Scoring in Mahjong - Definition

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 (皮胡 pi hu, sometimes 雞胡 ji hu) 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 agree on particular scoring rules before a game. Like with gameplay, many attempts have been made to create an international standard of scoring, but most are not widely accepted. In this article, the general mechanics of scoring and the specific mechanics of the Hong Kong and the Singapore styles will be covered in detail.

Criteria

大三元 - the three great scholars, where the winning hand contains melds of all three dragons.

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 翻 (pinyin: fān) while Taiwanese variants will use 台 (pinyin: tāi).

Because of the fact that 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.

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 (pinyin:zi mo, Japanese tsumo) - Known in English typically as a self-pick, the winning tile must be drawn (rather than discarded).
• 立直 (li zhi, Japanese riichi) - Known in English as a reach, the winning player wins after declaring riichi.
• 報聽 (bao ting) - The winning player (necessarily a non-dealer) wins after declaring riichi before any tiles are played.
• 獨聽 (du ting) - 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 (qiang gang, Japanese chan kan) - 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.
• 槓上開花 (gang shang kai hua) - Known in English typically as the extra tile win, this occurs if the player wins off of the extra tile drawn from declaring a Kong. In such a case, self-pick is awarded on the basis of how the Kong was obtained - an exposed Kong declaration would not earn the winner points for the self-pick.
• 槓上槓 (gang shang gang) - 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 (tian hu, Japanese 天和 ten hō) - 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 (di hu, Japanese 地和 chi hō) - Known in English typically as the earthly hand or the earthly victory, this occurs when a non-dealer wins off of 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.

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.

清一色 - the pure one suit hand, where the winning hand consists of tiles only of one suit, or only of honor tiles.

清么九 - the pure terminals hand, where the winning hand consists entirely of terminal tiles.

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

• 缺五 (que wu) - The winning hand does not contain a five.
• 斷么 (duan yao) - The winning hand does not contain terminal or honor tiles.
• 混么九 (hun yao jiu, Japanese 混老頭 hon rō tō) - Known in English as the mixed terminals hand, the winning hand must have only terminal or honor tiles.
• 清么九 (qing yao jiu, Japanese 清老頭 chin rō tō) - Known in English as the pure terminals hand, the winning hand must have only terminal tiles.
• 混一色 (hun yi se, sometimes 湊一色 cou yi se, Japanese hon'ichi) - Known in English as the mixed one suit hand, the winning hand must have only honor tiles and tiles from one suit. The version introduced by Babcock to America in the 1920s had this as a minimum winning hand requirement, along with a maximum of one Chow.
• 清一色 (qing yi se Japanese chin'ichi) - 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 (zi yi se) - Known in English as the pure honor hand, the winning hand must consist of all honor tiles.

Or the method in which melds are formed:

• 門清 (men qing) - 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.
• 半求 (ban qiu) - Known in English as a half-begging hand, the winning hand is one where every meld is formed from a discarded tile, but the winning tile was drawn.
• 全求 (quan qiu) - Identical to the half-begging hand, except that the winning tile is also discarded.

對對胡 - the triplets hand, a common hand in Mahjong. In variations where minimum point values exist, the minimum is often the point value for this hand.

一條龍 - the complete sequence, where the winning hand consists of at least three Chows forming a run from one to nine, all in the same suit.

