Japanese mahjong scoring rules: Difference between revisions

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[[Image:Scoring Table.png|right|350px]]
[[Image:Scoring Table.png|right|350px]]
[[Japanese mahjong]] features a very complex scoring system.  Every mahjong hand has a value in terms of ''han'' and ''fu'' associated with them.  The combination of ''han'' and ''fu'' then corresponds to values indicated from the scoring table, and/or the two numbers of ''han'' and ''fu'' factor into an equation, by which the scoring table is derived.
[[Japanese mahjong]] features a very complex scoring system.  Nearly every mahjong hand has a value in terms of '''han''' and '''fu''', the two scoring factors. The han and fu are plugged into an [[#Calculating basic points|equation]] to derive the value of the hand.  Certain [[yaku]] are instead given a value of [[yakuman]] (or sometimes [[multiple yakuman|double yakuman]]), the highest scoring hands.


By default, most games start players at 25,000 points, with the goal of scoring at least 30,000 to declare victory for the points leader.  Point settings may be flexible to vary both the starting score and the goal score.
Under usual rules, above 4 han, the score is capped. Fu become irrelevant and the hand is scored based solely on the han value. Since there are not a large number of possible hand values below 5 han, a [[scoring table]] is usually used, rather than calculating the values directly.
 
By default, most games start players at 25,000 points, with the goal of scoring at least 30,000 to declare victory for the points leader.  Both of these values are easily varied.  Any game can set the start and target scores to any desired but workable numbers.  Tournament play in particular often starts with 30,000 points.
 
Under the rarely-used [[aotenjou]] rules, there is no scoring cap, and every hand is evaluated for fu and han, regardless of value. This can result in absurdly high hand values.


== Scoring factors ==
== Scoring factors ==


=== Han ===
=== Han ===
{{main|List of yaku}}


'''Han''' {{kana|飜}} is the main portion of scoring, as each [[yaku]] is assigned a han number.  Some may factor being open or closed; for others, this would not matter.  Any [[dora]] in the winning hand provide one extra han each.  In general, an increase of value by one han doubles the number of points, until the cap of [[#Scoring table|mangan]].
'''Han''' {{kana|飜}} is the main portion of scoring, as each [[yaku]] is assigned a value in terms of han.  Most of the yaku are valued at either 1 or 2, but the values, not counting yakuman hands, go as high as 6 han for a closed [[chinitsu]]. Some yaku are worth [[Kuisagari|one fewer han when open]], and some cannot be scored with an open hand, but many yaku are not scored the same regardless of whether the hand is open or closed.
 
Afterwards, the [[dora]] are counted.  Each [[dora]] tile in the hand counts as additional han. Dora are ordinarily worth 1 han each.  Additional dora indicators may increase that value.


Yakuman do not have a han value. If a winning hand satisfies at least one yakuman, han and fu are not counted for the hand.  Points are awarded based on the yakuman value; and if [[multiple yakuman]] are allowed, then the yakuman values are multipled by the number of yakuman patterns in the hand.
In addition [[List of yaku|to knowing the yaku]], players are encouraged to know their han values. This gives them greater awareness on potential point values of the hand.  This knowledge may help aiding in various game decisions, particularly when [[Riichi strategy|calling riichi]] or [[Betaori|abandoning the hand]].


=== Fu ===
=== Fu ===
'''Fu''' {{kana|符}} (''pronounced as foo'') takes the hand composition into consideration in terms of [[mentsu|tile melds]], [[machi|wait patterns]] and/or win method.  In addition, every hand begins with a default start value of 20 fu.  To determine the final number of ''fu'', the sources of fu are added up along with the base number and then rounded up to the nearest 10.  One exception falls on the [[chii toitsu]] yaku, which is set to 25 fu by default.
{{main|Fu}}


Fu factors into the following elements:
'''Fu''' {{kana|符}} (''pronounced as foo'') takes the hand composition into consideration in terms of [[mentsu|tile groups]], [[machi|wait patterns]] and/or win method.  Every hand begins with a default start value of 20 fu.  To determine the final number of fu, the sources of fu are added up along with the base number and then rounded up to the next multiple of 10. The exception is the [[chiitoitsu]] yaku, which is fixed to 25 fu and is not rounded.  While fu may be counted for hands worth 5 han or greater, it is not necessary.  At 5 han and above, the hand value is dependent only on the han count, and the fu count is ignored. When playing with the uncommon [[aotenjou]] rule, however, the fu count is used for hands of any han value.


