Hong Kong mahjong scoring rules

Hong Kong mahjong scoring rules are used for scoring in mahjong, the game for four players, common in Hong Kong and some areas in Guangdong.

Criteria

A hand is considered a winning hand when it has 4 melds and a pair or is considered a special hand.

Points are obtained by matching the winning hand and the winning condition with a specific set of criteria, with different criteria scoring different values. Some of these criteria may be subsets of other criteria (for example, having a meld of one dragon versus having a meld of all of them), and in these cases, only the criteria with the tighter requirements are scored. The points obtained may be translated into scores for each player using some (typically exponential) function. When gambling with mahjong, these scores are typically directly translated into sums of money. Some criteria may also be in terms of both points and score.

The terminology of point differs from variation to variation. A common English term is double, as the point-to-score translation is typically exponential with a base of 2. Cantonese variants will use the term 番 (pinyin: fān / jyutping: faan¹).

Because points and score are two distinct concepts, this article will adopt the use of the term score unit to refer to a point in a player's score.

At the beginning of each game, each player is given a fixed score, usually in the form of scoring chips. In many cases, only the winner scores, with the winner's gain being deducted from the three losers' scores (that is, the losers pay the winner). In many cases, there exist other modifiers to the score. A common set of modifiers (for which this article will call the standard payment variations) include:

• In the case where a player wins by a discard (a player picks off an opponent), the player who performs the discard pays double
• In the case where a player wins by a draw (a player wins by self-pick), every losing player pays double.
• In the case where a player wins from a high-risk scenario (see below), the player who performs the discard pays for the other two losing players (in addition to the normal double share).

There is no universally followed rule determining when a player runs out of score units. In some circles, the match is immediately aborted, with the player furthest ahead in score declared the winner, while in others, a player out of scoring chips continues to play without risk of further losses.

Mahjong is sometimes played in a gambling setting. Poker chips are used for keeping score only. Since Mahjong is a zero-sum game, when one player loses all his chips, his chips are distributed among the other winners. In this case, the loser pays cash to buy back the chips from the winners and the game continues. Before the game starts, all players must agree upon how much one set of chips (100 unit) is worth. Some gamblers do away with chips and pay cash after each round depending on local laws regarding legality of gambling.

The criteria mentioned below are by no means exhaustive or common to every variation, but are common to many 13-tile and 16-tile variations.

Terminology

The following is a list of the different terms describing the progress of one's hand:

• 獨聽 (duk6 teng1) - Known in English typically as a one-shot win or a last-chance win, this occurs if the winner was looking for one and only one tile to win the hand (e.g., the middle tile in a Chow). In some variations, this may extend to cases where two or more tiles could win the hand, but all but one were previously discarded.
• 雞糊 (gai1 wu2) - Also known in some circles as 推倒胡 (tuī dǎo hú/teoi1 dit3 wu4) or 雞胡 (ji hú/gai¹ wu⁴ "Chicken Hand"), this is used to describe a winning hand worth zero fān, or no points. For games with a minimum fān score, this can also describe those with insufficient fān.
• 詐糊 (zaa3 wu2) - Known in English literally as a trick hand, used to describe a "false alarm" when a player claims to have won the amount claimed but in fact has not.
• 食糊 (sik6 wu2) - Winning off another player's discard.
• 叫糊 (giu3 wu2) - A "ready" or "waiting" hand, one tile away from winning.

Non-standard special hands

These hands are not standard hands, but can be used to win nonetheless. Because they diverge from the criteria for a normal winning hand, it is inherently risky to attempt these hands: effectively all pieces need to be self-drawn since melds are not useful to these hands

• Thirteen Orphans + any tile in the set - also known in English as thirteen terminal hand or thirteen wonders and known in Cantonese as 十三幺 (sap⁶ saam¹ jiu¹), this occurs in 13-tile variants when the winning hand consists of one of each one, nine, wind, and dragon, and a 14th tile. Because the hand is so greatly divergent from the standard hand, this hand is generally considered the highest scoring hand of any kind, although it is not the hand that is least likely to occur - the nine gates (1112345678999 in one suit, going out on any other tile in that suit) is said to be some 450 times more rare, barring criteria that are probabilistic in nature. Thus, in scoring systems where a maximum point value is imposed, this is often an automatic limit hand.

Scoring table

The largest group of criteria concern the contents of the winning hand. Typically, a hand that is more improbable will score higher than one that is more common, but this may not be the case. In variations with scoring minimums, it is generally accepted that, barring improbable high-scoring hands (such as the Heavenly Hand described below, even if the winning hand is otherwise scoreless), at least one point must be from this set of criteria. It is not uncommon for players to define minimum fan requirements for declaring a winning hand (typically 1 or 2), and at times a maximum fan cap or ceiling (for example at 7 or 8 fan). Also note that generally speaking in Hong Kong mahjong, 13 fan is considered the absolute limit for fan.

