There is a lack of English description of Japanese mahjong scoring. Here I attempt to describe it. Please forward all comments and corrections to me. This page is a revision of a text file I wrote back in 1998.
The most common version of Japanese Mahjong (Maajan [麻雀]) is Toudai-shiki [東大式], which means "version as used by Tokyo University" (I think, I'm not sure). It is one of the "Big 3" Japanese professional Mahjong associations. This is the version I try to describe here.
There are 136 tiles, composed of four copies of a 34 tile set. The set of tiles is called Jan-pai [雀牌]. ("Pai" means "tile" or "card"; possibly the term is simplified from Majan-pai [麻雀牌], but no one calls them that.) If you have a Chinese set (or some Japanese sets), your set may come with flowertiles and extra blank tiles. These are not used in Japanese Mahjong.
The tiles can be subdivided into four groups:
The Dots, Bams, and Craks are called the three SUITS, and are numbered from 1 through 9. As a group, all of them are called NUMBERS ([数牌] officially shuu-pai, commonly zu-hai). ("Dot," "Bam," and "Crak" are actually rather poor names, as they completely ignore the meanings of the symbols, but they are so common in English we're stuck with them.) The Japanese names for number tiles are created by combining a Chinese number prefix with a suit suffix, but with some idiomatic differences (shown in bold:
1 "Ii" | 2 "Ryan" | 3 "San" | 4 "Suu" | 5 "Uu" | 6 "Ryuu" | 7 "Chii" | 8 "Paa" | 9 "Chuu" | |
---|---|---|---|---|---|---|---|---|---|
Dot "pin" | Iipin | Ryanpin | Sanpin | Suupin | Uupin | Ryuupin | Chiipin | Paapin | Chuupin |
Bam "sou" | Iisou | Ryanzou | Sanzou | Sussou | Uusou | Ryuusou | Chiisou | Passou | Chuusou |
Crak "wan" | Iiwan | Ryanwan | Sanwan | Suuwan | Uuwan | Ryuuwan | Chiiwan | Paawan | Chuuwan |
The Chars are subdivided into four WINDS ([風牌] officially fon-tsu, commonly kaze-hai) and three ELEMENTS (dragons, sangen-pai [三元牌]). Their individual names are:
Note that the ordering of the elements (white-green-red) are reversed from traditional Chinese ordering (red-green-white).
Some other card terms:
Ends | Middles | |||
---|---|---|---|---|
Chars | Terminals | |||
Suits | Dots | |||
Bams | ||||
Craks | ||||
Winds | ||||
Elements |
Of the four winds, one is a ROUND WIND (bakaze [場風]), determined by which round the game is in; one is a POSITION WIND (menfon [門風] "door wind" or tsufon [自風] "self wind"), determined by the position the player is sitting in relative to the dealer (dealer's wind is East, player after dealer is South, player after South is West, player after West is North). If the round wind and the position wind is the same, it is called a DOUBLE WIND (renhoupai, dabu-kaze [ダブ風]). (Sometimes the wind name is in Japanese, e.g., "dabu-ton" is a double East.) All other (two or three) winds are called GUEST WINDs (ota-kaze [客風]).
Most Japanese only play two rounds, so West and North are rarely round winds.
Each tile has a successor. A suit tile's successor is simply a tile in the same suit that is one larger than it. A 9 tile's successor is a 1 tile. Among the winds, the succession sequence is East, South, West, North (the successor of East is South, etc.). Among the elements, the succession sequence is White, Green, Red.
A Winning hand is, except for two exceptions, composed of four MELDS (mentsu [面子]) and a PAIR (jantoo, [雀頭]). The two exceptions are the SEVEN PAIRS (chiitoitsu [七対子]) hands (covered in a later section) and the THIRTEEN ENDS (kokushimusoo [国士無双]) hands (covered later in the special hands section).
A pair is two identical tiles.
There are three types of melds:
This means that a winning hand must have 14+K tiles, where K is the number of quads in the hand.
