Japanese mahjong scoring rules
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. Any game can set the start and target scores to any desired but workable numbers. 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.
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.
Afterwards, the dora are counted. Each dora tile in the hand counts as additional han. Dora are ordinarily worth 1 han each. Additional dora indicators may increase that value.
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 「符」 (pronounced as foo) takes the hand composition into consideration in terms of tile groups, 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.
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.
Calculating basic points
To determine the point value of a hand, the following procedure is used:
- If the hand is a yakuman, then the hand scores 8,000 basic points.
- If double yakuman are used, a double yakuman scores 16,000 basic points.
- If multiple yakuman are used, and multiple single and/or double yakuman are completed, their values are added together.
- Otherwise, determine all of the hand's valid yaku.
- Some yaku combinations such as chanta + junchan are not compatible with each other.
- 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. The hand is scored 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 hand is not 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(2 + han)).
- If playing with kiriage mangan, round a 1,920-point hand up to a 2,000-point mangan.
- 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.
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.
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.
Oyakaburi 「親かぶり」 is when a non-dealer player wins by tsumo, causing the dealer to pay more than non-dealer players. This usually applies to a high value tsumo, as the dealer has to pay double of a non-dealer for tsumo payout. The effect of oyakaburi is bigger to dealer when the total value is high.
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.
- Japanese mahjong scoring rules in Japanese Wikipedia