Suji

Read the numbers across.

Suji 「筋」 is a defensive tactic that uses the furiten rule to determine which tiles are safer against a specific opponent. When a tile is suji, it is impossible for an opponent to have a certain type of wait without being in furiten. It only applies to number tiles (manzu, pinzu, souzu).

When using suji, it is helpful to know the "mahjong intervals" of 1-4-7, 2-5-8, and 3-6-9, as shown in the picture to the right. It may help to group the numbers into pairs, e.g. 1-4 or 2-5.

Basic Theory

A tile is safer against an opponent if they've discarded every type of tile (of the same suit) within an interval of three from your tile.

In other words:

• With a 1/2/3 or 7/8/9 tile: if an opponent has discarded a tile that is 3 away, that tile is safer.
• With a 4/5/6 tile: if an opponent has discarded two different tiles that are 3 away, that tile is safer.

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 safer than normal, but still relatively dangerous.)

Why suji works

Suji defends against open waits (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}.

• The most common type of wait is an open wait, which appears in ~50% of all winning hands, and ~58% of all riichi hands.
• Sequences are comprised of three sequential tiles, so an open wait always 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 a 2 or 5 of the same suit. This continues until you get the intervals of: 1-4, 4-7, 2-5, 5-8, 3-6, and 6-9.
• 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 the other tile 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 applies to the other forms of furiten, not just discard furiten. So long as a tile is genbutsu (an opponent would be furiten if they were waiting on that tile), then the tiles within "suji interval" of that tile are safe. Most importantly: after an opponent declares riichi, then any non-winning tile discarded by anyone becomes safe through furiten. Therefore, suji can also be applied to those discarded tiles. So if an opponent declares riichi, and the next opponent discards a 4, then 1 and 7 are considered suji against the riichi-declarer.

Intervals

There are 6 distinct suji intervals per suit; each suit has all 6 intervals shown below.

Wait pattern	Waiting for	Completion
		or
		or
		or
		or
		or
		or

The left column shows the tiles that could be in the player's hand, while the middle column shows the tiles needed in order to complete that tile group. If a hand is waiting for one tile, it is likely waiting for another tile in the suji interval.

Nakasuji

Nakasuji 「中筋」 is literally the "middle suji"; it refers to a 4/5/6 tile when both tiles in its suji interval have been discarded before.

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 proper "full" suji, both 1 and 7 have to be safe. So, if both 1 and 7 have been discarded, 4 is called a nakasuji tile.

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.

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, and "full" nakasuji (4,5,6), are the next safest. They can be targeted by a tanki, shanpon, or kanchan.
  • Nakasuji 4/5/6 are safer than suji 2/8.
• 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 about as safe as a non-suji 2 (which is not safe).

Non-terminal suji based off the riichi declaration tile are 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.)

How safe are suji?

Assuming its turn 8-12, and no other factors are in play:

• Suji 1/9 is about x25% as dangerous as a non-suji 1/9.
• Suji 3/7 is x50%-x60% as dangerous as a non-suji 3/7.

Against a turn 1-2 riichi, suji is ineffective since players are less likely to have a ryanmen wait. In the late game (turn 12+), non-suji tiles become relatively more dangerous due to the effect of suji counting, though suji tiles also become more dangerous in the late game.

Since suji is up to 60% as dangerous, when folding completely, you should discard 100% safe tiles before suji. Suji is best used if you have no other safe tiles, or when planning to use mawashi.

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)

If either tile in the suji interval has been discarded before, then that interval can be eliminated. (E.g., if a 1 is discarded, the 1-4 interval is eliminated. If 4 is discarded, both 1-4 and 4-7 intervals are eliminated.)

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 using 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