Scoring based on type of hand

English	Cantonese	Fān	Description
Common Hand	平糊; ping4 wu4*2	1	Every meld is a Chow
	----
All in Triplets	對對糊; deoi3 deoi3 wu4*2	3	Every meld is either a Pong or Kong
	----
Seven Pairs (played by some variants)	七對子; cat1 deoi3 zi2	4	Hand consists of seven pairs. Can stack with All Honor Tiles, Mixed One Suit and All One Suit; Bonus from Wall is not awarded
	------
Mixed One Suit	混一色; wan6 jat1 sik1	3	Only honor tiles and tiles from one suit
	----
All One Suit	清一色; cing1 jat1 sik1	7	All tiles from one suit
	----
All Honor Tiles	字一色; zi6 jat1 sik1	10 (3 fān from All in Triplets not counted)	All honor tiles
	----
Small Dragons	小三元; siu2 saam1 jyun4)	5	Melds of 2 dragons and a pair of the 3rd dragon
	----
Great Dragons	大三元; daai6 saam1 jyun4	8	Melds of all 3 dragons
	----
Small Winds	小四喜; siu2 sei3 hei2	6 (6+3 fan for mixed one suit, 6+3 for all in triplets, or 6+10 for all honours)	Melds of 3 winds and a pair of the 4th wind
	----
Great Winds	大四喜; daai6 sei3 hei2	13	Melds of all 4 winds
	----
Thirteen Orphans	十三么; sap6 saam1 jiu1	13	One of each one, nine, wind, and dragon, and a 14th tile (any other terminal or honor tile)
	---- + any tile in the set
All Kongs	十八羅漢; sap6 baat3 lo4 hon3 四槓子; sei3 gong3 zi2 槓槓和; gong3 gong3 wo4	13 (3 fān from All in Triplets not counted)	Hand containing four Kongs
Self Triplets	四暗刻; sei3 am3 hak1 坎坎糊; kaan2 kaan2 wu2	10	Hand containing four concealed (unmelded) Pongs. The bonus can only be won by self-pick unless the discarded winning tile forms the pair, not any of the four melds. The bonus fan of self-pick will be awarded but not for the bonus fan of winning from the wall.
Orphans	么九; jiu1 gau2	10 (3 fān from All in Triplets not counted)	Hand containing Pongs/Kongs of Ones and Nines only
	----
Nine Gates	九子連環; gau2 zi2 lin4 waan4	10	Hand in any one suit consisting of 1112345678999, must be totally concealed. Note that bonuses for win from wall and all one suit will not be considered in this case.
	-- + any tile in the set

Notes

Scoring based on presence of certain melds

English	Cantonese	Fān	Description	Example
Seat Wind	門風 (mun4 fung1)	1	A meld of the winner's seat wind	/ / /
Prevailing Wind	圈風 (hyun1 fung1)	1	A meld of the prevailing wind	/ / /
Red Dragon	紅中 (hung4 zung1)	1	A meld of the red dragon
Green Dragon	發財 (faat3 coi4)	1	A meld of the green dragon
White Dragon	白板 (baak6 baan2)	1	A meld of the white dragon
Mixed Orphans	混么九 (wan6 jiu1 gau2)	1	Only honor tiles, ones and nines

• A double wind, where a certain wind is both the winner's seat wind and the prevailing wind, counts as 2 fan.

Scoring based on winning condition

English	Cantonese	Additional Fān	Description	Example
Self-Pick	自摸 (zi6 mo1)	1	The winning tile is from the wall
Win from Wall	門前清 (mun4 cin4 cing1)	1	The whole hand was concealed until the winning tile was drawn or stolen
Robbing Kong	搶槓 (coeng2 gong3)	1	The winning tile is obtained from someone calling a Kong; a 12-piece penalty will be imposed on the player being robbed
Win by Last Catch	海底撈月 (hoi2 dai2 lau 4jyut6)	1	The winning tile is either the last tile from the wall or the last discard
Win by Kong	槓上開花 (gong3 soeng5hoi1faa1)	2 (1 bonus +1 from self-pick)	The winning tile is from a replacement tile due to a Kong or a Bonus Tile
Win by Double-Kong	槓上槓 (gong3 soeng5gong3)	9 (8 bonus +1 from self-pick)	Similar to 'Win by Kong', except that the tile used to make the Kong was itself an extra tile from declaring a Kong
Heavenly Hand	天糊 (tin1 wu4*2)	13	East wins with initial hand
Earthly Hand	地糊 (dei6 wu4*2)	13	Non-East player wins on East's first discard

• It is possible to obtain the maximum fan (13) from only bonuses. For example, a player draws the second last tile from the wall, declares a Kong and wins on the replacement tile.
• Depending on variation, there may also be the additional requirement of winning by self-pick, in which case, this is known as men qing zi mo, or purely concealed self-drawn hand.

