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| Closed kan || [[Kan|Ankan]] ||align=center| 16 fu ||align=center| 32 fu
| Closed kan || [[Kan|Ankan]] ||align=center| 16 fu ||align=center| 32 fu
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In other words:
*Each triplet is worth 4 fu, half if opened, and double if a terminal/honor.
*Each kan is worth 16 fu, half if opened, and double if a terminal/honor.


===Waits===
===Waits===
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===Yakuhai pair===
===Yakuhai pair===


If the hand's pair is of tiles that would score [[yakuhai]] in a koutsu, then this scores 2 fu. If the pair doubles up as both the round wind and the seat wind, it may score 2 fu, or 4 fu. That is dependent on which [[Scoring variations#Double Wind Fu|scoring rule]] is used for this case.
If the hand's pair is of tiles that would score [[yakuhai]] in a koutsu, then this scores 2 fu. If the pair is both the round wind and seat wind, it may score either 2 fu or 4 fu. Which value is used depends on the [[Scoring variations#Double Wind Fu|ruleset used]].


===Winning condition===
===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 ron with a closed hand is worth 10 fu. This is called ''menzen-kafu'' and does not interrupt [[pinfu]].
* A win by tsumo with an open or closed hand is worth 2 fu.
*A win by tsumo, whether open or closed, 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.
**If the hand qualifies for [[pinfu]], these 2 fu are waved, instead gaining the han for pinfu.
* Depending on the [[Scoring variations#Rinshan Fu|scoring rules]] used, a hand won with a kan replacement tile may also be ineligible for the 2 fu for tsumo, instead scoring only the han for [[rinshan kaihou]].
**In a few [[Scoring variations#Rinshan Fu|scoring variations]], a win by [[rinshan kaihou]] is also ineligible for the +2 fu fu.
* An open hand won by ron without any fu from koutsu or the waiting pattern (i.e. 20 fu) is forced to 30 fu. This is often described as being worth 2 fu for an open pinfu.


==Maximal Score==
===Special cases===
When a hand can be interpreted to have won with multiple different types of basic wait, the interpretation that scores the most final points is always used. This is always the interpretation that scores the most han; it may not score the most fu. The most common reason for this is for [[pinfu]].
*[[Chiitoitsu]] hands are set to 25 fu, no matter what.
*If an open hand has no other fu (i.e. is at 20 fu), it is set to 30 fu. This is often described as being worth 2 fu for an open pinfu.
 
==Maximum Score==
When a hand can be interpreted to have won with multiple different types of basic wait, the interpretation that scores the most ''final'' points is used. This is always the interpretation that scores the most han, but it may not score the most fu. The most common reason is for [[pinfu]].


'''Example 1:'''
'''Example 1:'''
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:{{#mjt:23345m567p446'78s}} Agari: {{#mjt:4m}}
:{{#mjt:23345m567p446'78s}} Agari: {{#mjt:4m}}


This is the same hand, except open. Pinfu cannot be scored when open. Therefore, the hand scores the +2 fu from kanchan, because that is worth more points. For this hand there is no functional difference (the hand ends up rounding to 30 fu either way), but it can matter for other hand compositions.
This is the same hand, except open. Pinfu cannot be scored when open. Therefore, the hand scores the +2 fu from the kanchan, because that is worth more points. For this hand there is no functional difference (the hand ends up rounding to 30 fu either way), but it can matter for other hand compositions.


'''Example 3:'''
'''Example 3:'''
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Pinfu is not the only example of this:
Pinfu is not the only example of this:


:{{#mjt:789m66678999p789s}} Agari: {{#mjt:5z}}
:{{#mjt:789m6678999p789s}} Agari: {{#mjt:6p}}


In this case, there are two options for interpreting the pinzu: either as {{#mjt:66p}}, {{#mjt:678p}}, and {{#mjt:999p}}, or as {{#mjt:666p}}, {{#mjt:789p}}, and {{#mjt:99p}}. Although the triplet of {{#mjt:9p}} is worth more fu, interpreting it as the triplet would deny [[sanshoku]], and so the hand must be interpreted as having the triplet of {{#mjt:6p}}.
In this case, there are two options for interpreting the pinzu: either as {{#mjt:66p}}, {{#mjt:678p}}, and {{#mjt:999p}}, or as {{#mjt:666p}}, {{#mjt:789p}}, and {{#mjt:99p}}. Although the triplet of {{#mjt:9p}} is worth more fu, interpreting it as the triplet would deny [[sanshoku]], and so the hand must be interpreted as having the triplet of {{#mjt:6p}}.
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== Example: 1 han 110 fu ==
== Example: 1 han 110 fu ==


A hand with 1 han and 110 fu is an exceptionally rare hand.  Its requirements are particularly limited, because the hand must be composed of all, not just some, the conditions in the following example.
For a 1 han hand, 110 fu is the highest amount of fu possible. It is exceptionally rare.
 
