Japanese mahjong scoring rules: Difference between revisions

Latest revision as of 15:31, 13 April 2024

Japanese mahjong features a very complex scoring system. Nearly every mahjong hand has a value in terms of han and fu, which are plugged into an equation to derive the hand's points. Alternatively, a scoring table can be used to find a hand's point value directly.

Generally, a game starts players with 25,000 points, with the goal of scoring at least 30,000 by the end for first place to declare victory. Both of these values can be changed; tournament play in particular often starts with 30,000 points.

Scoring factors

Han

Han 「飜」 is 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. Some yaku are worth -1 han with an open hand, and others cannot be scored at all with an open hand. Also, each dora in the hand grants +1 han. A hand's 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 base 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

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 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 article: 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.

Scoring procedure

Calculating basic points

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

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.
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.
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.
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.
To get the base points, plug in the equation fu × 2^{(2 + han)}
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.

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

Scoring Table

Main article: 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

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. 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

Main article: 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

麻雀の得点計算

Japanese mahjong scoring rules in Japanese Wikipedia

@@ Line 1: / Line 1: @@
 [[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.  From a [[scoring table]], the combination of han and fu then corresponds to values indicated   These values are derived using han and fu into the [[#Calculating basic points|points equation]].
+[[Japanese mahjong]] features a very complex scoring system. Nearly every mahjong hand has a value in terms of '''han''' and '''fu''', which are plugged into an [[#Calculating basic points|equation]] to derive the hand's points. Alternatively, a [[scoring table]] can be used to find a hand's 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.
+Generally, a game starts players with 25,000 points, with the goal of scoring at least 30,000 by the end for first place to declare victory. Both of these values can be changed; tournament play in particular often starts with 30,000 points.
 == Scoring factors ==
 === 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}} is 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]]. Some yaku are worth -1 han with an open hand, and others cannot be scored at all with an open hand. Also, each [[dora]] in the hand grants +1 han. A hand's yaku and dora are added up to produce a total han 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.  Finally, any hand that accumulates 13 or more han is counted for a [[kazoe yakuman]].
+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]].
+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 base 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 ===
 {{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.
 == Scoring procedure ==
@@ Line 23: / Line 33: @@
 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.
-# 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>'''; limit of '''basic points = 2,000''', for [[mangan]] and beyond.
 === Payment multipliers ===
@@ Line 39: / Line 52: @@
 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.  The dealer in this case pays 2 × basic points.
+*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 dealer scores 2 × basic points from all players.
+*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.
+*When the dealer goes out by ron, the discarding player pays the winner 6 × basic points.
-Finally with the multipliers applied, 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'''; points rounded up to the nearest 100.
-=== Scoring table ===
+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|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]].
 === Honba ===
 {{main|Honba}}
-'''Honba''' is an added counter to the number of consecutive hands, that did not produce a winning hand and/or the dealer position repeats.  For each honba count, every hand is worth a total of 300 extra points.  Once a winning hand does occur, the honba count resets back down to zero.  The event of [[chombo]] may or may not produce a increase in the honba count; the common practice does not.
+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.
+=== 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 ==
+{{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 ==
 {{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 ==
 {{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==
 {{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:Scoring]]