====Melds====
=== Yakuman ===
For shuntsu (sequences), the fu count is 0.  For koutsu (triplet) and kantsu (four-of-a-kind), the fu value depends on whether they are tanyaohai (simples) or jihai/routouhai (honor/terminals).
{{main|Yakuman}}


{| class="wikitable" width=40%
The highest-scoring combinations are the yakuman patterns. A hand completing a yakuman is not normally scored for han and fu, but depending on the rules, it may be possible to combine multiple yakuman for an even larger hand.
|-
! width=25%|English !! width=25%| Romaji !! width=25%| Simples !! width=25%| Honor/Terminal
|-
| Open triplet || [[Mentsu|Minkou]] ||align=center| 2 fu ||align=center| 4 fu
|-
| Open kan || [[Kan|Minkan]] ||align=center| 8 fu ||align=center| 16 fu
|-
| Closed triplet || [[Mentsu|Ankou]] ||align=center| 4 fu ||align=center| 8 fu
|-
| Closed kan || [[Kan|Ankan]] ||align=center| 16 fu ||align=center| 32 fu
|}


====Waits====
Under [[aotenjou]] rules, where there is no scoring limit, a yakuman is scored as a 13-han yaku.
{| class="wikitable"
|-
! English !! Romaji !! Fu value
|-
| Open wait || Ryanmen ||align=center| 0 fu
|-
| Closed wait || Kanchan ||align=center| 2 fu
|-
| Edge wait || Penchan ||align=center| 2 fu
|-
| Pair wait || Tanki ||align=center| 2 fu
|}
 
====Winning condition====
* Winning with a closed hand by ron, the hand is awarded 10 fu. These 10 fu are called ''menzen-kafu'' and do not count against the player for achieving [[pinfu]].
* A win by tsumo with an open or closed hand is worth 2 fu.
* An exception to the fu for tsumo is a closed hand that satisfies all other criteria for [[pinfu]]. Such a hand does not score 2 fu for tsumo and instead gains the han for pinfu.
* An open hand won by ron without any fu from koutsu or the waiting pattern gains 2 fu. This makes all open hands ineligible for pinfu.


== Scoring procedure ==
== Scoring procedure ==
Line 59: Line 35:


To determine the point value of a hand, the following procedure is used:
To determine the point value of a hand, the following procedure is used:
# If the hand is a [[List of yaku|yakuman]], then hand scores 8,000 basic points × number of yakuman.
# If the hand is a [[List of yaku|yakuman]], then the hand scores 8,000 basic points.
# Otherwise, determine the hand's valid [[yaku]].
## If double yakuman are used, a double yakuman scores 16,000 basic points.
## If multiple yakuman are used, and multiple single and/or double yakuman are completed, their values are added together.
# Otherwise, determine all of the hand's valid [[yaku]].
## Some [[Yaku compatibility|yaku combinations]] such as [[chanta]] + [[junchan]] are not compatible with each other.
# Count the han based on the yaku.
# Count the han based on the yaku.
# Count any number of dora to the han count.
# Count any number of dora to the han count.
# If the han count is 5 or more, then counting fu is no longer necessary. Score the hand according to its han value on the scoring table.
# If the han count is 5 or more, then counting fu is no longer necessary. The hand is scored according to its han value:
## 5 han: mangan hand worth 2,000 base points.
## 6-7 han: haneman hand worth 3,000 base points.
## 8-10 han: baiman hand worth 4,000 base points.
## 11-12 han: sanbaiman hand worth 6,000 base points.
# If the han count is 4 or less, then count fu.
# If the han count is 4 or less, then count fu.
# After determining the number of han and/or fu, refer to the [[Scoring#Scoring table|scoring table]].
## If the hand is not [[chiitoitsu|seven pairs]], round the fu up to the nearest 10.
 
# To get the base points, multiply the fu value by four, and then double it for each han ('''fu × 2<sup>(2 + han)</sup>''').
For any who prefer to use the equation, basic points for 5 han or less are computed as
# If playing with [[kiriage mangan]], round a 1,920-point hand up to a 2,000-point mangan.
 
# In any case, if the base points value would be above 2,000 for a hand with 4 or fewer han, it is instead a 2,000-point mangan.
: '''Basic points = fu × 2<sup>(2 + han)</sup>''', using '''basic points = 2,000''' if the former exceeds 2,000


=== Payment multipliers ===
=== Payment multipliers ===
Line 75: Line 57:
After determining the basic points, multiply based on the status as dealer and no-dealer as well as the win by ron or tsumo.
After determining the basic points, multiply based on the status as dealer and no-dealer as well as the win by ron or tsumo.