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

• 將 (jiang) - This occurs if there is a pair of twos, fives, or eights as the pair in the winning hand.
• 門風 (men feng) - The winning hand contains a meld of the winner's seat wind.
• 圈風 (quan feng) - 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 (hong zhong) - The winning hand contains a meld of the red dragon.
• 青發 (qing fa) - The winning hand contains a meld of the green dragon.
• 白板 (bai ban) - The winning hand contains a meld of the white dragon.
• 五門齊 (wu men qi) - Known in English typically as an all-category hand, the winning hand uses all five kinds of tiles (the three suits, the winds, and the dragons).
• 平胡 (ping hu) - Known in English as the sequence hand, this occurs when every meld is a Chow. Some variations make further restrictions in that the hand must be impure (ie. at least one meld is formed by discard), won by a discard, of multiple suits, or the pair not consisting of honor tiles.
• 姐妹花 (jie mei hua) - Known in English as the sister sequences, the winning hand contains three chows of the same three ranks, but of three different suits. (For example, a chow of 4, 5, and 6 of all three suits.)
• 姐妹碰 (jie mei peng) - Known in English as the sister triplets, the winning hand contains three pongs of the same rank, but of three different suits. Typically, this will also apply if any or all of the three melds are kongs.
• 一條龍 (yi tiao long, Japanese 一気通貫 ikki tsūkan) - Known in English as the complete sequence, the winning hand must consist of at least three Chows where the Chows form all of the numbers from one to nine in a single suit.
• 兩條龍 (liang tiao long) - Known in English as two complete sequences, the winning hand is the same as the complete sequence, except that the fourth meld is a duplicate Chow of the other three. Some variations have the further restriction that the fourth Chow is a 4-5-6 Chow.
• 對對胡 (dui dui hu, Japanese 対々和 toitoi hō) - 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.
• 將將碰 (jiang jian peng) - The winning hand is a triplets hand, but with the further restriction that each meld (and the pair) must be either of a 2, 5, or 8.

Special Hands

九蓮寶燈 - the nine gates, an entirely concealed ready hand consisting of three ones, three nines, and one each from two to eight, all in the same suit. Any suited tile will create a complete standard hand.

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 arbitary 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

十八羅漢 - the four Kongs hand or eighteen perfects, named for the 18 tiles(four Kongs), the maximum under 13-tile variants, needed in order to win with this hand.

大四喜 - the four great blessings, where the winning hand contains a meld of each wind.

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 (xiao san yuan, Japanese shō sangen) - 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 (da san yuan, Japanese dai sangen) - Known in English as the three great scholars, the winning hand contains melds in all three dragons.
• 小四喜 (xiao si xi, Japanese shō sūshī) - 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 (da si xi, Japanese dai sūshī) - Known in English as the four great blessings, the winning hand contains melds in all four winds.
• 九蓮寶燈 (jiu lian bao deng, alternately 九子連環 jiu zhi lian huan Cantonese gaau zhi lin wan) - Known in English as the nine gates, this occurs in 13-tile variants when the ready hand consists of three ones, three nines, and one each from two to eight, all in the same suit, all concealed. Careful analysis of this ready hand shows that any suited tile will always give a standard winning hand. Some variations, most notably Japanese variations, will allow any permutation of the 14 tiles as constructed above (eg. two ones, two twos, three nines, and one each from three to eight, and waiting for a one). Note that this hand is not considered special if some or all of the hand is exposed.
• 十八羅漢 (shi ba luo han, Japanese 四槓子 suu kantsu) - Known in English as the four Kongs hand or eighteen perfects, this occurs in 13-tile variants when the winning hand consists of four Kongs. There is typically no equivalent in 16-tile variants (ie. a hand with five Kongs), as these variants either employ the abortive draw where the game is drawn after the fourth Kong (or fifth, if the first four were made by the same player), or the hand is not considered special.

Nonstandard Special Hands

十三么 - the thirteen terminal hand, touted as the most difficult hand to obtain in mahjong, consists of one each of ones, nines, winds, and dragons, and a 14th tile that matches any of the other thirteen.

In addition to the standard hand where four melds (five in 16-tile variants) and a pair are required to win, there are also nonstandard hands that are accepted. In other words, the definition of these hands act as scoring criteria themselves. When viewed in this manner, scoring in American mahjong is a set of scoring criteria where there are little to no standard criteria and the majority of criteria are special hands.

In non-American variations, there are generally two nonstandard special hands that are accepted:

• 七對子 (qi dui zi, Japanese 七対子 chi to itsu) - Known in English as the seven pairs, this occurs in 13-tile variants when the winning hand contains seven pairs. Jiang may be scored if any of the seven pairs contains a two, five, or eight. The 16-tile equivalent to this is 八對半 (ba dui ban), or eight and a half pairs, where the winning hand consists of eight pairs and a 17th tile that matches any of the eight paired tiles (effectively, seven pairs and a concealed Pong).
• 十三么 (pinyin: shi san yao, Japanese 国士無双 kokushimusō) - 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 that matches any of the other 13. 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.