Example of a '''1 han and 110 fu''' hand:


South player at South round:
South player at South round:
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Total 102, round up to 110
Total 102, round up to 110


This is the greatest fu count for any hand worth 1 han, and is only attainable if double winds score 4 fu. If the hand is won by tsumo, then [[sanankou]] and [[mentsumo]] will be scored; if the triplet of [[ton|east]] is closed, then [[sanankou]] will still be scored. Finally, the last group must be a sequence, or [[toitoi]] would be scored. In these cases, this would add han to the hand.  
It is only obtainable if the double wind pair is worth 4 fu. If the hand is won by tsumo, then [[sanankou]] and [[mentsumo]] will be scored; if the triplet of [[ton|east]] is closed, then [[sanankou]] will still be scored. Finally, the last group must be a sequence, or [[toitoi]] would be scored. In these cases, this would add han to the hand.  


== Example: 2 han 110 fu ==
== Example: 2 han 110 fu ==
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This is the greatest fu count for any hand worth 2 han. The third quad means that [[sankantsu]] must be the only yaku, but one must still be open in order to avoid [[sanankou]]. Unlike the 1 han 110 fu example, there is a little bit of leeway: for instance, the hand could be completed on a ron without a double wind pair and still score 110 fu.
This is the greatest fu count for any hand worth 2 han. The third quad means that [[sankantsu]] must be the only yaku, but one must still be open in order to avoid [[sanankou]]. Unlike the 1 han 110 fu example, there is a little bit of leeway: for instance, the hand could be completed on a ron without a double wind pair and still score 110 fu.


With the [[mangan]] limit applied, counting this many fu for anything 3 han or higher is no longer relevant, because any han with 70 fu or more is capped at mangan.  If the [[aotenjou]] scoring system is used however, high fu counts remain relevant towards point calculation.
Because of the [[mangan]] limit, counting this many fu for anything 3 han or higher is no longer relevant, because any hand with 3 han 70 fu or more is capped at mangan.


== Open "pinfu" ==
== Open "pinfu" ==
Technically, [[pinfu]] cannot be a yaku while open. However, some open hands produce 0 fu based on composition alone.
Technically, [[pinfu]] cannot be a yaku while open. However, some open hands produce 0 fu based on composition alone.


{{#mjt:123m45p22s}} {{#mjt:2'34p6'57s}} Waiting on: {{#mjt:3p}} or {{#mjt:6p}}
{{#mjt:234m45p22s}} {{#mjt:2'34p6'57s}} Waiting on: {{#mjt:3p}} or {{#mjt:6p}}


This is an open "yakuless" hand.  When closed, it resembles that of pinfu. Counting the fu from this hand, it produces 0 fu other than the base 20 fu for every hand.  A hand like this can still gain yaku worth 1-han from either [[chankan]], [[haitei]], or [[houtei]]. As far as hands go, this pattern generates an exception to the rule behind counting fu; and as a special case, it is granted 2 fu in order to be rounded up to 30 fu.
This is an open "pinfu" hand - If closed, it would score pinfu. Counting the fu from this hand, it produces 0 fu (other than the base 20 fu). This pattern is subject to a special case: when winning, it is granted +2 fu in order to be rounded up to 30 fu.


== Shortcuts for Counting ==
== Shortcuts for Counting ==
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All of the above are worth 8 fu and thus may raise the total fu count by 10 when combined with the 2 fu for tsumo or for having difficult wait.
All of the above are worth 8 fu and thus may raise the total fu count by 10 when combined with the 2 fu for tsumo or for having difficult wait.


Counting fu for [[toitoi]] is a bit trickier but only ''open'' [[toitoi]] hands need to be considered: if you win a closed [[toitoi]] hand by tsumo, it's a yakuman ([[suuankou]]) and if you win a closed [[toitoi]] hand by ron, it's a mangan or higher ([[toitoi]] + [[sanankou]]). Also, a [[toitoi]] hand with only terminals/honors is [[honroutou]], also worth at least a mangan. Thus, an open [[toitoi]] hand with no quads for which counting fu actually matters will almost always score 40 fu.
Counting fu for [[toitoi]] is a bit trickier but only ''open'' [[toitoi]] hands need to be considered: if you win a closed [[toitoi]] hand by tsumo, it's a yakuman ([[suuankou]]) and if you win a closed [[toitoi]] hand by ron, it's a mangan or higher ([[toitoi]] + [[sanankou]]). Also, a [[toitoi]] hand with only terminals/honors is [[honroutou]], also worth at least a mangan. Thus, an open [[toitoi]] hand with no quads (for which counting fu actually matters) will almost always score 40 fu.


== External links ==
== External links ==
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