Scoring based on bonus tiles

English	Fān	Description	Example
Flower of own Wind	1	A flower of the winner's seat wind	/ / /
Season of own Wind	1	A season of the winner's seat wind	/ / /
All Flowers	2	All flower bonus tiles
All Seasons	2	All season bonus tiles
No Flowers or Seasons	1	No flower or season bonus tiles

Point translation function

The point translation function is, as stated above, typically an exponential function. The function itself is subject to variation, typically to set an upper bound:

• In the traditional style, there is a four-point maximum: a hand worth more than four points pays exactly the same as one worth exactly as a four-point hand. Thus, a limit hand scores 16 times the value of a scoreless hand.
• In some styles there is a rule stating that if a hand is worth one point or less it scores nothing.
• In the more modern style, which expands on the traditional style, a second limit (i.e. doubling) is set at the seventh point, and optionally, a third limit at the tenth point. Thus, a seven-point hand is worth double that of hands that are between four and six points. The English terms for each limit is typically titled full house (double full house for seven-to-nine-point hands, and so on). This modern style is commonly used by younger generations who find the traditional styles more boring, and by gamblers who require a minimum of one point to win.
• In the parlor style, named for mahjong parlors (officially mahjong schools) in Hong Kong, the translation function is constant. This is because gambling, with the exception of bets placed with the Hong Kong Jockey Club on horse racing and football, is forbidden, and thus the constant function is used as "prize money".
• In the most extreme of styles, there is no limit - every point doubles the score. Due to the fast growth of exponential functions the constant for a zero-point hand is set very low, and a minimum point value (typically three point) is imposed, as lower scores are often considered to be game spoilers.

Simplified faan point-base point table

The faan value of a hand is converted into base points which are then used to calculate the money (or "points") the losers pay the winner. The following is the Old Hong Kong simplified table, for other tables see Hong Kong Mahjong scoring rules.

Base points (Old Hong Kong Simplified)

Faan points	Base points
3	1
4	2
5	2
6	2
7	4
8	4
9	4
10+	8 (limit)

This table is based on play where 3 faan is the minimum needed in order to win with a legal hand. If a player has 3 faan then his hand is worth one base point. A winning hand with 9 faan is worth 4 base points. Losing players must give the winning player the value of these base points. Individual players must double the number of base-points owed for the following:

• If the winner wins from the wall the base points is doubled.
• If the hand was won by discard, the discarder doubles the number he owes the winner
• If the winner is east all losers double the basepoints
• If east player is a losing player he pays double the points to the winner.

If two of these criteria apply to any player...then the player must double and then redouble the points owed to the winner.

Examples

Hand 1 (West wins with 3 fan from the wall (base points of 1))

Player	base points
East (dealer)	1 (base points) x2 (doubling for winning from wall) x2 (doubling for being east) = -4
South	1 (base points) x2 (doubling for winning from wall) = -2
West	4 (from east) + 2 (from south) 2 (from north) = +8
North	1 (base points) x2 (doubling for winning from wall) = -2

Hand 2 (North wins with 6 fan on a discard from south (base points of 2))

Player	base points
East (dealer)	2 (base points) x2 (doubling for being east) = -4
South	2 (base points) x2 (discarding winning piece) = -4
West	2 (base points) = -2
North	4 (from east) + 4 (from south) 2 (from west) = +10

Hand 3 (East wins with 10 fan on discard from west (base points of 8)

Player	base points
East (dealer)	16 (from south) + 32 (from west) + 16 (from north) = +64
South	8 (base points) x2 (paying to east) = -16
West	8 (base points) x2 (paying to east) x2 (discarding winning piece) = -32
North	8 (base points) x2 (paying to east) = -16

Hong Kong Mahjong is essentially a payment system of doubling and redoubling where winning from the wall adds great value to the final payment and where the dealer is highly rewarded or penalized if he or she wins or loses.

Traditional faan point-base point table

The faan value of a hand is converted into base points which are then used to calculate the money (or "points") the losers pay the winner. The following is the Old Hong Kong simplified table, for other tables see Hong Kong Mahjong scoring rules.

