Scoring in Mahjong, a game for four players that originated in China, involves the players obtaining points for their hand of tiles, then paying each other based on the differences in their score and who obtained mahjong (won the hand). The points are given a monetary value agreed by the players. Although in many variations scoreless hands (推倒胡 tui dao hu in Mandarin, 雞糊 gai wu in Cantonese) are possible, many require that hands be of some point value in order to win the round.
While the basic gameplay is more or less the same throughout mahjong, the most significant divergence between variations lies in the scoring systems. Like the gameplay, there is a generalized system of scoring, based on the method of winning and the winning hand, from which Chinese and Japanese (among notable systems) base their roots. American mahjong generally has wildly divergent scoring rules (as well
Because of the large differences between the various scoring systems (especially for Chinese variants), groups of players will often need to agree on particular scoring rules before a game to eliminate possible disputes during the game. As with the gameplay, many attempts have been made to create an international scoring standard, but most are not widely accepted.
Criteria
Points are obtained for a hand by matching it against various criteria, with different criteria scoring different values. Criteria can include particular melds or other tiles held, how the (winning) hand was completed, possession of various special combinations, etc. 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 paid between players.
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. (This is not to be confused with the doubling applied to the basic point score in some variations.) Chinese variants will use the term 番 (pinyin: fan). Taiwanese mahjong, however, uses the term 台 (pinyin: tái) along with a linear scoring system.
Points and score relate to two distinct concepts - based on the points obtained in a round, and other factors, players pay each other money. Chips or similar tokens can be used instead, or a score can simply be calculated.
Each player begins the game with the same score. When settling up, in many cases only the winner is paid with the winner's gain being deducted from the three losers' scores (that is, the losers pay the winner). However, payment between players can be arranged in other ways. 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).
If playing with chips, there is no universal rule for the situation when a player runs out. 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 chips continues to play without risk of further losses. Alternatively, the loser may pay cash to buy back chips from the winners and the game continues.
The rules mentioned below are by no means exhaustive or common to every variation, but are common to many 13-tile and 16-tile variations.
Scoring rules
Hong Kong scoring
In the traditional Hong Kong scoring system or the Cantonese scoring system, scoring tends to be low due to the few criteria used.
The general scoring modifiers apply (see above), with the point translation function being a piecewise function: a constant amount is given for scoreless hands, and the score is doubled for each point (that is, an exponential function). Because zero-point hands are common, players often play with the additional restriction that a winning hand must be of some point value, often anywhere between one and five points, with three being the most common.