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nakasuji 4/5/6 is safer than suji 2/8. complete a sentence i forgot to finish. add a safety% section to defense, noting that you should not rely on suji for betaori
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(nakasuji 4/5/6 is safer than suji 2/8. complete a sentence i forgot to finish. add a safety% section to defense, noting that you should not rely on suji for betaori)
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'''Suji''' {{kana|筋}} is a [[defense|defensive]] tactic that uses the [[furiten]] rule to determine which tiles are safer against a specific opponent. When a tile is suji, a it is impossible for an opponent to have a [[ryanmen|certain type of wait]] without being in furiten. It only applies to number tiles ([[manzu]], [[pinzu]], [[souzu]]).
'''Suji''' {{kana|筋}} is a [[defense|defensive]] tactic that uses the [[furiten]] rule to determine which tiles are safer against a specific opponent. When a tile is suji, a it is impossible for an opponent to have a [[ryanmen|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.
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. Suji will group


==Basic Theory==
==Basic Theory==
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===Why suji works===
===Why suji works===
Suji defends against [[ryanmen]] waits
Suji defends against [[ryanmen|open]] [[wait]]s <small>([[ryanmen]] wait)</small>. 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 [[ryanmen|open]] [[wait]] (i.e. [[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.<ref>Riichi hands: https://docs.google.com/spreadsheets/d/1x1CYlIPYTeOodGY4bmPevlbyeZOIcmHICcQaoSjHJEk/edit?gid=295861978#gid=295861978</ref>
*[[Shuntsu|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, 5-8, 3-6, and 6-9.
* [[Sequence]]s 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.
* 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.  
* 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 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.
** 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 suji 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.
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==
==Intervals==
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Not all suji are equally safe. This is because some tiles can be targeted by [[kanchan]] (24) or [[penchan]] (12) waits.
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 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 2 and 8, and "full" 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.
** Nakasuji 4/5/6 are safer than suji 2/8.
*"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).
* 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).


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.)
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.)


===28 Suji vs 456 Nakasuji Safety===
=== How safe are suji? ===
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.
Assuming its turn 8-12, and no other factors are in play:<ref>https://pathofhouou.blogspot.com/2020/05/analysis-tile-deal-in-rates-by-live-suji.html</ref>
* 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.


In a game without [[Dora#Akadora|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
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|suji counting]], though suji tiles also become more dangerous in the late game.


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.
Since suji is up to 60% as dangerous, you should not depend on suji if you are planning to [[betaori|fold completely]]. Suji is best used if you have no other safe tiles, or when planning to use [[mawashi]].
 
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==
1,718

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