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[[Image:Junchan sanshoku baiman.jpg|thumb|right|250px|A single hand composed of six yaku to produce a baiman hand.]]
[[Image:Junchan sanshoku baiman.jpg|thumb|right|250px|A single hand composed of six yaku to produce a baiman hand.]]


This is a table showing the compatibilities of the different [[yaku]] with each other. While yaku may be combined in one hand, some yaku simply cannot combine with each other due to tile counts and patterns. In other cases, one yaku would always imply another. For instance, a [[junchan]] hand has a terminal or honour in every group (since it has a terminal in every group), and so it would qualify for [[chanta]]. By rule, two yaku cannot be combined if one always implies the other. There is a partial exception to this as [[shousangen]] always implies at least two [[yakuhai]] for sets of dragons, but they are not necessarily the same two yakuhai so they are counted in addition.
This is a table showing the compatibilities of the different [[yaku]] with each other. While yaku may be combined in one hand, it is simply impossible to combine certain yaku with each other.  
 
==Overview==
Yaku may not combine for two major reasons:
 
# Conflicting definitions. [[Tanyao]] requires the hand contains no honor tiles, but [[yakuhai]] requires a triplet of honor tiles, so the two cannot be combined.
# When a yaku always implies another yaku, they cannot score together. For instance, a [[junchan]] hand has a terminal in every group. [[Chanta]] requires that the hand has a terminal or honor in every group. Because every junchan hand would also qualify for chanta, chanta is not scored.
:There are two partial exceptions to this rule:
:*[[Shousangen]] always implies two dragon yakuhai, but does not guarantee you have any one of "haku", "hatsu", or "chun".
:*[[Ippatsu]] must be scored with a hand that declares [[riichi]]. However, "riichi" and "[[double riichi]]" are considered as 2 distinct yaku. Therefore, an ippatsu hand does not guarantee "riichi", since it could also be "double riichi".
 
When two yaku imply each other, as with reason #2, there are two alternate ways to define it in the rules:
*"Alter the yaku definitions so that they can never be scored together". In these rules, chanta is scored when there are honors/terminals in each group, and in addition, the hand ''must'' contain at least one honor tile.
*"Yaku that imply each other cannot be scored". In these rules, chanta is scored when there are honor/terminals in each group (not requiring an honor tile). However, chanta and junchan are never scored together. Junchan is worth more, so it supersedes chanta.
 
Both definitions are equivalent for any practical case. Most of these combinations, with the exception of toitoi + mentsumo, are based on the assumption that the yaku are defined using the second method.
 
===Indirectly illegal===
There are a few combinations that are indirectly impossible due to the implication rule.
 
Four combinations actually form yakuman:
 
* Toitoi + Junchan = Chinroutou
* Toitoi + Mentsumo = Suuankou
* Honroutou + Junchan = Chinroutou
* Double riichi + Chankan is only possible with a Kokushi musou hand
 
Some combinations form a different yaku which implies one component of the combination, and as a result can never be counted:
 
* Toitoi + Chanta = Toitoi + Honroutou
* Chiitoitsu + Chanta = Chiitoitsu + Honroutou
* Honitsu + Tanyao = Chinitsu + Tanyao
* Honitsu + Junchan = Chinitsu + Junchan
* Chinitsu + Chanta = Chinitsu + Junchan
 
These combinations are marked with {{or}} in the table below.


== Yaku ==
== Yaku ==
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| CHK || [[Chankan]]
| CHK || [[Chankan]]
|}
|}
Yaku strategy involves viability to form yaku and maximizing hand value, if possible.  This maximization often involves the recognition of the different yaku forming in one hand.  Often, this affects the decision which tiles to keep and which to discard.
Three combinations actually form yakuman:
* Toitoi + Junchan = Chinroutou
* Toitoi + Mentsumo = Suuankou
* Honroutou + Junchan = Chinroutou
Some combinations form a different yaku which implies one component of the combination, and as a result can never be counted:
* Toitoi + Chanta = Toitoi + Honroutou
* Chiitoitsu + Chanta = Chiitoitsu + Honroutou
* Honitsu + Tanyao = Chinitsu + Tanyao
* Honitsu + Junchan = Chinitsu + Junchan
* Chinitsu + Chanta = Chinitsu + Junchan
These combinations are marked with {{or}} in the table below.
Whether or not these combinations are actually combinations depends on the technical definition of the yaku. Some yaku are restricted versions of other yaku, such as junchan and chanta. There are two alternative ways to define this in the rules: either chanta can require that the hand contain at least one honour tile, or it can allow no honour terminals, but with a separate rule saying that chanta and junchan cannot both be counted. In this case, since junchan is higher-scoring, any chanta hand without honours, while qualifying for chanta, would never score it. Most of these combinations, with the exception of toitoi + mentsumo, are based on the assumption that the yaku are defined using the second method.


[[Nagashi mangan]] is excluded, because it is incompatible with anything, even riichi.
[[Nagashi mangan]] is excluded, because it is incompatible with anything, even riichi.
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{{main|Multiple yakuman}}
{{main|Multiple yakuman}}


Even different yakuman may be combined. As a result, point values may increase beyond single yakuman values as multiples of yakuman.  Of course, that's only if the rules allow extension into double yakuman and beyond.  Combinations involving three kinds of yakuman involve either tsuuiisou, tenhou, or chiihou. With this in mind, the options for combining different yakuman are limited.
Yakuman may not combine with regular yaku. However, in certain rulesets, different yakuman can combine with each other. As a result, hands can score multiple yakuman.
 
