Difference between revisions of "Japanese mahjong scoring rules"

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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.  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]], along with the appropriate multipliers.
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[[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, and 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 ==
For every winning hand, two scoring factors are used to determine point values: '''Han''' and '''Fu'''.
 
  
 
=== Han ===
 
=== Han ===
{{main|List of yaku}}
 
  
'''Han''' {{kana|飜}} is the main portion of scoring, as each [[yaku]] is assigned a han number.  Most of the yaku are valued at either 1-han or 2-han.  At most, a [[chinitsu|sole yaku]] can be worth 6-han.  Anything greater may be classed as [[yakuman]]. Naturally, different yaku can be [[Yaku compatability|combined]] to produce hands worth 2-han to [[kazoe|greater than 13-han]].
+
'''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.
 +
 
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A hand's han value is calculated by summing together the han values of its yaku, plus the han for each [[dora]] tile in the hand. Dora are ordinarily worth 1 han each, but a tile that is dora multiple times is worth correspondingly more han.
  
 
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]].
 
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]].
 
Some may factor being [[Kuisagari|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]].
 
 
For most applications, yakuman do not have a han value. For the rarely used [[aotenjou]] rules, they are defaulted at 13-han.  If a winning hand satisfies at least one yakuman, han and fu are not necessarily counted for the hand.  Points are awarded based on the yakuman value.  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]].
 
  
 
=== Fu ===
 
=== Fu ===
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'''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 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.
 
'''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 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|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, and a double yakuman as a 26-han yaku.
  
 
== Scoring procedure ==
 
== Scoring procedure ==
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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 hand scores 8,000 basic points.
# Otherwise, determine the hand's valid [[yaku]].
+
## If double yakuman are used, a double yakuman scores 16,000 points.
 +
## If multiple yakuman are used, and multiple single and/or double yakuman are completed, their values are added together.
 +
# Otherwise, determine the hand's valid [[yaku]]. Be sure not to count [[Yaku compatibility|invalid combinations]] such as [[chanta]] + [[junchan]].
 
# 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.
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# If the han count is 5 or more, then counting fu is no longer necessary. Score the hand 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]].
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## 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.
 
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# 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 ===
 
=== Payment multipliers ===
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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.  The dealer in this case pays 2 × basic points.
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*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 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.
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*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.
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*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:
 
'''Points = Basic points x Payment multiplier'''; points rounded up to the next 100.
 
  
=== Scoring table ===
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Each value to be paid is rounded up to the nearest 100.
{{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]].
+
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 ===
 
=== Honba ===
 
{{main|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.
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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.
 
 
===Summary===
 
 
 
#Determine Han
 
#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 ==
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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.  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-->
 
== 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.
 
  
 
==External links==
 
==External links==

Revision as of 22:23, 21 August 2015

Scoring Table.png

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, and 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.

A hand's han value is calculated by summing together the han values of its yaku, plus the han for each dora tile in the hand. Dora are ordinarily worth 1 han each, but a tile that is dora multiple times is worth correspondingly more han.

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

Fu 「符」 (pronounced as foo) takes the hand composition into consideration in terms of tile melds, 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

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, and a double yakuman as a 26-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 hand scores 8,000 basic points.
    1. If double yakuman are used, a double yakuman scores 16,000 points.
    2. If multiple yakuman are used, and multiple single and/or double yakuman are completed, their values are added together.
  2. Otherwise, determine the hand's valid yaku. Be sure not to count invalid combinations such as chanta + junchan.
  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. Score the hand 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

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.

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.

External links

Japanese mahjong scoring rules in Japanese Wikipedia