Fu

Fu 「符」 (pronounced as foo) is a component of scoring. Every hand begins with 20 fu, and it can gain more based on the hand's composition, its wait at tenpai, and the method of winning.

Counting Fu

All hands start with 20 fu by default. Each source of fu is added to the total, then the fu rounded up to the nearest 10 (unless the hand is chiitoitsu).

Tile groups

Sequences are always worth 0 fu. Each triplet and kan scores fu; the amount depends on whether the group is open or closed, and whether the group is composed of a simple tile (2-8) or a terminal/honor tile.

English	Romaji	Simples	Terminal/Honor
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

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

Each of the the five basic wait patterns are worth a certain amount of fu.

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 triplet, 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, depending on the ruleset used.

Winning condition

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, whether open or closed, is worth 2 fu.
- If the hand qualifies for pinfu, these 2 fu are waved, instead gaining the han for pinfu.
- In a few scoring variations, a win by rinshan kaihou is also ineligible for the +2 fu from tsumo.

Special cases

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.

After all sources of fu are accounted for, fu is rounded up to the nearest 10, unless the hand is chiitoitsu.

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

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

Tsumo:

This is the same hand, except that one of the sequences is replaced with a triplet and thus does not qualify for pinfu. Therefore, the hand scores the +2 fu from the kanchan, because that is worth more points.

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 4

Ron:

In this case, there are two options for interpreting the manzu:

, , and
, , and

Option 1 can qualify for sanankou and can be interpreted as tanki, therefore it is worth 2 han and (20+10+8+8+4+2=52, rounded up to) 60 fu in total.

Option 2 can qualify for sanshoku doukou, but because the hand is won by ron, the must be interpreted as an open triplet and thus denies sanankou. Therefore it is worth 2 han and (20+10+8+8+4=) 50 fu in total.

Because two options have the same han, the hand must be interpreted as option 1 because it has the higher fu value and thus the more points.

Example: 1 han 110 fu

For a 1 han hand, 110 fu is the highest amount of fu possible. It is exceptionally rare, and only obtainable if a double wind pair is worth 4 fu.

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

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. Any of these cases will 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, while lacking a double wind pair, and still score 110 fu.

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"

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 "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

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: a closed toitoi is, at minimum, a mangan (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