Zung Jung Mahjong Scoring System (v3.0)

中庸麻雀計分法 (v3.0)

(English version)

Alan Kwan

"Freedom of Count" rule

A question I frequently receive is: "If the hand can be arranged in multiple ways so as to form the sets to compose the regular hand, how should it be scored?" The following hand is an example:

win on:

To answer this question, we need to refer to the "Freedom of Count" rule. This is supposed to be a basic mahjong rule, so it has not been included in the Zung Jung documents.

Freedom of Count (自由數和):
If there are multiple ways of arranging the concealed tiles in order to compose the winning hand, the winning player may freely choose an arrangement which one feels is best for oneself, and score the hand according to that arrangement. A hand may only be scored according to one arrangement; patterns from different arrangements cannot be both counted. (For example, a hand cannot score both "Three Identical Sequences" and "Three Consecutive Triplets", nor both "Two Identical Sequences Twice" and "Seven Pairs".)

Let's looking at the sample hand above. Assume that the hand wins on a discarded . There are two ways of arranging the 3x3 block: either as Three Identical Sequences, or as Three Consecutive Triplets. We can choose the arrangement which gives the higher score. Let's compare them:

  120  Three Identical Sequences
   40  Mixed Lesser Terminals
   10  Red
  ---
  170

  100  Three Consecutive Triplets
   40  All Triplets
   10  Red
    5  Two Concealed Triplets
  ---
  155

For this case, we can see that "Three Identical Sequences" would score more points. Thus, the hand should be scored as "Three Identical Sequences", for 170 points.

Note that the patterns in the two lists differ, and not only in the first pattern. The identical sequences qualify for Mixed Lesser Terminals, but the consecutive triplets don't (the and triplets are not terminal triplets). And of course the identical sequences don't qualify for All Triplets. This example should illustrate the rule clearly enough. In practice, concealed 3x3 blocks themselves are rare enough, and the combination with Lesser Terminals even rarer; Three Consecutive Triplets would usually yield more points if the fourth set is a triplet (because you can count "All Triplets"), otherwise Three Identical Sequences would usually score more (because of its higher explicit value).

An interesting fact is that, if the win is on a self-drawn , then the consecutive triplets would score barely more points, because of "Three Concealed Triplets":

  100  Three Consecutive Triplets
   40  All Triplets
   10  Red
   25  Three Concealed Triplets
  ---
  175

Thus for the self-draw win, the hand would score 175 instead of 170.

On a side note, the above hand is actually calling for three tiles: , and . Among the three possibilities, gives a much bigger score than the others. gives "All Triplets" but without "Three Consecutive Triplets", while gives only "Two Identical Sequences", for a puny 20 point hand (with the Red).

The case with a concealed "Two Identical Sequences Twice" hand is simpler. Two Identical Sequences Twice always scores more than Seven Pairs, so you can go ahead and score the hand as Two Identical Sequences Twice, without considering Seven Pairs.

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