The ideal scoring chart with high fan values
by Cofa Tsui (Jan 3, 2009)
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Link to this article: http://www.imahjong.com/maiarchives211.html
Link to the spreadsheet of scoring chart suggestions: http://www.imahjong.com/maiarchives211.xls
The traditional way of scoring a winning hand in the Cantonese/Hongkong style of mahjong games is the "fan scoring system" where winning hands are scored with "fan value" which is then converted to "scores" according to a scoring chart.
An advantage of using the fan value over point value for the score elements is that the values of all elements are easier to memorize, and there is less confusion and uncertainty in determining the total scores of a winning hand and therefore less time is spent in the settlement process at the end of each game (hand).
This article is about discussions on how scoring charts with higher fan values (say, 10 fans or more) can be ideally established so that it can still be easy to memorize while the skill and difficulty factors associated to various fan values are also addressed.
The discussions are also about certain suggestions for a new scoring chart to be adapted to the International Mahjong Rules in its up coming revision.
(A) Some background information
In older games, scores are counted "double up" on each fan (e.g., 2, 4, 8, 16, 32, and so on, as the total fans of a hand increases). This works fine when games are played with the maximum total fan value that is normally restricted to a relatively low level, e.g., up to 双辣 "shuangla" ("double laak" or equivalent to 4 and/or 5 fans*) or to 爆棚 "baopeng" ("full house" or equivalent to 5 or 6 fans*), where the "doubling" will end at 32 (doubling starts at 2 and ends at the 5th level) or mostly at 64 (doubling starts at 4). (* Note: In some groups of players, 5 fans may still be considered as shuangla and be counted as 4 fans; in such case baopeng would have 6 fans. Other groups may simply consider 5 fans as baopeng.)
The above is common in and around the years 1970s, according to my memories.
As the stake increases in games in the later years (from early 1980s), limits set to a maximum of up to 10 or even as high as 13 fans are not uncommon. This makes the counting of the doubling a bit challenging; although it does not post significant difficulty to frequent players who would need really very little time to get used to the practice.
However, my discussion here is that involving such high stake is really uncommon in most common games which are generally played among family members and friends. On the other hand, in or around late 1980s and throughout the 1990s, increasing the maximum fan value of winning hands has been a trend, as people see the increased excitement these changes could bring into the game play. One of several solutions people adopted is to "discount" the doubling in half when a hand reaches a specific fan value, which is normally at 5 fans. With this solution, therefore and as an example, a 7-fan hand will have this doubling practice (with 1 fan = 2):
2, 4, 8, 16, 24, 32, 48
where 24 = 1.5 times of 16
thereafter, 32 = double the value 2 fans back, or 2 x 16
and 48 = double the value 2 fans back, or 2 x 24
and so on.
Another solution that is extremely common is the use of a small piece of paper where players would draw a scoring chart on it before the start of games. In this case, players can agree to whatever scores that could be assigned to the fan values. This practice seems to be perfect for individual occasions; but it is obviously a general disadvantage as it will not fit in all games in common standards, should such common standards exist.
The above practices are commonly seen in the late 1980s and throughout the 1990s, according to my experience.
(B) Discussions on the ideal scoring chart with high fan values
Setting the maximum fan value of a winning hand to higher levels would certainly increase the excitement of the games, especially when newer games tend to include more patterns and minimize or repel the gambling nature, as one can find these features in the International Mahjong Rules. As mentioned earlier, counting the scores at higher fan value could be challenging. As a matter of fact, it is challenging not only because a chart has to be easy to memorize, it is also because the scores cannot simply increase in a linear pattern according to the fan values. In contrast, scores have to be balanced with the skill and difficulty factors according to the fan values they are assigned.
The discussions would be better illustrated with actual examples of existing rule sets. Therefore, International Mahjong Rules will be used as examples in the following discussions.
As further discussions can be created online in the mahjong newsgroup forum (rec.games.mahjong), other writers are welcome to post other rule sets to add to the discussions.
(C) Ideal scoring chart with high fan values
In my opinion, a scoring chart should ideally have the following elements:
a) The chart should be easy to memorize
b) The score assigned to a fan value should be balanced with the skill and difficulty factors associated with that fan value
As the author and management of the International Mahjong Rules, I have tried to adopt the above elements when I prepared the current version of the rules - see article 30.1 of the online rule set at:
As a matter of fact, I am not satisfied with the current chart. It is difficult to memorize and the scores assigned to the higher fan values don't seem to be justified.
I now have some suggestions in mind. To better discuss about this I have prepared a spreadsheet on my website, IMJ InfoWeb, at:
On the chart accessed from the above link, groups 1, 2 and 3 have been discussed briefly above and I have no further comment here. Groups A, B and C represent my current suggestions, which I want to explain how the above ideal elements ("(a)" and "(b)") can be applied in the charts.
Group A: The total of 15 fan levels is divided into 5 groups of 3 fan levels each. In each group, fan values are multiplied by a multiple to reach a score value. The multiples increase when they apply to another group of higher fan levels. These multiples are 10, 20, 30, 50 and 100. The multiple jumps from 30 to 50 when it reaches the group of 10 to 12 fans; and from 50 to 100 for the group of 13 to 15 fans. My comments on this group: The differences between adjacent fans may not be perfect and the chart is somewhat hard to memorize.
Group B: The 15 fan levels are divided into 3 groups. The lower group contains 1 (including 0.5) to 3 fans and the score value is obtained by multiplying 10 to the fan value. The middle group covers 4 fans to 9 fans (all values are single digits). In this group, score values are obtained by multiplying a fan value by itself and then multiplying the result by 10. With the higher group which covers the 10 to 15 fans (all are double digits), the score for a fan value can be illustrated in this formula:
Score value = (fan value)*100 + (fan value - 10)*100
Group C: In this group, fans 1 (including 0.5) through 9 (all are single digits) are in one group and the score value assigned to a fan value is achieved by multiplying the fan value by itself and then multiplying the result by 10. For fans 10 to 15 (all are double digits), the score for a fan value can be illustrated in this formula:
Score value = (fan value)*100 + (fan value - 10)*200
In my opinion, both groups "B" and "C" have applied the "ideal elements" quite reasonably, with group "C" being more favourable in that the differences between adjacent fans in the lower fan group (fans 2, 3 and 4) are quite moderately acceptable.
(D) About the writer's IMJ Rules
International Mahjong Rules ("IMJ Rules") continue to adopt the "fan scoring system" and do not restrict the minimum fans of winning hands. With the IMJ Rules, winning hands can have a fan value as low as half fan (a hand containing the element "Coward" only), or as high as 15 fans. Due to the high fan values in the scoring chart, establishing a chart that is easy to memorize and has the skill and difficulty factors addressed, is an issue I have kept in mind to resolve for long. I hope the suggestion of "Group C" as outlined above could provide a direction.
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International Mahjong InfoWeb
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