The maximum number of distinct yakuman a hand can have is four: [[suuankou]], [[tsuuiisou]], [[daisuushii]], and one of [[tenhou]]/[[chiihou]]/[[suukantsu]]. In rulesets where suuankou tanki and daiisuushi are scored as double, the hand ends up with a sextuple (x6) yakuman.


=== Compatibility ===
=== Compatibility ===

Latest revision as of 04:03, 24 April 2024

This is a table showing the compatibilities of the different yaku with each other. While yaku may be combined in one hand, it is simply impossible to combine certain yaku with each other.

A single hand composed of six yaku to produce a baiman hand.

Overview

Yaku may not combine for two major reasons:

  1. Conflicting definitions. Tanyao requires the hand contains no honor tiles, but yakuhai requires a triplet of honor tiles, so the two cannot be combined.
  2. When a yaku always implies another yaku, they cannot score together. For instance, a junchan hand has a terminal in every group. Chanta requires that the hand has a terminal or honor in every group. Because every junchan hand would also qualify for chanta, chanta is not scored.
There are two partial exceptions to this rule:
  • Shousangen always implies two dragon yakuhai, but does not guarantee you have any one of "haku", "hatsu", or "chun".
  • Ippatsu must be scored with a hand that declares riichi. However, "riichi" and "double riichi" are considered as 2 distinct yaku. Therefore, an ippatsu hand does not guarantee "riichi", since it could also be "double riichi".

When two yaku imply each other, as with reason #2, there are two alternate ways to define it in the rules:

  • "Alter the yaku definitions so that they can never be scored together". In these rules, chanta is scored when there are honors/terminals in each group, and in addition, the hand must contain at least one honor tile.
  • "Yaku that imply each other cannot be scored". In these rules, chanta is scored when there are honor/terminals in each group (not requiring an honor tile). However, chanta and junchan are never scored together. Junchan is worth more, so it supersedes chanta.

Both definitions are equivalent for any practical case. Most of these combinations, with the exception of toitoi + mentsumo, are based on the assumption that the yaku are defined using the second method.

Indirectly illegal

There are a few combinations that are indirectly impossible due to the implication rule.

Four combinations actually form yakuman:

  • Toitoi + Junchan = Chinroutou
  • Toitoi + Mentsumo = Suuankou
  • Honroutou + Junchan = Chinroutou
  • Double riichi + Chankan is only possible with a Kokushi musou hand

Some combinations form a different yaku which implies one component of the combination, and as a result can never be counted:

  • Toitoi + Chanta = Toitoi + Honroutou
  • Chiitoitsu + Chanta = Chiitoitsu + Honroutou
  • Honitsu + Tanyao = Chinitsu + Tanyao
  • Honitsu + Junchan = Chinitsu + Junchan
  • Chinitsu + Chanta = Chinitsu + Junchan

These combinations are marked with   in the table below.

Yaku

Key
Abbrevation Yaku
RCH Riichi
DRI Double riichi
IPP Ippatsu
SMO Mentsumo
TAN Tanyao
PFU Pinfu
IPK Iipeikou
ITT Ittsu
YAK Yakuhai
SDJ Sanshoku doujun
SDO Sanshoku doukou
TOI Toitoi
SNA Sanankou
SNK Sankantsu
CHA Chanta
JUN Junchan
RPK Ryanpeikou
SSG Shousangen
HRO Honroutou
HON Honitsu
CHN Chinitsu
CHI Chiitoitsu
RIN Rinshan
HAI Haitei
HOU Houtei
CHK Chankan

Nagashi mangan is excluded, because it is incompatible with anything, even riichi.

Compatibility

^ Ippatsu requires riichi to be of any use.

RCH DRI IPP SMO TAN PFU IPK ITT YAK SDJ SDO TOI SNA SNK CHA JUN RPK SSG HRO HON CHN CHI RIN HAI HOU CHK
RCH                                                
DRI                                                
IPP                                                  
SMO                                                  
TAN                                                  
PFU                                                  
IPK                                                  
ITT                                                  
YAK                                                    
SDJ                                                  
SDO                                                  
TOI                                                  
SNA                                                  
SNK                                                  
CHA                                                  
JUN                                                  
RPK                                                  
SSG                                                  
HRO                                                  
HON                                                  
CHN                                                  
CHI                                                  
RIN                                                  
HAI                                                  
HOU                                                  
CHK                                                  

Yakuman

Main article: Multiple yakuman

Yakuman may not combine with regular yaku. However, in certain rulesets, different yakuman can combine with each other. As a result, hands can score multiple yakuman.

The maximum number of distinct yakuman a hand can have is four: suuankou, tsuuiisou, daisuushii, and one of tenhou/chiihou/suukantsu. In rulesets where suuankou tanki and daiisuushi are scored as double, the hand ends up with a sextuple (x6) yakuman.

Compatibility

KMU DSG SUA SSS DSS TSU RYU CHR CHU SUK TEN CHH
Kokushi musou KMU                      
Daisangen DSG                      
Suuankou SUA                      
Shousuushii SSS                    
Daisuushii DSS                    
Tsuuiisou TSU                      
Ryuuiisou RYU                      
Chinroutou CHR                      
Chuuren poutou CHU                      
Suukantsu SUK                      
Tenhou TEN                    
Chiihou CHH                    

External links

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