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 complex scoring system. Nearly every mahjong hand has a value in terms of '''han''' and '''fu''', which determine its point value. The han and fu are then plugged into an [[#Calculating basic points|equation]] to determine the score. Alternatively, a [[scoring table]] can be used to find the point value 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.  Point settings may be flexible to vary both the starting score and the goal score.


== 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 provides one extra han each. In general, an increase of value by one han roughly doubles the number of points, until the cap of [[#Scoring table|mangan]].
'''Han''' {{kana|飜}} are the main portion of scoring. Each [[yaku]] is assigned a value in terms of han: most are valued at 1-2, going up to 6 han for closed [[chinitsu]]. Each [[dora]] also grants +1 han. Han from yaku and dora are added up to produce a total han value.
 
Players are encouraged to know yaku, their han values, and how much points a given hand is worth. This knowledge may help with various game decisions, particularly when [[Riichi strategy|calling riichi]] or [[Betaori|abandoning the hand]].


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. Finally, any hand that accumulates 13 or more han is counted for a [[kazoe yakuman]].
As a general rule, for every +1 han, the hand roughly doubles in value until reaching 4 han. There is a "[[#Mangan|cap]]" at 2000 basic points (5 han; 4 han 40+ fu) - a hand that scores this much is called a [[#Mangan|mangan]] hand. Once reaching mangan, fu no longer matters for points, and han is reduced in value.


=== Fu ===
=== Fu ===
{{main|Fu}}
{{main|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. 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. Even a fu count of 32 gets rounded up to 40.  One exception falls on the [[chii toitsu]] yaku, which is fixed to 25 fu by default. While fu may be counted for hands worth 5 han or greater, it may no longer be necessary to count fu for [[Score table memorization|human memorization]]. Hands of this value become solely dependent on the han count, regardless of the fu count. All-in-all, '''counting fu is most relevant for hands worth 4 han or less'''.
'''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 of 20 fu. Any extra sources of fu are added, and then rounded up to the next multiple of 10. The exception is with [[chiitoitsu]] yaku, which is fixed to 25 fu (and not rounded).
 
Fu does not impact scoring for hands that have at least 5 han.
 
=== Yakuman ===
{{main|Yakuman}}
 
The highest-scoring combinations are the yakuman patterns. A hand completing a yakuman is not scored for han and fu, but depending on the rules, it may be possible to combine multiple yakuman for an even larger hand.
 
==Mangan==
[[Image:Mangan tsumo.png|thumb|right|250px|Hand scoring a mangan via [[tsumo]].]]
'''Mangan''' {{kana|満貫}} is a point cap which limits the impact of han and fu once a hand reaches 2000 "basic points". Since a regular player receives <code>4 × basic points</code> for winning, a mangan win is worth 8000 points (12000 points for dealers).
 
Mangan is reached with 3 han and 70 fu, 4 han and 40 fu, or 5 han. Once a hand reaches mangan, increasing fu will no longer affect scoring, and han has a reduced effect.
 
Below mangan, every han roughly doubles the hand's score. Past it, each han can still increase the hand's score, but in set intervals. These values, like mangan, have their own names:
 
* 6-7 han: '''Haneman''' {{kana|跳満}} = 12000 for a nondealer and 18000 for the dealer; 50% more than mangan (x1.5)
* 8-10 han: '''Baiman''' {{kana|倍満}} = 16000 for a nondealer and 24000 for the dealer; 100% more than mangan (double)
* 11-12 han: '''Sanbaiman''' {{kana|三倍満}} = 24000 for a nondealer and 36000 for the dealer; 200% more than mangan (triple)
* 13+ han: '''Kazoe yakuman''' {{kana|数え役満}} = 32000 for a nondealer and 48000 for the dealer; 300% more than mangan (quadruple)
** Some rulesets don't use kazoe yakuman, in which case 13+ han hands are worth sanbaiman.
* Yakuman: Points are the same as kazoe yakuman.
* Multiple yakuman: Points are the value of yakuman multiplied by the number of yakuman the hand contains.
 
===Kiriage mangan===
'''Kiriage mangan''' {{kana|切り上げ満貫}}, or "rounded up mangan", is a [[Scoring_variations#Kiriage_mangan|scoring variation]] that modifies mangan. When kiriage mangan is enabled, a 4 han and 30 fu hand, as well as a 3 han 60 fu hand, are considered mangan. The difference between a regular 4 han 30 fu hand (worth 7700 or 7900 points for non-dealers) and mangan is not very large, so these values are rounded up for convenience.
 
Kiriage mangan is reasonably common to see in real life play, though most computer clients do not use this rule.


== Scoring procedure ==
== Scoring procedure ==
Line 23: Line 52:


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 (>2) yakuman are used, points are multiplied accordingly.
# Count the han based on the yaku.
# Otherwise, determine all of the hand's valid [[yaku]] and determine the amount of [[dora]]. Count the number of han from these sources.
# Count any number of dora to the han count.
## Some [[Yaku compatibility|yaku combinations]] such as [[chanta]] + [[junchan]] are not compatible with each other.
# 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, plug in the equation <code>fu × 2<sup>(2 + han)</sup></code>
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 ===


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 non-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 ron, the discarding player pays the winner 4 × basic points, rounded up.
*When the dealer goes out by tsumo, the dealer scores 2 × basic points from all players, rounded up.
*When the dealer goes out by ron, the dealer earns 6 × basic points from the responsible non-dealer, rounded up.


