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

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 is 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").

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).

It is generally unknown what happens should 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. 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.

Winning criteria

A common group of criteria is conditions relating to how the winning player obtains the winning tile. For example, a player winning by drawing the winning tile typically earns points while a player winning by discard typically does not. These are often probabilistic in nature. The following is a common list of criteria associated with the conditions of winning:

* 自摸 (zì mō) - Known in English typically as a "self-pick", the winning tile must be drawn (rather than discarded).
* 獨聽 (dú tīng) - 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 (eg. 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.
* 搶槓 (qiǎng gàng) - Known in English typically as "robbing the Kong", the winning tile was also claimed by another player for a Kong. As claiming a tile for the win takes precedence over claiming a tile for a Kong, the player who claimed the winning tile for a Kong is said to be robbed.
* 槓上花 (gàng shàng huā) - Known in English typically as the "extra tile win", this occurs if the player wins off the extra tile drawn from replacing a flower or a Kong. In such a case, "self-pick" is awarded plus an extra point to denote the "self-pick" from the dead wall.
* 槓上槓 (gàng shàng gàng) - Known in English typlically as the "Kong on Kong win", this is similar to the "extra tile win", except that the tile that was used to make the Kong was itself an extra tile from declaring a Kong. Like the above case, whether "self-pick" is awarded is based on how the first Kong (the Kong not formed from an extra tile) is obtained. Variations may have further levels of extra-tile victory, and some variations may have similar criteria for extra tiles drawn from flower tiles.
* 天胡 (tiān hú) - Known in English typically as the "heavenly hand" or the "heavenly victory", this occurs when the winner, as the dealer, wins the round on the first turn (ie. with the tiles given after dealing and - in all versions except American - flower replacement). Because of its rarity, this criterion is often the one worth the greatest number of points.
* 地胡 (dì hú) - Known in English typically as the "earthly hand" or the "earthly victory", this occurs when a non-dealer wins off the dealer's first discard. This is typically the rarest and most valuable criterion for non-dealers. In Japanese variations, "chi hō" may also refer to a non-dealer winning on their first turn.
* 屁胡 (pì hú) - Also known in some circles as 推倒胡 (tuī dǎo hú) or 雞胡 (ji hú; "Chicken Hand"), this is used to describe a winning hand worth zero "fān," or no points.
* 詐胡 (zhà hú) - Known in English literally as a "trick hand", used to describe a "false alarm" when a player claims to have won but in fact has not.

Meld criteria

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.

Criteria may be formed from the presence or absence of certain groups or tiles in the winning hand:

* 混一色 - (3 "fān" ) - Known in English as the "mixed one suit hand", the winning hand must have only honor tiles and tiles from one suit.

* 清一色 (7 "fān" ) - Known in English as the "pure one suit hand", the winning hand must be either all honor tiles, or tiles all of the same suit. This is traditionally the highest value non-special hand, although newer variations have subsets that are of a higher point value. Some variations splinter hands of all honor tiles into a separate rule (below).

* 字一色 (8 "fān" ) - Known in English as the "pure honor hand", the winning hand must consist of all honor tiles.

Or the methods in which melds are formed:

* 門清 (1 "fān") - Known in English as a "pure hand" or a "purely concealed hand", this occurs if the winner wins without taking a discarded tile to form a meld. 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".

The most common criteria, however, are criteria based on the presence of certain melds, or certain combinations of melds:

* 門風 (1 "fān" x3) - The winning hand contains a meld of the winner's seat wind.

* 圈風 (1 "fān" x3) - The winning hand contains a meld of the prevailing wind. 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.

* 紅中 (1 "fān" ) - The winning hand contains a meld of the red dragon.

* 青發 (1 "fān" ) - The winning hand contains a meld of the green dragon.

* 白板 (1 "fān" ) - The winning hand contains a meld of the white dragon.

* 平胡 (1 "fān" )) - Known in English as the "sequence hand", this occurs when every meld is a Chow.

* 對對胡 (3 "fan" ) - Known in English as the "triplets hand", this occurs when every meld in the winning hand is either a Pong or Kong. Variations allowing for Joker tiles will also permit melds of five or more, but disallow an all-Joker meld.

Special hands

Special hands are either standard hands which are typically improbable to obtain, or are a predefined set of tiles that do not form a standard hand. In many cases, point values for special hands are arbitrarily assigned. In nonstandard hands, point assignment is arbitrary by necessity, while in standard special hands, the points given are often greater than the sum of the parts (for example, having one meld of each dragon is worth more than three times the value of a single dragon). These special hands are also part of the scoring criteria, thus more points can be obtained from criteria that are probabilistic in nature.

Standard special hands

Standard special hands are typical in their composition (as they are standard hands), but are regarded as special thanks to their contents (which are typically intersections of many criteria). Because of this, it is possible to obtain a hand that fulfills two or more "special criteria", or a combination of special and nonspecial criteria.

* 小三元 (3 "fān" ) - Known in English as the "three lesser scholars", the winning hand contains melds in two of the three dragons and a pair of the third dragon.

* 大三元 (6 "fān" ) - Known in English as the "three great scholars", the winning hand contains melds in all three dragons.

* 小四喜 (8 "fān" ) - Known in English as the "four small blessings", the winning hand contains melds in three of the four winds and a pair of the fourth wind. Some variations have a further restriction with the prevailing wind or the seat wind disallowed as the pair.

* 大四喜 (8 "fān" ) - Known in English as the "four great blessings", the winning hand contains melds in all four winds.

* 九蓮寶燈 ( + any tile in the same set) - A "Nine Gates hand" is one where a player has three 1s, a 2-8, and three 9s all in the same suit. The 14th tile may be any tile from the same suit. 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).

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

* 十三么 (13 "fān" + any tile in the set) - Known in English as the "thirteen terminal hand" or the "thirteen wonders", 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 maximum-point 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 (ie. 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.

ee also

*Scoring in Mahjong