A hand can be won in (basically) two ways:
A meld is OPEN (min [明] "exposed") if it was melded by the discards of another player (including a win on discard). Otherwise it is CLOSED (an [暗] "dark") if it was melded "naturally" in one's hand.
A hand is CLOSED (menzen [門前] "door front", short for menzenchin [門前清] "door front pure") if *all* melds that do not contain the winning tile (there are at least three, and four if the winning tile completes a pair) are closed. Otherwise the hand is OPEN. In other words, a closed hand is one where the player never called "chi," "pon," or "kan." (But he may have called "riichi," "tsumo," or "ron.")
A hand is STRONGLY CLOSED if it is closed and was won on self-draw.
A hand is WEAKLY CLOSED if it is closed and was won on discard.
Before a hand gets the winning tile, it must necessarily be in a WAITING (tenpai [聴牌] "listening to tiles") state, where the (usually 13-tile) hand needs one more tile to win.
This section provides an overview of the rest of the scoring section.
Only the winning hand is evaluated; all other hands are irrelevant.
First, a TALLY (fu [符]) value is calculated based on the composition of the hand and how the hand was won. (I called this term "abscissa" in an earlier version of this draft.) This number will be an integer, usually between 20 and 70.
Then, an EXPONENTIAL (fan [翻]) value is calculated. The significant portion of the exponential (but not all of it) is based on certain properties of the hand which award MULTIPLIERS (yaku [役]). (Since each multiplier will equal one exponential, you'll often see texts confusing the two terms.) The exponential will usually be less than 10.
The TALLY is multiplied by 2^EXPONENTIAL (2 raised to the power of EXPONENTIAL), and is then multiplied by another number depending on whether the winner was dealer or not. Finally, the number is rounded to the nearest LIMIT (kan [貫]) and/or hundred.
If the winning hand is a special hand, the tally and exponential method is not used.
[Note: this section has been revised heavily since the last version. Either they revised the rules, or, more likely, I got a lot of stuff wrong.]
The tally is a sum of five numbers; a BASE score, a CLOSURE bonus, a SELF-DRAW bonus, a COMPOSITION score, and a WAITING score. However, there are two exceptions: the SEVEN PAIRS (chiitoitsu [七対子]) hands and the ALL SEQUENCE (pinfu [平和]) hands.
In this section, the term "points" is used to represent tally points and has no relation with the final points.
The Base score is always 20 points.
If the hand is weakly closed (player won by opponents discard, but has not used any other discards), add 10 points.
If the hand was won by self-draw, add 2 points. (But note the exception for ALL SEQUENCE hands, below.)
This score is based on the composition of the hand, regardless of readiness or openness.
The pair is worth:
Each seq is worth:
Each tri is worth:
Each quad is worth:
This score is dependent on how exactly the winning tile came into the hand. There are five essential ways:
Note that a hand may be readying to win in more than one way. For instance, a hand may have three melds and the tiles 5557 in one suit. Then it is a central win if the winning tile is a 6, but a hanging win if the winning tile is a 7.
The readying score is calculated like this:
A rule of thumb to remember this is to think of the 2 points only given if the ready tile was "unique". But this is misleading because of hands that are ready to win in more than one of the five ways.
A Seven Pairs hand gets a tally of 25 points.
An All Sequence Hand gets a tally of 30 points if won by opponent's discard, and 20 points if won by self-draw. (Note that there is no self-draw bonus.)
The exponential (fan [翻]) is a sum of three numbers; the MULTIPLIER (yaku [役]) count, the DORA count, and a BASE exponential (bazoro [場ゾロ]).
The multipliers are the crux of the game, and have their own section.
The dora count is based on the dora tile(s), but is only counted for closed hands. At each game, a tile near the end of the wall is turned over, called the dora tile. The successor of that tile is now a scoring tile, adding one to the exponential count for each such tile the player has. Also note these common variants:
The base exponential is always 2.
Start with the tally. If it is even, round it up to the nearest multiple of 10. (The only possible case where the tally is not even is when it is 25 from a Seven Pairs hand.) and multiply it by 2^exponential (two raised to the power of the exponential score). This is the HAND VALUE.
