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 nihongo|ドボン|Dobon, 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.

teps 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.

# A winning hand is automatically awarded 20 "fu". This is called "fūtei" (副底).
# 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).
# Add "fu" of the melds. (See the list below.)
# Add "fu" according to how the waiting was. (See the list below.)
# 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".
# 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".
# 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: "nō" 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.

ee also

*Scoring in Mahjong