Japanese mahjong scoring rules are used for Japanese mahjong, a game for four players common in Japan. The rules were organized in the Taishō to Shōwa periods as the game became popular.
The scoring system uses structural criteria as well as bonuses. Player start scores may be set to any value. Usually, it is set to 20,000 to 30,000 points. Scores are counted using sticks of 10,000 points, 5,000 points, 1,000 points and 100 points. A game often ends when a player's score drops below zero, or (almost exclusively online rulesets use this) at zero or less, which is a situation called hakoten,Literally "(empty) box points." Japanese mahjong sets often have four boxes to store tiles, and they are often used for point sticks. (Japanese: ハコテン) dobon,Sound of something heavy like a stone falling into water. (Japanese: ドボン) buttobi,(Japanese: ぶっとび) etc. However, some settings allow the game to continue, even if a player's score dropped below zero.
There are two criteria for determining the winning points: han and fu, which correspond to a points table. Han is the unit for the value of yaku, which are particular patterns or conditions of a hand, as well as dora, which are tiles given bonus points for the round or as marked on the tile (red fives). Fu is the value of melds, waits and "going out". Hands with enough fu and/or han may be considered limit hands; limit hands use predefined values to determine the winning points. A rare ruleset, 青天井, Hepburn: aotenjou, completely removes mangan, haneman, baiman, etc. and the score is completely based on the equation.
Steps of calculation The payment to the winner of a hand is calculated as follows: 1. Counting han (飜) 2. If it is five han or more, it is mangan (満貫) or more and the calculation of basic points is omitted 3. Counting fu (符) 4. If it is clear that the han and fu yield more than mangan (3 han 70+ fu / 4 han 40+ fu), the calculation of basic points is omitted 5. Calculating the basic points based on the fu and han 6. Multiplying the basic points depending on whether the winner is the dealer or non-dealer, and whether the hand is won by tsumo or ron 7. Adding bonuses based on the number of counters (8. Adjusting the payment by the wareme rule)
In the case of a draw, points are transferred according to the nō-ten bappu rule. In the event of a penalty, such as claiming a win with an illegal hand, then points are transferred via the chombo rule.
Counting han
The total number of han (飜) of all the kinds of yaku (役; winning hand) in the hand is summed up. Each dora (ドラ) increases the han value of a hand. Dora are not regarded as yaku, and no hand can be won without a yaku even if there are some dora tiles.
If there is more than one way to arrange the winning hand, the arrangement with the highest han is used. For example, a hand could be either ryanpeikou (二盃口) or chiitoitsu (七対子), but since ryanpeikou is three han where chiitoitsu is two han, ryanpeikou should prevail. Some yaku have their han value reduced by one if the hand is not concealed.
If a hand has five han or more, it is always counted by mangan (満貫) as a unit and it is not necessary to calculate fu (符) or basic points unless the ruleset uses aotenjou.
Counting fu Fu (符) or minipoints (EMA EU) are counted in the order below and then rounded up to the tens. There may be variations of rules for counting it. Three han with 70 fu or more and four han with 40 fu or more yield more than mangan and there is no need to calculate basic points.
Winning with yaku which include seven pairs (chiitoitsu, 七対子) is counted as 25 fu altogether. No more fu can be added and the value is not rounded up to the tens. (Some rules list chiitoitsu as 50 fu and one han, especially in the Kansai region. However, such would turn haneman+ hands one han harder.)
Any other winning hand starts with 20 fu, and is then checked for the following bonuses:
An additional +10 fu is added if the winner had a closed hand and won by ron (claiming a discarded tile.)
Fu is added for each component of the hand (each of the four melds and the one pairAny seven pairs hand is always awarded exactly 25 fu; all other fu calculations are skipped (including the step where fu is rounded up by tens).). Different melds are worth different amounts of fu points; the sum value of all five components are awarded. The value of each component is listed in this table (with examples for each):
+ Fu from melds and pairs Sequence +0 fu Open triplet of simplesThe "simples" are the tiles numbered 2 to 8 inclusive. +2 fu Open triplet of honors or terminalsThe "terminals" are the tiles numbered one or nine: , , , , , . +4 fu Closed triplet of simples +4 fu Closed triplet of honors or terminals +8 fu Open quad of simples +8 fu Open quad of honors or terminals +16 fu Closed quad of simples +16 fu Closed quad of honors or terminals +32 fu Pair of dragons, the seat wind,The "seat wind" is whichever wind tile corresponds to the player's seat. For example, the seat wind of the player seated in the west seat would be the west tile . or the round wind +2 fuIf the seat wind and round wind are the same, a pair of that wind will instead award +4 fu. Any other pair +0 fu
If the winning tile was either part of the pair, the middle tile of a sequence, or a simple tile in a sequence also containing a terminal, the hand is awarded +2 fu.
If the winning tile was self-drawn, and the hand does not have the pinfu yaku, +2fu is awarded.
At this point, if the hand has not accumulated any fu past its starting balance of 20, and it is an open hand, it is awarded +2fu.
Finally, if the running tally of fu is not a multiple of 10, it is rounded up to the next highest multiple of 10. This is the final result.
Scoring the hand The method of calculating a winning hand's score from han and fu is somewhat tedious, so it is easier to use a pre-computed lookup table. Expert and professional players have this table memorized and can thus tell the value of a hand at a glance. Each of the table's point values is derived from the scoring equation and procedure with each corresponding han and fu value.
The formula itself is fu × 2(2+han). This produces the hand's "basic" points. If the dealer wins, they are owed 6 × basic; a non-dealer winner is owed 4 × basic. If it was a win by discard, the player who discarded the winning tile is fully liable. Otherwise, for a self-drawn win, all three other players split the bill (evenly if the dealer won; otherwise, the dealer pays half, and the other two players pay a quarter each). All payments are then rounded up to the nearest hundred. Even if the values of han and fu are the same, the points received for self-draw wins often slightly deviate from those received for discard wins because of rounding.
