Japanese mahjong scoring rules
Japanese mahjong features a very complex scoring system. Every mahjong hand has a value in terms of han and fu associated with them. The combination of han and fu then corresponds to values indicated from the scoring table, and/or the two numbers of han and fu factor into an equation, by which the scoring table is derived.
Scoring factors
Han
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 provide one extra han each. In general, an increase of value by one han doubles the number of points, until the cap of mangan.
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.
Fu
Fu 「符」 takes the hand composition into consideration in terms of tile melds, 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 chii toitsu yaku, which is set to 25 fu by default.
Fu factors into the following elements:
Melds
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
| English | Romaji | Fu value |
|---|---|---|
| Open wait | Ryanmen | 0 fu |
| Closed wait | Kanchan | 2 fu |
| Edge wait | Penchan | 2 fu |
| Pair wait | Tanki | 2 fu |
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.
- An open hand won by ron without any fu from koutsu or the waiting pattern gains 2 fu. This makes all open hands ineligible for pinfu.
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 hand scores 8,000 basic points × number of yakuman.
- Otherwise, determine the hand's valid yaku.
- Count the han based on the yaku.
- 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.
- If the han count is 4 or less, then count fu.
- After determining the number of han and/or fu, refer to the scoring table.
For any who prefer to use the equation, basic points for 5 han or less are computed as
- Basic points = fu × 2(2 + han), using basic points = 2,000 if the former exceeds 2,000
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 earns 1 × basic points from the other non-dealers, rounded up to a full 100. The dealer in this case pays 2 × basic points, rounded up to a full 100.
- When a non-dealer wins by ron, the discarding player pays the winner 4 × basic points, rounded up.
- When the dealer goes out by tsumo, the dealer scores 2 × basic points from all players, rounded up.
- When the dealer goes out by ron, the dealer earns 6 × basic points from the responsible non-dealer, rounded up.
So finally, a hand's point value is finally expressed as:
- Points = Basic points x Payment multiplier
Aotenjou
Aotenjou 「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.
Honba
In the event of ryuukyoku or a dealer win, the honba or tsumibou count increases by 1 for the next hand. If someone wins a hand and East does not, the honba count resets back to zero.
This count increases hand values increases by a total of 300 per honba. For ron, the discarder pays the additional 300 points. For tsumo, everyone pays an additional 100 each. These extra points are added to the hand value after the capping as mangan, haneman, etc., so a non-dealer mangan tsumo with 2 honba costs 2,200 for a non-dealer and 4,200 for the dealer.
In the case of sekinin barai, the yakuman tsumo payment is borne entirely by the discarder of the ponned tile, who also has to pay 300 per honba. On a ron, the yakuman value is split between the discarder of the winning tile and the discarder of the earlier ponned tile. Most rules have the winning tile discarder pay for all honba.
End game score
At the end of the game, the raw points are used to calculate the end game score.
Mangan
Scoring table
The score table is generated using the Basic points and the Payment multipliers. Similar to a multiplication, the awarded points are arranged in accordance to Han and Fu values. With known Han and Fu values, the points can simply be read straight off the table.
Dealer
| Han/Fu | 20 | 25 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | |
| 1 han | -- -- |
-- -- |
500 1500 |
700 2000 |
800 2400 |
1000 2900 |
1200 3400 |
1300 3900 |
1500 4400 |
1600 4800 |
1800 5300 | |
| 2 han | 700 2000 |
-- 2400 |
1000 2900 |
1300 3900 |
1600 4800 |
2000 5800 |
2300 6800 |
2600 7700 |
2900 8700 |
3200 9600 |
3600 10600 | |
| 3 han | 1300 3900 |
1600 4800 |
2000 5800 |
2600 7700 |
3200 9600 |
3900 11600 |
4000 12000 | |||||
| 4 han | 2600 7700 |
3200 9600 |
3900 11600 |
4000 12000 | ||||||||
| Mangan (5 han) |
4000 12000 | |||||||||||
| Haneman (6,7 han) |
6000 18000 | |||||||||||
| Baiman (8,9,10 han) |
8000 24000 | |||||||||||
| Sanbaiman (11,12 han) |
12000 36000 | |||||||||||
| Yakuman (13+ han) |
16000 48000 | |||||||||||
Nondealer
| Han/Fu | 20 | 25 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | |
| 1 han | -- -- |
-- -- |
300/500 1000 |
400/700 1300 |
400/800 1600 |
500/1000 2000 |
600/1200 2300 |
700/1300 2600 |
800/1500 2900 |
800/1600 3200 |
900/1800 3600 | |
| 2 han | 400/700 1300 |
-- 1600 |
500/1000 2000 |
700/1300 2600 |
800/1600 3200 |
1000/2000 3900 |
1200/2300 4500 |
1300/2600 5200 |
1500/2900 5800 |
1600/3200 6400 |
1800/3600 7100 | |
| 3 han | 700/1300 2600 |
800/1600 3200 |
1000/2000 3900 |
1300/2600 5200 |
1600/3200 6400 |
2000/3900 7700 |
2000/4000 8000 | |||||
| 4 han | 1300/2600 5200 |
1600/3200 6400 |
2000/3900 7700 |
2000/4000 8000 | ||||||||
| Mangan (5 han) |
2000/4000 8000 | |||||||||||
| Haneman (6,7 han) |
3000/6000 12000 | |||||||||||
| Baiman (8,9,10 han) |
4000/8000 16000 | |||||||||||
| Sanbaiman (11,12 han) |
6000/12000 24000 | |||||||||||
| Yakuman (13+ han) |
8000/16000 32000 | |||||||||||