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Haneman

Japanese Mahjong scoring rules

Japanese Mahjong scoring rules are used for Mahjong, a game for four players common in Japan, which were organized in Taishō to Showa period as it became popular.

The scoring system

The scoring system uses both criteria and meld as well as the way the winning hand was made. A complex but systematic point system is used but there are several scoring rules that may also be used. Players start with 20,000 to 30,000 points. These are counted using bars of 10,000 points, 5,000 points, 1,000 points and 100 points. When a complete round of games is played, or, under an often used optional rule, when a player loses all his points (in Japanese , etc.), a game ends.

Final points and place

After the game is finished, the number of points which each of three players other than the winner has is rounded off to the nearest 1,000. The winner's points are the difference between 120,000 (30,000 × 4) and the total of these three players' points. The number of points is divided by 1,000, and 30 is finally subtracted from it. The sum of these final points is always zero. In most cases there are some additional points of awards or penalties related to the players' final place.

Example: The initial points are 25,000 each. A (winner): 43,600, B: 14,500, C: 15,400, D: 26,500, and rounded off to B:15,000, C:15,000, D:27,000. The number of the winner's points is calculated as follows irrespective of initial points: 120,000 − (15,000 + 15,000 + 27,000) = 63,000 (There sometimes happens the case like this. The result of the winner differs from 64,000 that was counted rounding 43,600 off and adding 4 × 5,000 (difference between 30,000 and initial points)). The final points and place: A:+33 (1st), D:−3 (2nd), C:−15 (3rd), B:−15 (4th). The 1st place is also counted like: (30 − 15) + (30 − 15) + (30 − 27) = +33.

Steps of calculation

The score is calculated by following order.
I. Counting han (飜)
II. If it is five han or more, it is mangan (満貫) or more and calculation of basic points is omitted
III. Counting fu (符)
IV. If it is clear that those han and fu yield more than mangan, the calculation of basic points is omitted
V. Calculating basic points by multiplying fu by han
VI. Adjusting the points when the winner is the dealer
VII. Distributing the payment to all other players if won drawing the tile
VIII. Adjusting the score by the number of rounds continued (See Honba)
IX. Transferring the points of penalty when a round is a draw (See Tenpai and nō-ten bappu)
X. (Adjusting the score by wareme (割目) rule)

Counting han

The total number of han (飜) of all the kinds of yaku (役; winning hand) in the hand is summed up. 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 any more.

Some yaku are counted only if the hand is concealed, where some yaku have their han value deducted by one if the hand is not concealed.

If there are more than one way to arrange the winning hand, count the way in which the han is higher. For example, a hand could be either ryanpeikou (二盃口) or chītoitsu (七対子), but since ryanpeikou is three han where chītoitsu is two han, ryanpeikou should prevail.

Each dora (ドラ) tile counts as one han. Dora is not regarded as yaku and no winning hand could be reached without any yaku even if there are some dora tiles.

Counting fu

Fu (符) is counted by adding all points of the winning hand and then rounded up to tens. It may also be rounded up by four or six in some rules, while in some cases the fu may be 20, 25, 30, 35 and so on.

[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.

  1. A winning hand is automatically awarded 20 fu. This is called fūtei (副底).
  2. If one wins by picking a discarded tile with a hand concealed, 10 fu is awarded. This is called menzen-kafu (門前加符).
  3. Add fu of the melds. (See the list below.)
  4. Add fu according to how the waiting was. (See the list below.)
  5. Add two fu if one wins by self-drawn. This way of winning is called tsumo (自摸, or ツモ). However, if the resulting hand includes pinfu (平和) when it is treated as a possible winning hand, in most cases the two fu is not awarded exceptionally and the hand is counted as a total of 20 fu.
  6. Winning by chī toi tsu (七対子; Chinese 七對子 qi dui zi) is counted as 25 fu altogether and two han (with some more yaku available), or in Kansai 50 fu and one han.
  7. As an exception, if one wins by picking a discard with an open hand with melds and waits to which no fu is awarded at all, the hand is not 20 fu but counted as a total of 30 fu.

Fu of melds

The list for third step:

min-kōtsu (明刻子)
(open same three tiles meld)
2 fu for non-terminal or honor tiles, four fu for terminal or honor tiles
an-kōtsu (暗刻子)
(concealed same three tiles meld)
4 fu for non-terminal or honor tiles, eight fu for terminal or honor tiles
min-kantsu (明槓子)
(open kan/kong)
8 fu for non-terminal or honor tiles, 16 fu for terminal or honor tiles
an-kantsu (暗槓子)
(concealed kan/kong)
16 fu for non-terminal or honor tiles, 32 fu for terminal or honor tiles
shuntsu (順子)
(sequential meld)
0 fu
toitsu (対子)
(two pieces meld, or eyes)
2 fu for player's wind tiles, prevailing wind tiles or dragon tiles. Four fu when player's and prevailing wind match. 0 fu for other tiles

