Japanese mahjong scoring rules

Revision as of 07:14, 11 January 2014 by KyuuAA (talk | contribs) (→‎Aotenjou)

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:

  1. If the hand is a yakuman, then hand scores 8,000 basic points × number of yakuman.
  2. Otherwise, determine the hand's valid yaku.
  3. Count the han based on the yaku.
  4. Count any number of dora to the han count.
  5. 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.
  6. If the han count is 4 or less, then count fu.
  7. 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

External links

Online hand scoring calculator