Fān-Laak Table

Fān	Chips	By Discard	By Self-Draw
0	1	1+1+2=4	N/A
1	2	2+2+4=8	4+4+4=12
2	4	4+4+8=16	8+8+8=24
3	8	8+8+16=32	16+16+16=48
4-6	16	16+16+32=64	32+32+32=96
7-9	32	32+32+64=128	64+64+64=192
10+/Limit	64	64+64+128=256	128+128+128=384

This table is similar to simplified but allows payments for hands of less than 3 faan. If a player has 3 faan then his hand is worth eight base points. A winning hand with 9 faan is worth 32 base points. Losing players must give the winning player the value of these base points. Individual players must double the number of base-points owed for the following:

• If the winner wins from the wall the base points is doubled.
• If the hand was won by discard, the discarder doubles the number he owes the winner
• If the winner is east all losers double the basepoints
• If east player is a losing player he pays double the points to the winner.

If two of these criteria apply to any player...then the player must double and then redouble the points owed to the winner.

Examples

Hand 1 (West wins with 4 fan from the wall (base points of 16))

Player	base points
East (dealer)	16 (base points) x2 (doubling for winning from wall) x2 (doubling for being east) = -64
South	16 (base points) x2 (doubling for winning from wall) = -32
West	64 (from east) + 32 (from south) + 32 (from north) = +128
North	16 (base points) x2 (doubling for winning from wall) = -32

Hand 2 (North wins with 7 fan on a discard from south (base points of 32)

Player	base points
East (dealer)	32 (base points) x2 (doubling for being east) = -64
South	32 (base points) x2 (discarding winning piece) = -64
West	32 (base points) = -32
North	64 (from east) + 64 (from south) + 32 (from west) = +160

Hand 3 (East wins with 10 fan on discard from west (base points of 64)

Player	base points
East (dealer)	128 (from south) + 256 (from west) + 128 (from north) = +512
South	64 (base points) x2 (paying to east) = -128
West	64 (base points) x2 (paying to east) x2 (discarding winning piece) = -256
North	64 (base points) x2 (paying to east) = -128

Canton Fan point-base point table

The faan value of a hand is converted into base points which are then used to calculate the money (or "points") the losers pay the winner. The following is the Old Hong Kong simplified table, for other tables see Hong Kong Mahjong scoring rules.

Base points (Old Hong Kong Simplified)

Faan points	Base points
3	8
4	16
5	24
6	32
7	48
8	64
9	96
10	128
11	192
12	256
13	384 (Limit)

This table is based on play where 3 faan is the minimum needed in order to win with a legal hand. If a player has 3 faan then his hand is worth eight base points. A winning hand with 9 faan is worth 128 base points. Losing players must give the winning player the value of these base points. Individual players must double the number of base-points owed for the following:

• If the winner wins from the wall the base points is doubled.
• If the hand was won by discard, the discarder doubles the number he owes the winner
• If the winner is east all losers double the basepoints
• If east player is a losing player he pays double the points to the winner.

If two of these criteria apply to any player...then the player must double and then redouble the points owed to the winner.

Examples

Hand 1 (West wins with 4 fan from the wall (base points of 16))

Player	base points
East (dealer)	16 (base points) x2 (doubling for winning from wall) x2 (doubling for being east) = -64
South	16 (base points) x2 (doubling for winning from wall) = -32
West	4 (from east) + 2 (from south) + 2 (from north) = +128
North	1 (base points) x2 (doubling for winning from wall) = -32

Hand 1 (West wins with 7 fan from the wall (base points of 48))

Player	base points
East (dealer)	48 (base points) x2 (doubling for winning from wall) x2 (doubling for being east) = -192
South	48 (base points) x2 (doubling for winning from wall) = -96
West	192 (from east) + 96 (from south) + 96 (from north) = +384
North	48 (base points) x2 (doubling for winning from wall) = -96

Hand 3 (East wins with 12 fan on discard from west (base points of 256)

Player	base points
East (dealer)	512 (from south) + 1024 (from west) + 512 (from north) = +2048
South	256 (base points) x2 (paying to east) = -512
West	256 (base points) x2 (paying to east) x2 (discarding winning piece) = -1024
North	256 (base points) x2 (paying to east) = -512

Hong Kong Mahjong is essentially a payment system of doubling and redoubling where winning from the wall adds great value to the final payment and where the dealer is highly rewarded or penalized if he or she wins or loses.

Penalties

English	Cantonese	Description	Example
9 Pieces Penalty	九張包	Discarder pays all losses for enabling winner to go out with Pure Hand after winner had already melded 3 sets (9 tiles) of the same suit
12 Pieces Penalty	十二張包自摸	Winner goes out with Self-Picked Pure Hand after discarder has allowed them to meld a 4th set of the same suit; Discarder pays all losses
Fifth Tile Penalty	五子包生	Discarder pays all losses for discarding a "fresh" (previously unseen anywhere on the table) tile when there are 5 or less tiles left in the wall, allowing winner to go out
Maximum Penalty

See also

• Scoring in Mahjong