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.

Contents

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 / 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:

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.

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:

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:

Or the methods in which melds are formed:

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

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.

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

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:

See also