To use the table, simply look up the values that correspond to the han and fu counts of the hand. The top numbers in each cell indicate the payout from a player who discards a winning tile. The numbers in brackets indicate the payout for each player in the event the winning tile is self-drawn. If the winner is the dealer, each player pays the same amount. If the winner is a non-dealer, then the other two non-dealers pay the smaller number, while the dealer pays the larger number.
Winner is dealer Fu Winner is non-dealer4 han 3 han 2 han 1 han 1 han 2 han 3 han 4 han— ()— ()— ()—20 fu—— (/)— (/)— (/) () () (—)—25 fu— (—) (/) (/) () () () ()30 fu (/) (/) (/) (/) () () ()40 fu (/) (/) (/) () () ()50 fu (/) (/) (/) () () ()60 fu (/) (/) (/) () ()70 fu (/) (/) () ()80 fu (/) (/) () ()90 fu (/) (/) () ()100 fu (/) (/) () ()110 fu (/) (/)
Mangan When it is clear that a hand reaches basic points of more than 2,000, it is limited to full basic points of 2,000 and called mangan (満貫). A hand of five han or more is always counted as a multiple of mangan. In those cases, there is no need to calculate basic points.
One han cannot reach mangan because 110 fu × 2(2+1) = 880 < 2,000. (With one han, 110 fu is the maximum.)
Two han cannot reach mangan because 110 fu × 2(2+2) = 1,760 < 2,000. (With two han, 110 fu is also the maximum.)
When a hand has 120 fu or more, it always has some yaku of three han or more.
Name Han value Point value Mangan 3 han, 70 fu or more; 4 han, 40 fu or more; 5 han 1 × mangan 12,000 (dealer)8,000 (non-dealer)[Three han with 70 fu or more] is mangan as 70 × 2(2+3) = 2,240 > 2,000. The basic points become 2,000.
[Four han with 40 fu or more] is mangan as 40 × 2(2+4) = 2,560 > 2,000. (In some rules [four han with 30 fu] is regarded as mangan because 30 × 2(2+4) = 1,920 is close to 2,000. [Three han with 60 fu] is the same.)
Five han is automatically mangan irrespective of fu since 20 fu × 2(2+5) = 2,560 > 2,000. Haneman 6 or 7 han 1.5 × mangan 18,000 (dealer)12,000 (non-dealer)A 6 or 7 han hand is considered haneman (跳満, or hane-mangan 跳満貫) and the basic points are 3,000. Baiman 8−10 han 2 × mangan 24,000 (dealer)16,000 (non-dealer)An 8−10 han hand is considered baiman (倍満, or bai-mangan 倍満貫) and the basic points are 4,000. Sanbaiman 11 or 12 han 3 × mangan 36,000 (dealer)24,000 (non-dealer)An 11 or 12 han hand is considered sanbaiman (三倍満, or sanbai-mangan 三倍満貫) and the basic points are 6,000. Kazoe-yakuman 13 or more han 4 × mangan 48,000 (dealer)32,000 (non-dealer)In most rules, a hand with 13 han or above is considered kazoe-yakuman (数え役満; counted yakuman). It has the same scoring as yakuman (役満). Some rules prohibit kazoe yakuman. In such rules, 13+ han hands are worth sanbaiman. Kazoe yakuman may be referred to as yonbaiman. Yakuman Limit 4 × mangan 48,000 (dealer)32,000 (non-dealer)A yakuman (役満, or yaku-mangan 役満貫) is awarded to some rare hands which are particularly hard to achieve, like kokushi-musō (国士無双; thirteen orphans) or sū-ankō (四暗刻; four closed melds of the same three tiles). The basic points are 8,000. Multiple yakuman Multiple limit NA Multiplied yakuman valueIf the winning hand can be interpreted as combined forms of rare hands, multiple yakuman points are awarded. For example, a hand consisting of four closed quads of wind tiles plus a pair of dragon tiles would be worth six yakuman.
Example calculations Example 1: The player on the right of the dealer goes out by self-draw. (The dealer's wind is always East in Japanese rules.) The winner's hand is closed and has a closed triplet (ankō) of Souths. The player also has two Whites as the pair (toitsu) and the winning tile is a White. The yaku are "self-pick" (menzenchin-tsumo-hō) and "honor tiles" (yakuhai), and they yield a total of two han. The sum of fu is 20 (fūtei) + 8 (a closed triplet of Souths) + 2 (a pair of Whites) + 2 (pair wait) + 2 (self-draw) = 34 fu, rounded up to 40 fu.
The basic points are thus 40 × 2(2+2) = 640. The dealer pays the winner 640 × 2 = 1,280, rounded up to 1,300 points. The other two non-dealers pay the winner 640, rounded up to 700 points.
Example 2: The same player goes out by the same hand, except this time the winning tile was discarded by the player on the right. The resulting hand has one han of honor tiles. The number of fu is 20 (fūtei) + 10 (ron with a closed hand) + 8 (a closed triplet of Souths) + 2 (the pair of Whites) + 2 (pair wait) = 42 fu, rounded up to 50 fu.
The basic point is thus 50 × 2(2+1) = 400. The discarder pays the winner 400 × 4 = 1,600 points. The other two players pay the winner nothing.
One han 110 fu It is possible for a hand to have one han with 102 fu (rounded up to 110 fu) if the rules allow a pair to have four fu when it is made of wind tiles that are both the seat wind and the prevailing wind. Some rules consider that such a pair is still worth two fu, making the hand have exactly 100 fu.
An example of a hand that has one han with 110 fu (winning by a discard):