So finally, a hand's point value is finally expressed as:
*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.
:'''Points = Basic points x Payment multiplier'''
*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.


=== Scoring table ===
Each value to be paid is rounded up to the nearest 100. Because of how this rounding works, a tsumo win may result in a few hundred more points than a ron of the same value. (For example, a 1 han 30 fu hand scores 240 basic points. Without rounding, a ron would score 960 points, and a tsumo would also score 240+240+480 = 960 points. As each individual player's payment is rounded, ron scores 1000, and tsumo scores 300+300+500 = 1100, or 100 more than ron.)
{{main|Scoring table}}


The points derived from the equation and the payment multipliers are arranged in a scoring table.  Players have the option of knowing the point scores by either deriving from the equation or [[Score table memorization|brute force memorization]].
To explain this in different terms: when hand wins by ron, the ronned player pays 100% of the hand's value. When a hand wins by tsumo, each player splits the payment evenly (with the dealer paying double).


=== Honba ===
=== Honba ===
[[Image:Honba 10.png|thumb|right|Game extended to 10 honba [http://tenhou.net/0/?log=2014010103gm-00a9-0000-ca27a20c&tw=2&ts=9].]]
{{main|Honba}}
In the event of [[ryuukyoku|exhaustive draw]], [[abortive draw]], or a dealer win, the '''honba''' {{kana|本場}} or '''tsumibou count''' increases by 1 for the next hand.  This count increase for each time either the dealer wins a hand, [[ryuukyoku|exhaustive draw]] occurs (even after a dealer rotation), or any [[abortive draw]].  When any non-dealer wins a hand, then the honba count resets back down to zero.


'''This count increases hand values 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.  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.
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, for every [[renchan]], the value of a winning hand slowly increases


For online play, the honba count is automatically noted.  However, with real tiles, the current dealer indicates the honba count by using [[tenbou|100-point sticks]] and placing them on the dealer indicator or on the table.  These 100-point sticks are merely counters.  If a non-dealer player wins a hand, the honba count resets back to zero.  If ryuukyoku occurs where the dealer is not tenpai, then the wind seating rotates and the honba count increases by 1.   For any time the wind seating rotates, the 100-point sticks are returned to the dealer; and the next dealer assumes responsibility of tracking the honba count.
=== 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 term usually refers to high value tsumos, which can cause the dealer to drop down placement.


A custom rule named '''basengo''' {{kana|場千五}} may be used, by which the honba value is five times the normal value.  With this rule, instead of 300 points per honba, it is 1500 points per honba.  This rule is not commonly used; and instead, it can be found under gambling situations.
== Scoring Table ==
{{Main|Scoring table}}


===Summary===
Since the han and fu equation is always the same, it is possible to use a scoring table to score the hand. Simply calculate the hand's han and fu, then find the values on the table. See [[scoring table]] for the actual table.


#Determine Han
For details on how to memorize scoring, see [[score table memorization]].
#Determine Fu
#Refer to the [[scoring table]], or [[Score table memorization|memorize the corresponding point values]]
#Factor in honba and riichi bets


== End game score ==
== End game score ==
{{main|Final scores}}
{{main|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. <!-- To this day, I don't know why this system exists-->
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. For example:
*A player ends the game with 40,000 points.
*The starting value of 25,000 points is subtracted, leaving +15,000 points.
*To make the values easier to read, 15,000 is divided by 1,000, for a value of +15.0 points.
*This +15 value may be affected by [[uma]] (a bonus/penalty for placing 1st/2nd/etc.).


== Aotenjou ==
== Aotenjou ==
{{main|Aotenjou}}
{{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.
[[Aotenjou]] is a rarely played variant which removes the [[mangan]] limit. Under aotenjou:
*Each han doubles the hand value without limit. E.g., a 5 han 30 fu hand is 8000 in standard rules, and 15360 in aotenjou.
*Fu matters even for hands with 5 or more han.
*Yakuman are scored as 13-han yaku.


==External links==
==External links==
{{jpwiki|麻雀の得点計算}}
{{jpwiki|麻雀の得点計算}}
* [http://jbcs.info/Mahjong/hand/calculator.html Online hand scoring calculator]
* [http://mahjong.onevis.net/ Online hand scoring calculator]
* [https://scoringtrainer.konbamwa.net/ Hand scoring trainer]


[[Category:Game rules]]
[[Category:Scoring]]

Latest revision as of 18:51, 22 August 2024

Japanese mahjong features a complex scoring system. Nearly every mahjong hand has a value in terms of han and fu, which determine its point value. The han and fu are then plugged into an equation to determine the score. Alternatively, a scoring table can be used to find the point value directly.

