early, then a non-suji 4-pin is at least somewhat more dangerous than normal. 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 would not discard any non-safe non-suji tiles unless you had to. Even if you did, you wouldn't discard a middle tile if you could avoid it.
• If you were attacking, you would discard ura suji anyways, because an ura suji is not so much more dangerous than a regular non-suji tile.
• In addition, ura suji theory assumes your opponent is going for maximum tile efficiency. If an opponent had sacrificed efficiency for points, it doesn't work.

The reason ura suji is not that much more dangerous than normal is because it assumes a (35) kanchan had existed in the first place. The 5-pin could have been an unrelated tile, or it could have been part of a 57 kanchan, or part of a completed 556 shape, or part of a completed 135 shape, etc. Even if the kanchan did exist, an opponent could have completed the 23 sequence before reaching tenpai.

External links

• 筋_(麻雀)

Suji in Japanese Wikipedia

• Identifying Dangerous Suji

Osamuko strategy article on suji