Saturday, August 20, 2011

Rules of Singapore Style Mahjong: Scoring

Scoring in mahjong is a crucial part of the flavours of the different regional variants. Since the gameplay (i.e. the mechanism of the game) is largely identical across variants of mahjong, the differentiation between variants lies in the different ways scoring is done, which in turn motivates different strategies and approaches to playing mahjong.

Scoring is fundamentally about assigning different values to different ways of winning, and the values are usually correlated to the difficulty of achieving such ways of winning. More difficult methods have higher value and less difficult methods have lower value. So, the mahjong player has to decide how he wants to win his hand, in accordance with the score he wants to achieve.

The scoring system of Singapore Style mahjong is largely inherited from Chinese Classical scoring. However, there have been many changes, the most significant one being the removal of calculating basic points from the possession of certain tile combinations and the replacement with a fixed base stake.

In Singapore Style mahjong, points can be won from opponents by winning a hand with one or more scoring elements or by achieving certain tile combinations. Scoring elements (番种 fānzhǒng) are the various tile combinations, patterns, and winning situations that can give value to a winning hand. This value is expressed in the form of doubles (台 tái or 番 fān). Each scoring element has a value, which can range from 1 double to 10 (or more) doubles. Many of the scoring elements can be combined, so the final value of a winning hand can be quite high!

This article will discuss the various concepts and practices of scoring:
1. payment system;
2. doubles;
3. base stake;
4. limits;
5. unlimited scoring.

Payment System
Mahjong is a four-player game, and whenever one player wins, three players will lose. However, the three losers do not necessarily pay the same number of points to the winner.

There are two kinds of situations for a player making a winning hand: the winning hand is completed by a tile discarded by another player (this is a win by discard); or the winning hand is completed by a tile picked by the player himself (this is a self-drawn win).

When a player wins with a tile discarded by one of his opponents, the two non-discarder losers pays the winner the amount of points for the score calculated from the value of the winning hand, and the discarder pays the winner that same amount of points doubled. The discarder has to pay more because he is responsible for his mistake and is penalised accordingly. The winner therefore wins an amount of points 4 times the calculated score.

When a player wins by self-draw, the losers all pay the winner the same amount of points, doubled from the score calculated from the value of the winning hand. The winner therefore wins an amount of points 6 times the calculated score. This rewards the winner for making a win that is not dependent on mistakes by the opponents.

Some groups of players in Singapore favour the 'shooter' system of payments. In this system, unlike the typical one where all three losers pay in every deal, the two non-discarder losers do not pay the winner and only the discarder pays, and this discarder pays on behalf of the other two losers. So, in effect, the discarder always pays four times the calculated score.

This system is supposed to emphasise defensive play. However, without an orderly discard system and sacred discard rules as found in riichi majan, defence is not easy, and the winning tile is less predictable. Discarding a winning tile for another player cannot be easily attributed to poor defensive skills, and the 'shooter pays' system can therefore penalise good players unnecessarily. The rule that the discarder has to pay for the other two losers also reduce the role of bao penalties (explained in another article), and therefore dilutes the flavour of Singapore Style mahjong. Based on these reasons, the 'shooter pays' system is not recommended for tournaments.

Doubles are the way the value of a winning hand is expressed, and actually represents how the score and points for payment between winners and losers are calculated. The 'double' is the literal English translation of the Chinese word 番 fān, which means 'to double'.

In Singapore, it is very typical to hear players use the term 台 tái, which means 'platform', instead. 台 is more commonly used by players who speak Southern Min languages (i.e. Southern Chinese languages such as Hokkien [i.e. Xiamen/Quanzhou/Zhangzhou dialect-group], and Teochew), and which was probably borrowed from Taiwanese usage. The majority (some 60%) of Chinese Singaporeans are of Hokkien and Teochew descent and share a linguistic heritage with the Taiwanese, who also speak Southern Min languages (a mixture of Xiamen/Quanzhou/Zhangzhou dialects). (In Taiwanese 16-tile mahjong, however, tai are actually used to calculate scores in a different manner from fan.) Singaporean players who speak Yue (i.e. Cantonese) or Mandarin tend to use 番, following more common practice in Hong Kong and China.

Either way, both 番 and 台 are used in the same manner in Singapore Style mahjong: each double adds a multiply of 2 to the base (points) to arrive at the final score. The more doubles, the more times the base is multplied by 2.

For example, in a game where the base is set at 10 points, a winning hand with 4 doubles will earn 160 points. This score of 160 points is arrived through the following formula:

base × 2^(number of doubles)
= 10 × 2^4
= 10 × (2 × 2 × 2 × 2)
= 10 × 16
= 160

Basically, the base of 10 points is doubled 4 times to obtain 160 points. If the base of 10 points is just doubled once, the score is 20 points; if the base is doubled twice, the score becomes 40 points; and so on.

If a winning hand does not contain any double, the score for this hand is calculated to be exactly that of the base stake. So, if the base is set at 10 points, the score of a 0 double hand is simply 10 points. In Singapore Style mahjong, however, there is a minimum requirement for a winning hand to contain at least 1 double, so hands without any doubles (i.e. valueless hands) is considered to be illegal wins and are penalisable.