*When a non-dealer wins by tsumo, the player earns 1 × basic points from the other non-dealers, rounded up to a full 100.  The dealer in this case pays 2 × basic points, rounded up to a full 100.
*When a non-dealer wins by tsumo, the player is paid 1 × basic points by the other non-dealers, and 2 × basic points by the dealer.
*When a non-dealer wins by ron, the discarding player pays the winner 4 × basic points, rounded up.
*When a non-dealer wins by ron, the discarding player pays the winner 4 × basic points.
*When the dealer goes out by tsumo, the dealer scores 2 × basic points from all players, rounded up.
*When the dealer goes out by tsumo, the player is paid 2 × basic points from all other players.
*When the dealer goes out by ron, the dealer earns 6 × basic points from the responsible non-dealer, rounded up.
*When the dealer goes out by ron, the discarding player pays the winner 6 × basic points.


So finally, a hand's point value is finally expressed as:
Each value to be paid is rounded up to the nearest 100.
:'''Points = Basic points x Payment multiplier'''


=== Aotenjou ===
The numbers for a ron payment are obtained by having the ronned player pay every other players points. Because rounding is done after this reassignment of points, it is sometimes the case that a win by tsumo is worth a few hundred more points than a win by ron.
{{main|Aotenjou}}
 
Aotenjou {{kana|青天井}} is the practice of scoring hands without any limit imposed. This practice is rarely used, because without scoring limits, hands can produce ridiculously high point values.  Naturally, that is induced by the exponential function of the basic points equation.


=== Honba ===
=== Honba ===
{{main|Honba}}


In the event of [[ryuukyoku]] or a dealer win, the '''honba''' or '''tsumibou count''' increases by 1 for the next hand. If someone wins a hand and East does not, the honba count resets back to zero.
In addition to the points for the hand, the winner is paid a small sum of points based on the number of honba counters on the table. Thus, as a hand is [[renchan|repeated]], its value goes up slowly.


This count increases hand values increases by a total of 300 per honba.  For ron, the discarder pays the additional 300 points.  For tsumo, everyone pays an additional 100 each. These extra points are added to the hand value after the capping as mangan, haneman, etc., so a non-dealer mangan tsumo with 2 honba costs 2,200 for a non-dealer and 4,200 for the dealer.
== Oyakaburi ==
'''Oyakaburi''' 「親かぶり」 is when a non-dealer player wins by tsumo, causing the dealer to pay more than non-dealer players.  This usually applies to a high value tsumo, as the dealer has to pay double of a non-dealer for tsumo payout. The effect of oyakaburi is bigger to dealer when the total value is high.


In the case of [[sekinin barai]], the yakuman tsumo payment is borne entirely by the discarder of the ponned tile, who also has to pay 300 per honba. On a ron, the yakuman value is split between the discarder of the winning tile and the discarder of the earlier ponned tile. Most rules have the winning tile discarder pay for all honba.
== End game score ==
{{main|Final scores}}


=== End game score ===
At the end of the game, the raw points are used to calculate the end game score.  These are the two or three digit +/- numbers used to reflect a player's score.  Instead of 30,000 points, a player's score may actually be displayed as +40.0.  <!-- To this day, I don't know why this system exists-->
{{main|Uma}}


At the end of the game, the raw points are used to calculate the end game score. <!-- To this day, I don't know why this system exists-->
==External links==
 
{{jpwiki|麻雀の得点計算}}
=== Mangan ===
* [http://mahjong.onevis.net/ Online hand scoring calculator]
 
* [https://scoringtrainer.konbamwa.net/ Hand scoring trainer]
==Scoring table==
{{Main|Score table memorization}}
 
