Fu

Fu 「符」 (pronounced as foo) is a component of scoring. It takes the hand composition into consideration in terms of tile groups, 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 yaku chiitoitsu, which is defined and set at 25 fu, regardless of other factors.

Counting Fu

Tile groups

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).

English	Romaji	Simples	Honor/Terminal
Open triplet	Minkou	2 fu	4 fu
Open kan	Minkan	8 fu	16 fu
Closed triplet	Ankou	4 fu	8 fu
Closed kan	Ankan	16 fu	32 fu

Waits

The different basic wait patterns count for fu as well.

English	Romaji	Fu value
Open wait	Ryanmen	0 fu
Dual pair wait	Shanpon	0 fu*
Closed wait	Kanchan	2 fu
Edge wait	Penchan	2 fu
Pair wait	Tanki	2 fu

* Gains fu by completing a triplet.

Complex waits can always be split into multiple types of basic wait. For example, a 23456 sanmentan can be considered as either as {23} wait or a {56} wait. Both these are ryanmen, so a sanmentan is considered a type of ryanmen wait. Other examples:

A nobetan can be counted as two individual tanki waits, so it always scores 2 fu from tanki.
A ryantan counts as ryanmen if it wins by completing the sequence, and a tanki if it wins by completing the pair.
A 12345 sequence that wins off a 3 may count as either a {12} penchan wait or a {45} ryanmen wait.

When a hand can be interpreted in multiple ways, such the 12345 example above, the interpretation that scores the most points is used. In this example, it would be counted as a ryanmen if the hand could score pinfu (due to pinfu's +1 han), or a penchan otherwise (due to +2 fu). See below for more information.

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 rule is used for this case.

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.
Depending on the 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.
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

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.

Example 1:

(MahjongTile error: unrecognised or stray character: n) Agari:

If the hand is viewed as waiting on the ryanmen , then it qualifies for pinfu. If, however, the hand is viewed as waiting on the kanchan , then it does not. It must be scored as pinfu because that is worth more points.

Example 2:

Agari:

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.

Example 3:

Pinfu is not the only example of this:

Agari:

In this case, there are two options for interpreting the pinzu: either as , , and , or as , , and . Although the triplet of is worth more fu, interpreting it as the triplet would deny sanshoku, and so the hand must be interpreted as having the triplet of .

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.

Example of a 1 han and 110 fu hand:

South player at South round:

Ron:

1 han from yakuhai
base fu: 20
closed hand ron: 10
composition of hand:
- open triplet: 4
- closed quad: 32
- closed quad: 32
- double wind pair: 4

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 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

A hand with 2 han and 110 fu is also possible, as in the following for the East player in the East round:

Tsumo:

2 han from sankantsu
base fu: 20
tsumo: 2
pair wait: 2
composition of hand:
- open quad: 16
- closed quad: 32
- closed quad: 32
- double wind pair: 4

Total 108, round up to 110

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.

Open "pinfu"

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

Waiting on: or

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.

Shortcuts for Counting

To be able to announce hand scores quickly, it helps to know some shortcuts for counting fu. These shortcuts take advantage of the fact that fu is always rounded up to the next 10.

chiitoitsu: fixed at 25 fu
toitoi: almost always 40 fu (see below)
pinfu: ron is always 30 fu, tsumo is always 20 fu
Closed hand without pinfu: ron is almost always 40 fu, tsumo is almost always 30 fu
Open hand: almost always 30 fu

These shortcuts don't work for hands that have quads since those are worth enough fu by themselves to have a significant influence on the total. In that case, it's better to simply count the fu properly.

"Almost always" means that there are a few exceptions which may raise the fu past the shortcut value. In particular, look for these elements in the hand's composition:

at least one concealed set of terminal/honor tiles
at least two open sets of terminal/honor tiles
one open set of terminal/honor tiles and one concealed set of simples
at least two concealed sets of simples

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.

External links

符

Fu in Japanese Wikipedia