Scoring in Mahjong
From Wikipedia, the free encyclopedia
Scoring in Mahjong, a gambling game for four players that originated in China, involves points, with a monetary value for points agreed upon by 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 greatest 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 greatly divergent scoring rules (as well as greatly divergent gameplay rules).
Because of the large differences between the various systems of scoring (especially for Chinese variants), groups of players will often need to agree on particular scoring rules before a game, in order to eliminate possible disputes during the game. Like with gameplay, many attempts have been made to create an international standard of scoring, but most are not widely accepted.
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[edit] 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. Chinese variants will use the term 番 (pinyin: fān). Taiwanese mahjong, however, uses the term 台 (pinyin: tái) along with a linear scoring system.
Because points and score relate to 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. 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.
[edit] Scoring rules
[edit] Chinese classical scoring
Scoring in the Chinese Classical system, from which the Babcock system is derived, is a "point-and-double" system, where actual score is collected, and doubled based on the number of points (or doubles) a hand earns (thus, the point translation function is an exponential one). At the end of each round, points are tallied up for all individuals (not only the player with the winning hand) and doubled if necessary. Afterwards, each losing player pays the winner the difference in scores. Traditionally, the dealer must pay or receive double such a difference, but many players play with the payment variations listed above.
Many variations of such a scoring system exist: for example, variations exist where losing players may "gain back" lost score from other losing players with smaller point totals. In some variations, only the winner receives doubles, to prevent negative differences (such as when a losing player is aiming for a high scoring hand and the winning hand has a low score).
[edit] Hong Kong scoring
The traditional Hong Kong scoring system, or the Cantonese scoring system, is widely considered to be the most popular scoring systems, as scoring tends to be low due to the low amount of 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 (i.e., 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.
[edit] Taiwanese scoring
Unlike Hong Kong scoring, Taiwanese scoring employs a linear relationship between tai (points in the Taiwanese system) and scoring units. When a win occurs in Taiwanese Mahjong, the number of tai of the winning hand is multiplied by a factor and then added to a base score. For example, if the base and factor are 3 and 2, respectively, then the loser to a 5-tai hand pays the winner 13 scoring units (3+2x5).
The Taiwanese system follows a different payment procedure from the standard procedure mentioned earlier:
- In the case where a player wins by a discard (a player picks off an opponent), the player who performs the discard pays each winner (there may be more than one).
- In the case where a player wins by a draw (a player wins by self-pick), each player except the winner pays the winner.
When the dealer is involved in either the winning or losing side of a hand, extra tai (one plus twice the number of times the dealer has consecutively retained dealership) are added to the dealer's winnings or losses.
[edit] Shanghai scoring
In contrast, the scoring system used in the Shanghai variant is high, due to the diverse number of scoring criteria and inflated values for rarer hands such as the thirteen terminals. Because of the inflated point values, there is generally a minimum point value in the Shanghai variant.
[edit] Singaporean scoring
Singaporean scoring is similar to that of the Chinese Classical system, but accounts for the different set of tiles used therein. Again, standard payment variations apply, although variants exist where the dealer must also pay and receive double.
[edit] Japanese scoring
The Japanese scoring system is the system that is found in many Mahjong video games. In this variation, each player starts with anywhere between 20000 to 30000 score units, which are typically represented by a series of bars resembling elongated Chinese dominoes, in four denominations: 10000, 5000, 1000, and 100. Should a player lose all their score units, the game immediately ends, with the player furthest ahead in points declared the winner.
[edit] American scoring
When the Babcock version of mahjong was becoming popular in the 1920s with American players, a side effect of the Babcock scoring system was that many players frequently sought after limit hands rather than hands of smaller value. Because of this, the common hands were eventually abandoned, and the only way one could win was to match a hand from a list of hands.
Today, in the American variations, players use a card that define a small set of hands that are the only valid winning hands, with a point value given for each hand. This system is used by the two major governing bodies of Mahjong in the United States, the National Mah Jongg League and the American Mah-Jongg Association, with new cards that define the valid winning hands released annually.
Typically, each card contains scoring criteria that makes references to the year the scoring cards are released. For example, the 1985 scoring hand will have hands containing "melds" of a one, nine, eight, and five of a certain suit.
[edit] Scoring limits
Some variations may impose a scoring limit - a maximum to the number of points for a given hand. In many cases where limits exist, there may be either multiple limits, or ways to obtain multiples of a limit. In many cases where limits exist, the typical point translation function is exponential, where a constant score is assigned to points up to the first limit, and afterwards increases (often doubles) as further limits are reached. The Taiwanese system does not employ scoring limits.
A scoring limit may be more of a gambling incentive: for example, if six and nine points were scoring limits, a seven- or eight-point hand would be worth the same as a six-point hand, which may be an incentive for players to go for nine-point hands.
[edit] High-risk discards
Many variations may also impose penalties for discards that are considered to be "high risk" when the size of the wall is winding down. If a player wins from a high-risk discard, the player who discards the winning tile often must suffer an additional scoring penalty. It is interesting to note that the winner is not usually affected by a high-risk discard, and frequently the other two losing players are "off the hook". Typical high-risk scenarios include scenarios where a player is threatening to win with a (necessarily highly exposed) high-point hand.