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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 general rule for 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.
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.
聽糊 (teng1 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 十三么 (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 victory above, even if the winning hand is otherwise scoreless), at least one point must be from this set of criteria.

Scoring based on type of hand
English	Cantonese	Fān	Description
Sequence Hand	平糊 (ping⁴ wu^4*2	1	Every meld is a Chow
Triplets Hand	對對糊 (deoi³ deoi³ wu^4*2)	3	Every meld is either a Pong or Kong
Mix Pure Hand	混一色 (wan⁶ jat¹ sik¹)	3	Only honor tiles and tiles from one suit
Pure Hand	清一色 (cing¹ jat¹ sik¹)	7	All tiles from one suit
Pure Honor Hand	字一色 (zi⁶ jat¹ sik¹)	Limit	All honor tiles
Seven Pairs	七對子 (cat1 deoi3 zi2) / 七姊妹	4	Hand consisting of only pairs
Three Lesser Scholars	小三元 (siu2 saam1 jyun4)	3	Melds of 2 dragons and a pair of the 3rd dragon
Three Great Scholars	大三元 (daai6 saam1 jyun4)	6	Melds of all 3 dragons
Four Small Blessings	小四喜 (siu2 sei3 hei2)	8	Melds of 3 winds and a pair of the 4th wind
Four Large Blessings	大四喜 (daai6 sei3 hei2)	10	Melds of all 4 winds
All Kongs	十八羅漢 / 四槓子 / 槓槓和	Limit	Hand containing four Kongs
Hidden Treasure	四暗刻	Limit	Hand containing four concealed (unmelded) Pongs, won by Self-Pick
Jade Dragon	翡翠龍	Limit	Hand containing Pongs/Kongs of the Stick suit only and Pong/Kong of the Green Dragon
Ruby Dragon	紅寶龍	Limit	Hand containing Pongs/Kongs of the Characters suit only and Pong/Kong of the Red Dragon
Pearl Dragon	珍珠龍	Limit	Hand containing Pongs/Kongs of the Dots suit only and Pong/Kong of the White Dragon
All Terminal	清么九	Limit	Hand containing Pongs/Kongs of Ones and Nines only
Nine Gates Hand	九子連環	Limit	Hand in any one suit consisting of 1112345678999

Note: For Four Small Blessings, some variations have a further restriction with the prevailing wind or the seat wind disallowed as the pair.

Note: A Nine Gates Hand. It is called nine gates because there are 9 tiles that the player can win with. In some games it is required that the hand be totally concealed (i.e. the three 1s and 9s must be drawn from the wall and not taken from a discard).

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 (gyun6 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

In some variations, a double wind, where a certain wind is both the winner's seat wind and the prevailing wind, may result in a point bonus.

Scoring based on winning condition
English	Cantonese	Fān	Description
Self-Draw	自摸 (zi⁶ mo²)	1	The winning tile is from the wall
Concealed Hand	門前清 (mun⁴ cin⁴ cing¹)	1	The winner did not form a meld by discard
Robbing the Kong	搶槓 (coeng² gong³)	1	The winning tile is obtained from someone calling a Kong
Win on Last Tile	海底撈月 (hoi² dai² lou⁴ jyut⁶)	1	The winning tile is either the last tile from the wall or the last discard
Win on Replacement Tile	槓上開花 (gong³ soeng⁵ hoi¹faa¹)	1	The winning tile is from a replacement tile due to a Kong or a Bonus Tile
Win on double Replacement Tile	槓上槓 (gong³ soeng⁵ gong³)	1	Similar to 'Win on Replacement Tile', except that the tile used to make the Kong was itself an extra tile from declaring a Kong
Heavenly Hand	天糊 (tin¹ wu^4*2)	Limit	East wins with initial hand
Earthly Hand	地糊 (dei⁶ wu^4*2)	Limit	Non-East player wins on East's first discard

It is possible to obtain all 3 bonus Fan. For example, a player draws the second last tile from the wall, declares a Kong and win 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.

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 to 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.

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

Penalties

English	Cantonese	Description
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

Scoring in Mahjong

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