Fu of waits

The list for fourth step:
ryanmen-machi (両門待ち)
(sequential tile waits for both sides)
0 fu
kanchan-machi (嵌張待ち)
(sequential single tile waits for a middle tile)
two fu (waiting for one kind of tile)
penchan-machi (辺張待ち)
(sequential single tile waits for a right or left side (number 3 or 7))
tanki-machi (単騎待ち)
(single tile waits for two pieces meld)
shanpon-machi (双碰待ち)
(waits for either of melds of same three tiles)
0 fu
However, a meld of same three tiles would be made after winning, so two, four, or eight fu is added

Calculating basic point

The basic point of a hand is calculated as follows:

[basic point = fu × 2(2+han) ]

The actual point given has to be rounded up to the nearest 100.

  • When a non-dealer (ko, 子: child) goes out by self-drawn, the dealer (oya, 親: parent) pays him 2 × basic point, and the other two non-dealers pay him 1 × basic point.
  • When a non-dealer goes out by discard, the discarding player pays him 4 × basic point.
  • When the dealer goes out by self-drawn, all the three non-dealers pay him 2 × basic point.
  • When the dealer goes out by discard, the discarding non-dealer pays him 6 × basic point.

It is noted that even the number of han and fu is the same, the points received by self-drawn often slightly deviate from those received by discard because of rounding.

Example calculations

Example 1: The player on the right of the dealer goes out by self-drawn. (The dealer's wind is always East in Japanese rules.) He got an an-kōtsu of Souths, and his hand is concealed. He also uses two Whites as the toitsu and the winning tile is that White. The winning hands are menzenchin-tsumo-hō (門前清自摸和) and yakuhai (役牌), and they yield a total of two han. The sum of fu is 20 (fūtei) + 8 (South an-kōtsu) + 2 (White toitsu) + 2 (tanki-machi) + 2 (tsumo) = 34 fu, rounded up to 40 fu.

The basic point is thus 40 × 2(2+2) = 640. The dealer pays him 640 × 2 = 1,280, rounded up to 1,300 points. The other 2 non-dealers pay him 640, rounded up to 700 points.

Example 2: The same player goes out by the same hand, except this time the winning tile was a discard by the player on his right. There is only one han of yakuhai, since it is not a tsumo at all. The number of fu is 20 (fūtei) + 10 (menzen-kafu) + 8 (South an-kōtsu) + 2 (White toitsu) + 2 (tanki-machi) = 42 fu, rounded up to 50 fu.

The basic point is thus 50 × 2(2+1) = 400. The discarder pays him 400 × 4 = 1,600 points. The other two players pay him nothing.

Scoring tables

Since the method of calculating a winning hand's score in mahjong is quite tedious, many players refer to a scoring table to look up the final score of a hand. Expert and professional players have this table memorized and can thus tell the value of a hand at a glance.

Dealer Non-dealer
4 3 2 1 Han/Fu Han/Fu 1 2 3 4
7700
(2600)
3900
(1300)
2000
(700)
N/A 20 20 N/A 1300
(400/700)
2600
(700/1300)
5200
(1300/2600)
11 600
(3900)
5800
(2000)
2900
(1000)
1500
(500)
30 30 1000
(300/500)
2000
(500/1000)
3900
(1000/2000)
7700
(2000/3900)
Mangan 7700
(2600)
3900
(1300)
2000
(700)
40 40 1300
(400/700)
2600
(700/1300)
5200
(1300/2600)
Mangan
Mangan 9600
(3200)
4800
(1600)
2400
(800)
50 50 1600
(400/800)
3200
(800/1600)
6400
(1600/3200)
Mangan
Mangan 11 600
(3900)
5800
(2000)
2900
(1000)
60 60 2000
(500/1000)
3900
(1000/2000)
7700
(2000/3900)
Mangan
Mangan Mangan 6800
(2300)
3400
(1200)
70 70 2300
(600/1200)
4500
(1200/2300)
Mangan Mangan

To use the table, simply look up the table that corresponds fu and han 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.

A note about the 20-fu line of the chart. The reason why there are no scores in the 1 han/20 fu cell is that it cannot possibly exist. Here's why.

The only 20-point hands are the no-points, or "pinfu" hand where the winning tile is self-drawn. In such cases, the fu-count is exaclty 20; however, since a no-points hand must be closed, making the win via a self pick tile off the wall automatically adds 1 han value to the hand. Therefore, a 20-fu, 1-han hand cannot possibly exist.

Seven-pairs scoring table

As stated above, a seven pairs hand is worth 25 fu. As such, it requires its own scoring table.

Dealer Han Non-dealer
2400
(800)
2 1600
(400/800)
4800
(1600)
3 3200
(800/1600)
9600
(3200)
4 6400
(1600/3200)

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 multiple of mangan. In those cases there is no need to calculate basic points.