Scoring factors

Han

Han 「飜」 are the main portion of scoring. Each yaku is assigned a value in terms of han: most are valued at 1-2, going up to 6 han for closed chinitsu. Each dora also grants +1 han. Han from yaku and dora are added up to produce a total han value.

Players are encouraged to know yaku, their han values, and how much points a given hand is worth. This knowledge may help with various game decisions, particularly when calling riichi or abandoning the hand.

As a general rule, for every +1 han, the hand roughly doubles in value until reaching 4 han. There is a "cap" at 2000 basic points (5 han; 4 han 40+ fu) - a hand that scores this much is called a mangan hand. Once reaching mangan, fu no longer matters for points, and han is reduced in value.

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 of 20 fu. Any extra sources of fu are added, and then rounded up to the next multiple of 10. The exception is with chiitoitsu yaku, which is fixed to 25 fu (and not rounded).

Fu does not impact scoring for hands that have at least 5 han.

Yakuman

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

Mangan

Hand scoring a mangan via tsumo.

Mangan 「満貫」 is a point cap which limits the impact of han and fu once a hand reaches 2000 "basic points". Since a regular player receives 4 × basic points for winning, a mangan win is worth 8000 points (12000 points for dealers).

Mangan is reached with 3 han and 70 fu, 4 han and 40 fu, or 5 han. Once a hand reaches mangan, increasing fu will no longer affect scoring, and han has a reduced effect.

Below mangan, every han roughly doubles the hand's score. Past it, each han can still increase the hand's score, but in set intervals. These values, like mangan, have their own names:

  • 6-7 han: Haneman 「跳満」 = 12000 for a nondealer and 18000 for the dealer; 50% more than mangan (x1.5)
  • 8-10 han: Baiman 「倍満」 = 16000 for a nondealer and 24000 for the dealer; 100% more than mangan (double)
  • 11-12 han: Sanbaiman 「三倍満」 = 24000 for a nondealer and 36000 for the dealer; 200% more than mangan (triple)
  • 13+ han: Kazoe yakuman 「数え役満」 = 32000 for a nondealer and 48000 for the dealer; 300% more than mangan (quadruple)
    • Some rulesets don't use kazoe yakuman, in which case 13+ han hands are worth sanbaiman.
  • Yakuman: Points are the same as kazoe yakuman.
  • Multiple yakuman: Points are the value of yakuman multiplied by the number of yakuman the hand contains.

Kiriage mangan

Kiriage mangan 「切り上げ満貫」, or "rounded up mangan", is a scoring variation that modifies mangan. When kiriage mangan is enabled, a 4 han and 30 fu hand, as well as a 3 han 60 fu hand, are considered mangan. The difference between a regular 4 han 30 fu hand (worth 7700 or 7900 points for non-dealers) and mangan is not very large, so these values are rounded up for convenience.

Kiriage mangan is reasonably common to see in real life play, though most computer clients do not use this rule.

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. If multiple (>2) yakuman are used, points are multiplied accordingly.
  2. Otherwise, determine all of the hand's valid yaku and determine the amount of dora. Count the number of han from these sources.
    1. Some yaku combinations such as chanta + junchan are not compatible with each other.
  3. 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.
  4. 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.
  5. To get the base points, plug in the equation fu × 2(2 + han)
  6. If playing with kiriage mangan, round a 1,920-point hand up to a 2,000-point mangan.
  7. 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 non-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. Because of how this rounding works, a tsumo win may result in a few hundred more points than a ron of the same value. (For example, a 1 han 30 fu hand scores 240 basic points. Without rounding, a ron would score 960 points, and a tsumo would also score 240+240+480 = 960 points. As each individual player's payment is rounded, ron scores 1000, and tsumo scores 300+300+500 = 1100, or 100 more than ron.)

To explain this in different terms: when hand wins by ron, the ronned player pays 100% of the hand's value. When a hand wins by tsumo, each player splits the payment evenly (with the dealer paying double).

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, for every renchan, the value of a winning hand slowly increases

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 term usually refers to high value tsumos, which can cause the dealer to drop down placement.

Scoring Table

Since the han and fu equation is always the same, it is possible to use a scoring table to score the hand. Simply calculate the hand's han and fu, then find the values on the table. See scoring table for the actual table.

For details on how to memorize scoring, see score table memorization.

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. For example:

  • A player ends the game with 40,000 points.
  • The starting value of 25,000 points is subtracted, leaving +15,000 points.
  • To make the values easier to read, 15,000 is divided by 1,000, for a value of +15.0 points.
  • This +15 value may be affected by uma (a bonus/penalty for placing 1st/2nd/etc.).

Aotenjou

Aotenjou is a rarely played variant which removes the mangan limit. Under aotenjou:

  • Each han doubles the hand value without limit. E.g., a 5 han 30 fu hand is 8000 in standard rules, and 15360 in aotenjou.
  • Fu matters even for hands with 5 or more han.
  • Yakuman are scored as 13-han yaku.

External links

Japanese mahjong scoring rules in Japanese Wikipedia