If the player was dealer, multiply the hand value by 6 (representing each other player paying twice the hand value). If the player was not dealer, multiply the hand value by 4 (representing dealer paying twice the hand value, and the other two players paying the hand value). The resulting product is called the PAYOFF, and should represent approximately what the winner should get.
If the hand was won by discard, then the discarder pays the winner the entire payoff, rounded to the nearest hundred. (If the discarder is dealer, he does not pay double.)
Otherwise, the hand was won by self-draw. Then each player pays the winner the hand value, rounded up to the nearest hundred. (The hand value is doubled if either the winner or the payer is dealer.)
Note that the winner should receive a total amount close to that of the payoff.
If the hand value is greater than 2000, then instead of using the "actual" hand value, the hand value is reduced to a LIMIT (mankan [満貫]) of 2000 points. (This is reached at about 3 exponentials for tallys greater than 70, about 4 exponentials for tallys greater than 40, and 5 exponentials for smaller tallys.) (Some books will refer to the limit as 8000 or 12000 points. They're talking about the PAYOFF limit.)
The only way to get more than the limit as a hand value is to have a lot of exponentials. The higher values are:
Hand value chart. The following represents how much each hand is worth. This is the amount that would be paid, if there were no dealer bonuses, no limits, and cash were not rounded to 100s. Asterisks represent hand values that are over the limit cutoff (2000). Note that exponentials of less than 3 are not possible in a normal game (there's a base of 2, and a minimum of 1 multiplier).
Tally | Exponential | ||||||||
---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | |||
20 | 40 | 80 | 160 | 320 | 640 | 1280 | 2560* | ||
25 | 50 | 100 | 200 | 400 | 800 | 1600 | 3200* | ||
22-30 | 60 | 120 | 240 | 480 | 960 | 1920 | 3840* | ||
32-40 | 80 | 160 | 320 | 640 | 1280 | 2560* | 5120* | ||
42-50 | 100 | 200 | 400 | 800 | 1600 | 3200* | 6400* | ||
52-60 | 120 | 240 | 480 | 960 | 1920 | 3840* | 7680* | ||
62-70 | 140 | 280 | 560 | 1120 | 2240* | 4480* | 8960* | ||
72-80 | 160 | 320 | 640 | 1280 | 2560* | 5120* | 10240* | ||
82-90 | 180 | 360 | 720 | 1440 | 2880* | 5760* | 11520* |
Dealer wins by self-draw, each player pays twice the hand value, rounded up:
Tally | Exponential | ||||||||
---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8-9 | 10-12 | 13+ | Special | |
20 | NP | 700 | 1300 | 2600 | 4000 (limit) |
6000 (1.5x limit) |
8000 (2x limit) |
12000 (3x limit) |
16000 (4x limit) |
25 | NP | NP | 1600 | 3200 | |||||
22-30 | 500 | 1000 | 2000 | 3900 | |||||
32-40 | 700 | 1300 | 2600 | 4000 (limit) | |||||
42-50 | 800 | 1600 | 3200 | ||||||
52-60 | 1000 | 2000 | 3900 | ||||||
62-70 | 1200 | 2300 | 4000 (limit) | ||||||
72-80 | 1300 | 2600 | |||||||
82-90 | 1500 | 2900 |
Dealer wins by discard, the discarding player pays six times the hand value, rounded up:
Tally | Exponential | ||||||||
---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8-9 | 10-12 | 13+ | Special | |
20 | NP | 2000 | 3900 | 7700 | 12000 (limit) |
18000 (1.5x limit) |
24000 (2x limit) |
36000 (3x limit) |
48000 (4x limit) |
25 | NP | 2400 | 4800 | 9600 | |||||
22-30 | 1500 | 2900 | 5800 | 11600 | |||||
32-40 | 2000 | 3900 | 7700 | 12000 (limit) | |||||