The score table is generated using the '''Basic points''' and the '''Payment multipliers'''. Similar to a multiplication, the awarded points are arranged in accordance to '''Han''' and '''Fu''' values. With known '''Han''' and '''Fu''' values, the points can simply be read straight off the table.
===Dealer===
{{Score table horizontal
|1and30tsumo=500
|1and30ron=1500
|1and40tsumo=700
|1and40ron=2000
|1and50tsumo=800
|1and50ron=2400
|1and60tsumo=1000
|1and60ron=2900
|1and70tsumo=1200
|1and70ron=3400
|1and80tsumo=1300
|1and80ron=3900
|1and90tsumo=1500
|1and90ron=4400
|1and100tsumo=1600
|1and100ron=4800
|1and110tsumo=1800
|1and110ron=5300
|2and20tsumo=700
|2and20ron=2000
|2and30tsumo=1000
|2and30ron= 2900
|2and40tsumo=1300
|2and40ron=3900
|2and50tsumo=1600
|2and50ron=4800
|2and60tsumo=2000
|2and60ron=5800
|2and70tsumo=2300
|2and70ron=6800
|2and80tsumo=2600
|2and80ron=7700
|2and90tsumo=2900
|2and90ron=8700
|2and100tsumo=3200
|2and100ron=9600
|2and110tsumo=3600
|2and110ron=10600
|3and20tsumo=1300
|3and20ron=3900
|3and30tsumo=2000
|3and30ron=5800
|3and40tsumo=2600
|3and40ron=7700
|3and50tsumo=3200
|3and50ron=9600
|3and60tsumo=3900
|3and60ron=11600
|4and20tsumo=2600
|4and20ron=7700
|4and30tsumo=3900
|4and30ron=11600
|mangantsumo=4000
|manganron=12000
|hanemantsumo=6000
|hanemanron=18000
|baimantsumo=8000
|baimanron=24000
|sanbaimantsumo=12000
|sanbaimanron=36000
|yakumantsumo=16000
|yakumanron=48000
}}


===Nondealer===
[[Category:Scoring]]
{{Score table horizontal
|1and30tsumo=300/500
|1and30ron=1000
|1and40tsumo=400/700
|1and40ron=1300
|1and50tsumo=400/800
|1and50ron=1600
|1and60tsumo=500/1000
|1and60ron=2000
|1and70tsumo=600/1200
|1and70ron=2300
|1and80tsumo=700/1300
|1and80ron=2600
|1and90tsumo=800/1500
|1and90ron=2900
|1and100tsumo=800/1600
|1and100ron=3200
|1and110tsumo=900/1800
|1and110ron=3600
|2and20tsumo=400/700
|2and20ron=1300
|2and30tsumo=500/1000
|2and30ron=2000
|2and40tsumo=700/1300
|2and40ron=2600
|2and50tsumo=800/1600
|2and50ron=3200
|2and60tsumo=1000/2000
|2and60ron=3900
|2and70tsumo=1200/2300
|2and70ron=4500
|2and80tsumo=1300/2600
|2and80ron=5200
|2and90tsumo=1500/2900
|2and90ron=5800
|2and100tsumo=1600/3200
|2and100ron=6400
|2and110tsumo=1800/3600
|2and110ron=7100
|3and20tsumo=700/1300
|3and20ron=2600
|3and30tsumo=1000/2000
|3and30ron=3900
|3and40tsumo=1300/2600
|3and40ron=5200
|3and50tsumo=1600/3200
|3and50ron=6400
|3and60tsumo=2000/3900
|3and60ron=7700
|4and20tsumo=1300/2600
|4and20ron=5200
|4and30tsumo=2000/3900
|4and30ron=7700
|mangantsumo=2000/4000
|manganron=8000
|hanemantsumo=3000/6000
|hanemanron=12000
|baimantsumo=4000/8000
|baimanron=16000
|sanbaimantsumo=6000/12000
|sanbaimanron=24000
|yakumantsumo=8000/16000
|yakumanron=32000
}}
 
==External links==
[[Category:Game rules]]
[http://jbcs.info/Mahjong/hand/calculator.html Online hand scoring calculator]

Revision as of 01:22, 28 February 2023

Japanese mahjong features a very complex scoring system. Nearly every mahjong hand has a value in terms of han and fu, the two scoring factors. The han and fu are plugged into an equation to derive the value of the hand. Certain yaku are instead given a value of yakuman (or sometimes double yakuman), the highest scoring hands.

Under usual rules, above 4 han, the score is capped. Fu become irrelevant and the hand is scored based solely on the han value. Since there are not a large number of possible hand values below 5 han, a scoring table is usually used, rather than calculating the values directly.

By default, most games start players at 25,000 points, with the goal of scoring at least 30,000 to declare victory for the points leader. Both of these values are easily varied. Any game can set the start and target scores to any desired but workable numbers. Tournament play in particular often starts with 30,000 points.

Under the rarely-used aotenjou rules, there is no scoring cap, and every hand is evaluated for fu and han, regardless of value. This can result in absurdly high hand values.

