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, 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 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.
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. In many cases, there exist other modifiers to the score. A common set of modifiers include:
- In the case where a player wins by a discard, the player who performs the discard pays double
- In the case where a player wins by a draw, every losing player pays double.
- In the case where a player wins from a high-risk scenario, the player who performs the discard pays for the other two losing players.
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 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 - 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. 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 - Also known in some circles as 推倒胡 or 雞胡, this is used to describe a winning hand worth zero fān, or no points.
- 詐糊 - 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 - Winning off another player's discard.
- 叫糊 - A "ready" or "waiting" hand, one tile away from winning.
Non-standard special 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, 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 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
;Notes
| English | Cantonese | Fān | Description | Example |
| Seat Wind | 門風 | 1 | A meld of the winner's seat wind | / / / |
| Prevailing Wind | 圈風 | 1 | A meld of the prevailing wind | / / / |
| Red Dragon | 紅中 | 1 | A meld of the red dragon | |
| Green Dragon | 發財 | 1 | A meld of the green dragon | |
| White Dragon | 白板 | 1 | A meld of the white dragon | |
| Mixed Orphans | 混么九 | 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.
| English | Cantonese | Additional Fān | Description | Example |
| Self-Pick | 自摸 | 1 | The winning tile is from the wall | - |
| Win from Wall | 門前清 | 1 | The winner did not form a meld by discard | - |
| Robbing Kong | 搶槓 | 1 | The winning tile is obtained from someone calling a Kong | - |
| Win by Last Catch | 海底撈月 | 1 | The winning tile is either the last tile from the wall or the last discard | - |
| Win by Kong | 槓上開花 | 2 | The winning tile is from a replacement tile due to a Kong or a Bonus Tile | - |
| Win by Double-Kong | 槓上槓 | 9 | 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 | Limit | East wins with initial hand | - |
| Earthly Hand | 地糊 | Limit | Non-East player wins on East's first discard | - |
- It is possible to obtain the maximum Fan from only bonuses. 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
- 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 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. 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 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 is imposed, as lower scores are often considered to be game spoilers.
Simplified faan point-base point table
| Faan points | Base points |
| 3 | 1 |
| 4 | 2 |
| 5 | 2 |
| 6 | 2 |
| 7 | 4 |
| 8 | 4 |
| 9 | 4 |
| 10+ | 8 |
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 amount 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 amount 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.
Examples
| Player | base points |
| East | 1 x2 x2 = -4 |
| South | 1 x2 = -2 |
| West | 4 + 2 2 = +8 |
| North | 1 x2 = -2 |
| Player | base points |
| East | 16 + 32 + 16 = +64 |
| South | 8 x2 = -16 |
| West | 8 x2 x2 = -32 |
| North | 8 x2 = -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 the losers pay the winner. The following is the Old Hong Kong simplified table, for other tables see Hong Kong Mahjong scoring rules.| 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 amount 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 amount 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.
Examples
| Player | base points |
| East | 16 x2 x2 = -64 |
| South | 16 x2 = -32 |
| West | 4 + 2 + 2 = +128 |
| North | 1 x2 = -32 |
| Player | base points |
| East | 32 x2 = -64 |
| South | 32 x2 = -64 |
| West | 32 = -32 |
| North | 64 + 64 + 32 = +160 |
| Player | base points |
| East | 128 + 256 + 128 = +512 |
| South | 64 x2 = -128 |
| West | 64 x2 x2 = -256 |
| North | 64 x2 = -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 the losers pay the winner. The following is the Old Hong Kong simplified table, for other tables see Hong Kong Mahjong scoring rules.| Faan points | Base points |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 48 |
| 7 | 64 |
| 8 | 96 |
| 9 | 128 |
| 10+ | 256 |
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 amount 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 amount 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.
Examples
| Player | base points |
| East | 16 x2 x2 = -64 |
| South | 16 x2 = -32 |
| West | 4 + 2 + 2 = +128 |
| North | 1 x2 = -32 |
| Player | base points |
| East | 48 x2 x2 = -192 |
| South | 48 x2 = -96 |
| West | 192 + 96 + 96 = +384 |
| North | 48 x2 = -96 |
| Player | base points |
| East | 512 + 1024 + 512 = +2048 |
| South | 256 x2 = -512 |
| West | 256 x2 x2 = -1024 |
| North | 256 x2 = -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 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" tile when there are 5 or less tiles left in the wall, allowing winner to go out | |
| Maximum Penalty |