42-50 | 2400 | 4800 | 9600 | ||||||
52-60 | 2900 | 5800 | 11600 | ||||||
62-70 | 3400 | 6800 | 12000 (limit) | ||||||
72-80 | 3900 | 7700 | |||||||
82-90 | 4400 | 8700 |
Non-dealer wins by self-draw, non-dealer players pay the hand value, rounded up:
Tally | Exponential | ||||||||
---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8-9 | 10-12 | 13+ | Special | |
20 | NP | 400 | 700 | 1300 | 2000 (limit) |
3000 (1.5x limit) |
4000 (2x limit) |
6000 (3x limit) |
8000 (4x limit) |
25 | NP | NP | 800 | 1600 | |||||
22-30 | 300 | 500 | 1000 | 2000 | |||||
32-40 | 400 | 700 | 1300 | 2000 (limit) | |||||
42-50 | 400 | 800 | 1600 | ||||||
52-60 | 500 | 1000 | 2000 | ||||||
62-70 | 600 | 1200 | 2000 (limit) | ||||||
72-80 | 700 | 1300 | |||||||
82-90 | 800 | 1500 |
Non-dealer wins by self-draw, dealer pays twice the hand value, rounded up:
Tally | Exponential | ||||||||
---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8-9 | 10-12 | 13+ | Special | |
20 | NP | 700 | 1300 | 2600 | 4000 (limit) |
6000 (1.5x limit) |
8000 (2x limit) |
12000 (3x limit) |
16000 (4x limit) |
25 | NP | NP | 1600 | 3200 | |||||
22-30 | 500 | 1000 | 2000 | 3900 | |||||
32-40 | 700 | 1300 | 2600 | 4000 (limit) | |||||
42-50 | 800 | 1600 | 3200 | ||||||
52-60 | 1000 | 2000 | 3900 | ||||||
62-70 | 1200 | 2300 | 4000 (limit) | ||||||
72-80 | 1300 | 2600 | |||||||
82-90 | 1500 | 2900 |
Non-dealer wins by discard, the discarding player pays four times the hand value, rounded up:
Tally | Exponential | ||||||||
---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8-9 | 10-12 | 13+ | Special | |
25 | NP | 1600 | 3200 | 6400 | 8000 (limit) |
12000 (1.5x limit) |
16000 (2x limit) |
24000 (3x limit) |
32000 (4x limit) |
22-30 | 1000 | 2000 | 3900 | 7700 | |||||
32-40 | 1300 | 2600 | 5200 | 8000 (limit) | |||||
42-50 | 1600 | 3200 | 6400 | ||||||
52-60 | 2000 | 3900 | 7700 | ||||||
62-70 | 2300 | 4500 | 8000 (limit) | ||||||
72-80 | 2600 | 5200 | |||||||
82-90 | 2900 | 5800 |
When the last tile is drawn and discarded with no wins, each player shows their hand and announces whether they are ready (tenpai, one tile away from winning) or not ready (noo-ten). The non-ready players have to give a penalty tally (bappu [罰符]), a collective amount of 3000, to the ready players:
Obviously, if all four are in the same status, then no money is exchanged.
If the game is drawn in some other fashion besides running out, then this does not apply.
First off, a dealer may continue to be dealer as long as he wins. (If a situation such as (2.5) occurs, being ready is enough to let the dealer continue.)
For every "extra" dealer round (i.e., for every round the same person remains dealer except the initial), the dealer takes out a single 100 unit stick and places it on his right. There may be many such sticks if the dealer has remained dealer for a long time.
When dealer wins, in addition to the normal payment, they collect 300 points for each such stick placed out. This payment comes from the discarder if it is a win by discard, and split among the players if it is a win by self-draw. (Another way to think of it is that all players must pay the amount that is in the pot, but in the case of a discard, the discarder pays for the other players as well.)
Once another player has won, the dealer takes these sticks back.
However, if it is a drawn game and dealership changes, then the sticks are "passed" on to the next player, who adds a stick of his own.
