Hong Kong mahjong scoring rules
 | This article needs additional citations for verification. (December 2007) |
Hong Kong mahjong scoring rules are the rules used for scoring in mahjong, specifically the rules common in Hong Kong and some areas in Guangdong.
Overview of scoring
[edit]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.
Non-standard special hands
[edit]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.
Criteria for scoring faan
[edit]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. 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 faan 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 faan). Also note that generally speaking in Hong Kong mahjong, 13 faan is considered the absolute limit for faan.
The tables following list common criteria for faan based on the contents of the hand.
| English | Cantonese | Faan | 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) [1] | 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 [a] | 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[b] | 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
- ^ For Small Winds, some variations have a further restriction with the prevailing wind or the seat wind disallowed as the pair.
- ^ 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:
| 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.
Other scoring criteria are based on the winning condition - how the winner won.
| 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) only from winning condition criteria. 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.
Some criteria for faan are based on "bonus tiles" - the flowers and the seasons. See the following table:
| 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
[edit] | This section may be confusing or unclear to readers. In particular, in the subsections of scoring tables, at the very least prior to my (Eletroboss') edit in July 2024, it was very unclear what each of these tables were referring to, due to contradictory page titles, subsection names, and each table having a paragraph beforehand explaining that they were the "Simplified Old Hong Kong scoring rules" and to "see Hong Kong Mahjong Scoring Rules for more information" (paraphrased). As this article is Hong Kong Mahjong Scoring Rules, and they are not all the same, these paragraphs have been removed. The contradictory table label has been marked as such, but the table labels themselves have not been changed. (July 2024) |
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.
Simplified faan point-base point table
[edit]| 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 they 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
[edit]| 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 |
| 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 |
| 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 they win or lose.
Traditional faan point-base point table
[edit]| 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 section may be confusing or unclear to readers. In particular, the table contains unexplained arithmetic. (July 2024) |
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
[edit]| 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 |
| 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 |
| 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 Faan point-base point table
[edit]| 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
[edit]| 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 |
| 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 |
| 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
[edit]| 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 |
Hand progress terminology
[edit]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.