Base Stake
Since mahjong is typically played casually among friends for small stakes, the base for scoring can vary. It can be $0.05 (i.e. five cents), $0.30 (thirty cents), $1, $100, or even higher! Of course, any base stake of more than $1 can hardly be considered small stakes gambling.

Below are examples of how some bases are doubled. The first example of the 0.5/1 base is the most commonly used base because of the ease in calculating the scores.

Score Table for Singapore Style Mahjong, Base of 0.5/1 Point
Number of DoublesWin by DiscardWin by Self-Draw

A base of 0.5/1 point is quite common. 0.5/1 typically refers to a base of $0.50 (i.e. 50 cents) and $1. Two values are always quoted when referring to the base, the second value being doubled from the first. This doubling occurs because whenever a player wins a hand by self-draw, the score is doubled once as a bonus for the self-draw, this is not part of the normal doubling earned from scoring elements.

This 0.5/1 point base is considered to be the easiest to use because with the required minimum of 1 double to win in Singapore Style mahjong, scores will start on 1 and 2 points (for 1 double), then increased accordingly for more doubles. This base therefore uses basic and naturally round figures, and is convenient for players who play for small stakes.

In the score table above, notice that when the score consists of many doubles (particularly, when more than 6 doubles), the score becomes disproportionately high. This is because the doubling mechanism results in a geometric progression, and the increase in the score is exponential and low stakes gambling becomes unsustainable for friendly play. The result is that limits (typically 5 doubles) are imposed to prevent an unperceived unfairness in the scoring amongst players.

Score Table for Singapore Style Mahjong, Base of 0.3/0.6 Points (Before Rounding Up)
Number of DoublesWin by DiscardWin by Self-Draw

A base of 0.3/0.6 points is also rather commonly used. The use of a fairly odd figure like 0.3 results in many non-round figures for scoring. Therefore, all the scores are rounded up to produce round figures.

Score Table for Singapore Style Mahjong, Base of 0.3/0.6 Points (After Rounding Up)
Number of DoublesWin by DiscardWin by Self-Draw

With rounding up, all the scores are now round, and the effect of the rounding up results in figures that are easier to handle, particularly because such a base and its calculations are used in small stakes gambling. Values of $1, $2, $3, $5, $10, $20, and so on, are much easier to exchange amongst players when scoring winning hands, compared to awkward values like $1.20, $2.40, $4.80 etc. The strange effect of the unequal rounding up is that it is slightly more profitable to play for 2 to 3 doubles in a game with a 0.3/0.6 point base than in a game with a 0.5/1 point base.

In a tournament setting, a 0.5/1 point base is preferred, for the ease in calculation and handling, and it avoids distortions to the profit-value correlation that using a 0.3/0.6 points base causes.

In a scoring system based on exponential increment, winning hands with many doubles can score many thousands more points than hands with one or two doubles. This creates a situation where this unbalanced scoring leads to uncompetitiveness amongst players. For example, a player might be lucky and win a hand (on a discard) with 10 doubles. He therefore wins 2048 points. If his opponents only keep winning hands with only 1 or 2 doubles, earning at most 4 to 12 points each time, it is not possible for them to catch up to this lucky player, since high-scoring hands are not very easy to achieve. These opponents would therefore feel it is pointless to continue playing the game, since they are unlikely to catch up and recover their losses. In fact, it is quite likely that players in general would not want to play with a scoring system that does not have a reasonable cap on such high scores.

So, for such practical reasons of game balance and competitiveness, a limit is typically imposed in Singapore Style mahjong. This limit is the maximum number of doubles that will be counted during scoring, and any extra doubles beyond the limit are ignored during scoring. The payment between players will be capped to this limit. Limits are typically 5 or 6 doubles, depending on the agreement between players. A limit of 5 doubles is most common, for reasons of game balance and consistency of value of certain scoring elements (this would be elaborated in other articles).

If a player wins with a 10-double hand in a game with a 5-double limit, the losers only pay the winner the score for 5 doubles.

Unlimited Scoring
Some players feel that the use of limits reduces the values of some special hands (which are typically pereceived to be valued beyond 5 doubles). These include scoring elements like Big Four Winds, All Honours, Thirteen Orphans etc. High-scoring hands built on a combination of luck (doubles from bonus tiles) and hard work (doubles from scoring elements like Pure Suit and All Pungs) scoring beyond the limit are also not valued accordingly. So, some players do not play with limits, and these are usually players who play for rather high stakes, and if really high-scoring hands are won, the losers pay the price without complaint.

So using the exponential increment system of doubles can be quite damaging to the game balance. For players who want to make hands that score more than the limit and yet not deal with unreasonable losses, a compromise can be made by using bonuses for scores over the limit. For example, every extra double beyond the limit may earn an extra 10 points (regardless of wins by self-drawn or by discard), so high-scoring hands are still rewarded, but not in a game-breaking manner.

Score Table for Singapore Style Mahjong, Base of 0.5/1 Point, 10-point Bonus Per Double Over Limit
Number of DoublesWin by DiscardWin by Self-Draw

Related Posts
Rules of Singapore Style Mahjong: Index

Updated at 17:45, 21st August 2011

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