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.

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.

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.

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).

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 (ie. 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.

The 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 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 the various mahjong parlors in Hong Kong under British rule, the translation function is constant. This is because gambling, with the exception of horse racing, was forbidden under British rule, and thus the constant function was used as "prize money". These gaming parlors died out over time because plastic mahjong sets became so cheap that almost every family could afford a set. Besides the fun of mahjong is to aim for the high scoring hands and a flat rate scoring practically ruins the game when the challenge is eliminated. This scoring system is no longer in use in Hong Kong.
• 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.

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.

Singapore Scoring

Singapore 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.

The Point Translation Function

The point translation function in Singapore scoring is exponential, with one unit of score given to a zero-point hand. There is a maximum scoring limit of five points. Points are given out as follows:

• A meld of any dragon scores one point.
• A meld of the seat wind or the prevailing wind scores one point.
• Each animal tile collected scores one point. One more point (for a total of five) is awarded if all four animals are collected.
• Each flower tile that matches a player's seat wind scores one point.
• A complete group of flower tiles scores one point.
• A mixed terminals hand scores one point.
• An extra tile win, either off a Kong or off of a Flower tile, scores one point.
• Robbing the Kong scores one point.
• Winning on the last available tile scores one point.
• A sequence hand scores one point, unless no flower tiles have been collected, when it scores four points.
• A triplets hand or a mixed one suit hand scores two points.
• The three lesser scholars hand scores three points.
• A pure one suit hand and the four lesser blessings score four points.
• Any winning hand where seven flower tiles have been collected scores five points.
• A pure terminals hand, and the three great scholars, four great blessings, and thirteen terminals score five points.

Instant Payment

In Singapore scoring, scores may be paid out immediately when performed. That is, a player may earn points during the game that are kept regardless of whether the hand is won or lost. The points are paid from each of the other three players (eg. an instant payout of two points results in the player who receives the instant payment the equivalent of six points). These points, as they are given out during the course of the game, and not at the end of each round, do not contribute to any scoring limit.

• Exposing a Kong will pays out two points.
• Obtaining both the Red and Black flowers that match the Player's seat wind pays out two points, four if both tiles are in a player's initial 13 tiles (before Flower replacement).
• Obtaining the cat and mouse animal tiles, or the centipede and chicken animal tiles, pays out two points, four if the two animal tiles are in a player's initial 13 tiles (before Flower replacement).
• Obtaining an entire group of flower tiles pays out four points.

Paying For All Players

High-risk discards are also an element of Singapore-style scoring, with the player making such a discard paying for the other two losing players, in addition to their own (the other two losing players are vindicated - they do not pay anyone anything). High-risk scenarios only occur when a player is visibly near victory, with that player winning because of a high-risk discard.

The following is a typical list of high-risk scenarios:

• Dragon Tile Set Scenario - Player A has two Dragon Pongs or Kongs exposed. Player B discards a third Dragon and the Player A is able to Pong/Kong it, forming a third set of Dragons. If Player A wins the game with Player B's discard or his own tile, Player B pays all winnings.

• Wind Tile Set Scenario - Same as Dragon Tile Set Scenario, but requires three exposed Wind sets and completing a fourth with a discard.

• Double Limit Scenario - Player A has the maximum number of doubles (typically 5) exposed. Player B discards a Dragon tile, a Prevailing Wind or a Player Game Wind that is taken by A. If Player A wins the game with Player B's discard or his own tile, Player B pays all winnings.

• Full Color Scenario - Player A has 3 or 4 sets of the same suit (bamboo, number, character) exposed. If Player B discards a tile of the same suit and Player A uses it to win, Player B pays all winnings.

• Fresh Discard Scenario - There are less than 7 tiles remaining in the wall. If Player B discards a fresh tile (one not previously discarded) and Player A wins with it, Player B pays all winnings.

Japanese Scoring

Main article: Japanese Mahjong Scoring Rule

The Japanese scoring system is the system that is found in many Mahjong video games, many of which cater to male audiences and feature pictures of women in various states of undress after a round is won. 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, 10000, and 100. Should a player lose all their score units, the game immediately ends, with the player furthest ahead in points declared the winner.

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.