One han cannot reach mangan because 100 fu × 2(2+1) = 800 < 2,000. (It is known that when a hand has 110 fu, it cannot avoid having some yaku of two han.)

Two han cannot reach mangan because 110 fu × 2(2+2) = 1,760 < 2,000. (It is known that when a hand has 120 fu or more, it cannot avoid having some yaku of three han or more.)

  • Mangan

[Three han with 70 fu or more] is mangan as 70 × 2(2+3) = 2,240 > 2,000. The basic points become 2,000. The dealer (when he wins, ditto) gets 12,000 and non-dealer gets 8,000.

[Four han with 40 fu or more] is mangan as 40 × 2(2+4) = 2,560 > 2,000. (In some cases [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 − 7 han) (1.5 × mangan)

A 6 − 7 han hand is considered haneman (跳満, or hane-mangan 跳満貫) and the basic point is 3,000. Dealer gets 18,000 and non-dealer gets 12,000.

  • Baiman (8 − 10 han) (2 × mangan)

An 8 − 10 han hand is considered baiman (倍満, or bai-mangan 倍満貫) and the basic point is 4,000. Dealer gets 24,000 and non-dealer gets 16,000.

  • Sanbaiman (11 − 12 han) (3 × mangan)

An 11 − 12 han hand is considered sanbaiman (三倍満, or sanbai-mangan 三倍満貫) and the basic point is 6,000. Dealer gets 36,000 and non-dealer gets 24,000.

  • Kazoe-yakuman (13 han or more) (4 × mangan)

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) (see below).

  • Yakuman (4 × mangan) and Multiple Yakuman

See below.

Yakuman (yaku-mangan)

A yakuman (役満, or yaku-mangan 役満貫) is awarded to some rare hands which is particularly hard to achieve, like kokushi-musō (国士無双; thirteen terminals) or sū-ankō (四暗刻; four concealed melds of same three tiles). The basic point is 8,000 (4 × mangan). The winning dealer gets 48,000, and a winning non-dealer gets 32,000. If the winning hand can be interpreted as different forms of rare hands, multiple yakuman points are awarded (for example, all hands are concealed, contain only four triplets of direction tiles plus a pair of dragon tiles as eyes).

Honba

Honba (本場) is a unit of numbers of continuing kyoku (局; round). To be exact, hon (本) is a unit of numbers of some bars and so on, and ba (場) means a scene or a situation.

A winner of a round gets additional points calculated multiplying 300 by the number of honba.

The dealer offers the same number of bars of 100 points as the number of honba as mere marks (not for payment) on some part of the table (usually the right side of the dealer).

In a state of n honba (suppose n is a number), when a player wins a round by tsumo (self-drawn), he gets additional n × 100 points from each of other three players as a total of n × 300, and when he wins by ron (栄; picking a discard), he gets additional n × 300 from the discarder.

The initial number of honba is zero. The number of honba increases by one when (1) the dealer won a round, (2) a round was a ryūkyoku (流局; draw) or (3) an abortive draw happened in a round. In case of (1) or (3), a round continues. In case of (2), when the dealer cannot declare tenpai (聴牌), a round goes to next. In other cases the number of honba is reset to zero (namely when a non-dealer wins).

There is a possible rule in which players must win by hands with two han or more in a round of five honba or more, which is called ryanhan-shibari (二飜縛り; literally "two-han binding").

There may be some variation of rules.

Example: The round of a game is Eastern 4th round 0 honba (東4局0本場). The dealer (East) wins and the next round is Eastern 4th round 1 honba (東4局1本場). The dealer remains the dealer and puts one bar of 100 points as a mark on the table. In this round the North wins by ron (picking a discard) getting additional 300 points from the discarder. The next round becomes Southern 1st round 0 honba (南1局0本場). The dealer changes and the former dealer takes the bar of 100 points back to himself.

Tenpai and nō-ten bappu

Tenpai (聴牌) means one tile short of winning hands. To be tenpai a hand needs no yaku partly because winning by the last discard is yaku itself. When a hand is not tenpai, the situation is called nō-ten (ノー聴: is English "no" and ten for tenpai).

In case a round is a draw, players ended with nō-ten pay points of penalty to other players whose hands are tenpai. The points are called nō-ten bappu (ノー聴罰符; fu of penalty for nō-ten).

When a round ended in a draw, in case the hand(s) of (1) one player is in a state of tenpai, he gets 1,000 points from each of other three players and gets total of 3,000, (2) two players are tenpai, they get 1,500 each and other two players pay 1,500 each, (3) three players are tenpai, they get 1,000 each and the other player pays 3,000, (4) all the players are or are not tenpai, no payment is made.

A player ended with tenpai must show whole his hand when a round is a draw. In some cases a player doesn't always have to declare tenpai and can keep his hand concealed.

See also

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