Scoring factors

Han

Han 「飜」 is the main portion of scoring, as each yaku is assigned a value in terms of han. Most of the yaku are valued at either 1 or 2, but the values, not counting yakuman hands, go as high as 6 han for a closed chinitsu. Some yaku are worth one fewer han when open, and some cannot be scored with an open hand, but many yaku are not scored the same regardless of whether the hand is open or closed.

Afterwards, the dora are counted. Each dora tile in the hand counts as additional han. Dora are ordinarily worth 1 han each. Additional dora indicators may increase that value.

In addition to knowing the yaku, players are encouraged to know their han values. This gives them greater awareness on potential point values of the hand. This knowledge may help aiding in various game decisions, particularly when calling riichi or abandoning the hand.

Fu

Main article: Fu

Fu 「符」 (pronounced as foo) takes the hand composition into consideration in terms of tile groups, wait patterns and/or win method. Every hand begins with a default start value of 20 fu. To determine the final number of fu, the sources of fu are added up along with the base number and then rounded up to the next multiple of 10. The exception is the chiitoitsu yaku, which is fixed to 25 fu and is not rounded. While fu may be counted for hands worth 5 han or greater, it is not necessary. At 5 han and above, the hand value is dependent only on the han count, and the fu count is ignored. When playing with the uncommon aotenjou rule, however, the fu count is used for hands of any han value.

Yakuman

Main article: Yakuman

The highest-scoring combinations are the yakuman patterns. A hand completing a yakuman is not normally scored for han and fu, but depending on the rules, it may be possible to combine multiple yakuman for an even larger hand.

Under aotenjou rules, where there is no scoring limit, a yakuman is scored as a 13-han yaku.

Scoring procedure

Calculating basic points

To determine the point value of a hand, the following procedure is used:

  1. If the hand is a yakuman, then the hand scores 8,000 basic points.
    1. If double yakuman are used, a double yakuman scores 16,000 basic points.
    2. If multiple yakuman are used, and multiple single and/or double yakuman are completed, their values are added together.
  2. Otherwise, determine all of the hand's valid yaku.
    1. Some yaku combinations such as chanta + junchan are not compatible with each other.
  3. Count the han based on the yaku.
  4. Count any number of dora to the han count.
  5. If the han count is 5 or more, then counting fu is no longer necessary. The hand is scored according to its han value:
    1. 5 han: mangan hand worth 2,000 base points.
    2. 6-7 han: haneman hand worth 3,000 base points.
    3. 8-10 han: baiman hand worth 4,000 base points.
    4. 11-12 han: sanbaiman hand worth 6,000 base points.
  6. If the han count is 4 or less, then count fu.
    1. If the hand is not seven pairs, round the fu up to the nearest 10.
  7. To get the base points, multiply the fu value by four, and then double it for each han (fu × 2(2 + han)).
  8. If playing with kiriage mangan, round a 1,920-point hand up to a 2,000-point mangan.
  9. In any case, if the base points value would be above 2,000 for a hand with 4 or fewer han, it is instead a 2,000-point mangan.

Payment multipliers

After determining the basic points, multiply based on the status as dealer and no-dealer as well as the win by ron or tsumo.

  • When a non-dealer wins by tsumo, the player is paid 1 × basic points by the other non-dealers, and 2 × basic points by the dealer.
  • When a non-dealer wins by ron, the discarding player pays the winner 4 × basic points.
  • When the dealer goes out by tsumo, the player is paid 2 × basic points from all other players.
  • When the dealer goes out by ron, the discarding player pays the winner 6 × basic points.

Each value to be paid is rounded up to the nearest 100.

The numbers for a ron payment are obtained by having the ronned player pay every other players points. Because rounding is done after this reassignment of points, it is sometimes the case that a win by tsumo is worth a few hundred more points than a win by ron.

Honba

Main article: Honba

In addition to the points for the hand, the winner is paid a small sum of points based on the number of honba counters on the table. Thus, as a hand is repeated, its value goes up slowly.

Oyakaburi

Oyakaburi 「親かぶり」 is when a non-dealer player wins by tsumo, causing the dealer to pay more than non-dealer players. This usually applies to a high value tsumo, as the dealer has to pay double of a non-dealer for tsumo payout. The effect of oyakaburi is bigger to dealer when the total value is high.

End game score

Main article: Final scores

At the end of the game, the raw points are used to calculate the end game score. These are the two or three digit +/- numbers used to reflect a player's score. Instead of 30,000 points, a player's score may actually be displayed as +40.0.

External links

Japanese mahjong scoring rules in Japanese Wikipedia
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