At the end of the agreed upon number of rounds (usually two rounds, an East round and a South round, composed of at least eight hands), points are converted into "final scores" as follows:
First, everyone subtracts 30,000 from their score. Then, the player who has the most points gets a 12,000 bonus (called an "oka").
Another way to think of this is: Every player started with 30,000 points, but contributed 3,000 each to a "pot," which is given to the winning player.
The four scores should add up to 0. These values are then converted to money or match points linearly, as the case may be. Note that this means you could end up with more points than you started with (e.g., 29,000) and still be losing money!
(Sometimes these scores will be rounded to the nearest 1000.)
Essentially, certain properties of the hand give multipliers (yaku [役]). At least one multiplier is necessary for the hand to win.
For each property listed here, the number of multipliers it gives is given in parenthesis. (S) denotes a special hand (i.e., gives quadruple limit). Example hands are given, but they are often not the only possible hand with that multiplier. In these example hands, open melds are denoted with the melded discard lying on its side, and closed quads are denoted with two tiles face down.
Most exponentials can be combined with other exponentials; some supersede weaker ones; some require that the hand be closed (but not necessarily strongly closed) -- those are marked with an asterisk (*).
Type | Closed | Open | Property | Short Description |
---|---|---|---|---|
Winning | 1 | Strongly Closed Hand | no use of discards | |
1 | Riichi | declaring ready | ||
2 | Double Riichi | declaring ready first turn | ||
1 | 1 | Quad Steal | winning on quad tile | |
1 | 1 | Flower on the Mountain | winning on post-quad drawn tile | |
1 | 1 | Scooping the Moon From the Sea | winning on last drawn tile | |
1 | 1 | Scooping the Fish From the Rivers | winning on last discard | |
S | Heaven | dealer winning on initial deal | ||
S | Earth | non-dealer winning on first turn | ||
Sequences | 1 | All Sequence | all sequence, two-sided ready | |
1 | Double Sequence | same sequence twice | ||
1+2 | Double Double Sequence | two sequences twice | ||
2 | 1 | One Breath | 123456789 | |
2 | 1 | Three Suit Same Sequence | ||
Tris/Quads | 2 | 2 | Double-Double | no sequences |
2 | 2 | Three Suit Same Triple | same numbers in three suits | |
2 | 2 | Three Closed Triples | ||
2 | 2 | Three Quads | ||
S | S | Four Closed Triples | ||
S | S | Four Quads | ||
Ends | 1 | 1 | End-less | no ends |
2 | 1 | Dirty End-Full | each meld has an end | |
1+2 | 1+1 | Pure End-Full | each meld has a terminal | |
Terminals | 2+3 | 2+3 | Dirty Terminals | each meld is only ends |
2+2 | 2+2 | Dirty (Seven Pairs) Terminals | each pair is only ends | |
S | S | Pure Terminals | only terminals | |
Characters | 1 | 1 | Special Chars | elements, round wind, position wind |
S | S | Pure Chars | only characters | |
2+2 | 2+2 | Little Three Elements | ||
S | S | Big Three Elements | ||
S | S | Little Four Joys | ||
S | S | Big Four Joys | ||
Suits | 3 | 2 | Dirty One-Suiter | one suit with characters |
3+3 | 3+2 | One-Suiter | one suit, no characters | |
Structure | 1 | All Sequence | ||
2 | Seven Pairs | |||
2 | 2 | Double-Double | no sequences | |
Specific | S | S | Pure Green | only green tiles |
S | S | Nine Lanterns | 1112345678999 | |
S | S | Peerless Kingdom | one of each end |
A strongly closed hand (i.e., closed and won on self-draw) gives
an exponential.
A tri or a quad in the following give one multiplier each:
A hand with no tri or quad melds. Also, the following
conditions must be met:
During the course of play, if a player's hand is closed and is a ready hand, he may declare riichi on his turn. He exclaims "riichi", positions a 1000-unit counter near his discards, discards a tile and positions it horizontally on his discard line, and covers his remaining (usually 13) tiles.
The 1000-unit counter goes to the next person to win a hand. If the round is drawn, it stays in a pot with the dealer's ante, until someone has won a hand.
