Hong Kong mahjong scoring rules

What is commonly referred to as a point or double will be referred to as faan in this article, from the Cantonese term 番 (pinyin: fān / jyutping: faan1).

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

Faan are obtained by matching the winning hand and the cause of winning 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 faan 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.

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, the change in score is modified by how the winner wins. These rules are called modifiers. Some common modifiers are:

• 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^{[clarification needed]}, 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 for what happens when a player runs out of score (i.e. their score goes below zero). 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 outlined in this article are by no means exhaustive or common to every variation, but are common to many 13-tile and 16-tile variations.

The largest group of criteria for scoring faan 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. It is not uncommon for players to define minimum faan requirements for declaring a winning hand (typically 1, 2, or 3), and at times a maximum faan cap or ceiling (for example at 7 or 8 faan). High-scoring hands (Chinese: 例牌,^[1] translated to "capped hands" in this article) are only scored based on the hand and winning conditions, but not winds, dragons, or flowers. In Hong Kong mahjong, 13 faan is considered the absolute limit for faan.

The general equation for total faan is:

${\displaystyle {\text{Total Faan}}={\begin{cases}\max(13,{\text{Hand}}+{\text{Winning Condition}}),{\text{if hand is a capped hand,}}\\\max(13,{\text{Hand}}+{\text{Wind and Dragon}}+{\text{Flower}}+{\text{Winning Condition}}),{\text{if otherwise.}}\end{cases}}}$

Hand Faan

The tables following list common criteria for faan based on the contents of the hand.

More information English, Cantonese ...

English	Cantonese	Faan	Description
Common Hand (i.e., all sequences)	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
	----
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
	----
Mixed Orphans	花幺九	4	Hand containing Pongs/Kongs of Ones, Nines, or Honor Tiles only
	----
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 [a]	小四喜; siu2 sei3 hei2	6 (6+3 faan 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
	----
Seven Pairs (played by some variants)[2]	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. In some variants, Kongs are not permitted in this hand.
	------

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Certain high-scoring hands are "capped hands" that are ineligible for additional faan awarded based on winds, dragons, or flowers.^[3] Even if the capped hand satifies other hand criteria (e.g., all honor tiles must also be all triplets), the faan from the other criteria are not counted. If a winning hand satisfies more than one capped hand criterion (e.g., great winds where the pair is dragons, therefore also an all honor tile hand), only the criterion with the highest score applies.

More information All Honor Tiles, Self Triplets ...

Capped Hands

All Honor Tiles	字一色; zi6 jat1 sik1	10	All honor tiles
	----
Self Triplets	四暗刻; sei3 am3 hak1 坎坎糊; kaan2 kaan2 wu2	10	Every meld is either a concealed (unmelded) Pong or concealed Kong.[b] The bonus can only be won either (a) by self-pick or (b) from a discarded winning tile that forms the pair, i.e., the discard cannot form the melds.
Orphans	么九; jiu1 gau2	10	Hand containing Pongs/Kongs of Ones and Nines only
	----
Nine Gates[c]	九子連環; gau2 zi2 lin4 waan4	10	Hand in any one suit consisting of 1112345678999, must be totally concealed.
	-- + any tile in the set
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	Hand containing four Kongs

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Notes

1. [a]

   For Small Winds, some variations have a further restriction with the prevailing wind or the seat wind disallowed as the pair.
2. [b]

   In Hong Kong Mahjong, if a player draws all four tiles, they can declare a concealed Kong meld. All tiles face down. The meld cannot be undone. The player replenishes a tile from the end of wall.
3. [c]

   It is called nine gates because there are 9 tiles that the player can win with. It is required that the hand be totally concealed (i.e. the only tile that can be taken from a discard is the extra tile in the set). This animation shows how any one tile in the same suit will create a winning hand:

Wind and Dragon Faan

More information English, Cantonese ...

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

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

Flower Faan

Some criteria for faan are based on "bonus tiles" - the flowers and the seasons (which are also collectively called flowers). See the following table:

More information English, Cantonese ...

English	Cantonese	Fān	Description	Example
No Flowers or Seasons	无花 (mou4 faa1)	1	No flower or season bonus tiles
Flower of own Wind	正花 (zing3 faa1)	1	A flower of the winner's seat wind	/ / /
Season of own Wind	正花 (zing3 faa1)	1	A season of the winner's seat wind	/ / /
All Flowers	一台花 (jat1 toi4 faa1)	2	All flower bonus tiles
All Seasons	一台花 (jat1 toi4 faa1)	2	All season bonus tiles

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Under certain custom rules, a player who draws 7 bonus tiles can declare a win worth 3 faan on the spot; a player who draws all 8 bonus tiles can declare a win worth 13 faan.^[4]

As mentioned in the #Overview of scoring, the point translation function is the function used to convert the number of faan to score.

The point translation function is typically an exponential function. The function itself is subject to variation. In most variations this is 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.

The following is a list of 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.

• Scoring in Mahjong