After this call, he may no longer discard any tiles from his original hand during play.
He may extend a tri to a closed quad if he draws the fourth
tile (but not when an opponent discards it). Some play with the
rule that a tri cannot be extended to a closed quad
if the set of readying tiles changes, e.g.:
In this hand, the set of ready tiles is , but if the player draws a
and creates a closed quad, the set of ready
tiles is reduced to just . Some variants
would disallow such a quad creation.
A win by a player who has declared riichi gets a multiplier. He gets two multipliers if he has successfully called riichi on his very first discard; this is called a "double" riichi.
Some players play that the horizontal discarded tile is necessary for the riichi; if it is taken, the player must call riichi again on their next turn.
One multiplier when the winning tile is a result of drawing the extra tile after completing a quad. The win counts as a self-draw win regardless of how the quad was completed. Some players will play a variant where the payment is all paid by the discarding player if the quad was completed by a discard.
Winning on the last legal tile in the wall. (The identity of that tile changes during quads, of course.)
Winning on the last legal discard in the game (by another player, of course).
Three melds are composed of the tiles from 1 through 9 of the
same suit.
Every meld must have at least one end card, and the pair must be
of an end card.
The same numerical seq in three suits.
The same numerical triple in all three suits. Some play this as
worth 3 multipliers.
No melds, just seven pairs. The seven pairs must be distinct
(you cannot have four identical tiles and call them two
pairs), although some variants relax that
restriction. This hand is necessarily closed, and
can be combined with exponents that are not meld-specific, such as
End-Less.
No seq melds. Note that if this hand is closed, it will
also score for Three Closed Triples
or Four Closed Triples.
All tiles are in the same suit or a char. (I.e., two suits are
completely absent.) There must be chars
in the hand (otherwise
the hand is a Pure One-Suiter instead).
The pair and all melds contain an end, and there are no chars.
(I.e., every meld contains at least one terminal tile.)
Some variants play this as only two multipliers (i.e., no bonus, as if it were just two doubles).
Cannot be combined with Seven Pairs.
All tiles are ends. Technically, only two multipliers --
add two for the Double-double and one
for the End-Full (but no bonus, even
if the hand is closed) to get a total of 5.
If the hand is a Seven Pairs, it's only four multipliers -- two from Dirty Terminals, two for the Seven Pairs. Sometimes such a hand is called "honroochiitoi."
Some variants play this as only four multipliers total instead of five.
All tiles are of one-suit. Cannot add extra suit exponentials like
Dirty One-Suiter -- that's already counted.
5 multipliers if open, 6 if closed.
Several of these hands have a special rule. A player X (not holding the special hand) can be "responsible" for the special hand (usually by discarding the danger tile that was required to make it special). The "responsible" player must pay the entire payoff if the special hand wins by self-draw, and must pay half the payoff if the special hand wins by discarder (and discarder pays the other half).
Note that once a hand is special, all other multipliers are irrelevant. "Doubly-special" hands are meaningless (unless previously agreed upon).
Responsible Player: If all three melds are open, the player who discarded the tile leading to the third open meld is responsible.
Responsible Player: If all three melds are open, the player who discarded the tile leading to the third open meld is responsible.
Responsible Player: If all four melds are open, the player who discarded the tile leading to the fourth open meld is responsible.
All tiles are "green only"; i.e., a winning hand composed
only of
. (These
tiles are usually all green in Japanese sets, but not so in
most Chinese sets.)
Sextuple limit if the actual ready hand is 1112345678999.
One of each of the 13 ends, and any other end. Note that the extra
end need not be the winning tile -- but if it is, it's a sextuple limit.
Some play this as a simple limit, some play this as a triple limit, and some play this as a yakuman.
Some players force the dealer to "retire" after this win, others allow the dealer to continue, winning a yakuman each time from then on.
Here are some variations I've heard of or seen. These are definitely not Toudai-shiki, and I'm not sure I got all of these right. Some don't really apply to scoring.