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FAQ #22. Chinese Official Scoring Explained

The most frequently asked questions about Chinese Official mah-jongg concern the scoring. Especially, newcomers to this variant ask about which scoring patterns (fan) may or may not be combined. This FAQ assumes that the reader is already aware of the basics of Chinese Official scoring:

1. The winning hand must score a minimum of eight points, not including points for flowers;
2. when the hand is obtained by discard, discarder pays score total plus eight points, and non-discarders pay eight points;
3. When the hand is obtained by self-pick, all non-winners pay the winner the score total plus eight points.

     

There are other books besides those pictured above, in a variety of languages. See FAQ 3.

INCLUSIONS AND COMBINATIONS IN SCORING

When scoring a hand, points for numerous scoring elements (fan) may be added to arrive at the hand's final score. The rules permit some latitude in this matter, but the rules do prohibit including certain combinations of scoring elements.

Depending on which rulebook the player is using, some permissible and prohibited inclusions may be already noted and documented. Most books are woefully inadequate in providing complete information about what may and may not be included when adding points.

The term "set" is used herein to refer to a pung, chow, kong, or pair. In case it helps some readers understand the concept of "sets" in mah-jongg, consider: most mah-jongg hands are comprised of sets or groupings of tiles. (Exceptions: Thirteen Orphans and the two Knitted & Honors hands, which are comprised of particular single tiles rather than sets or groupings of tiles.)

Here's How It Works

When scoring a hand...

Step 1. The usual practice is to begin by deciding what is to be your main scoring element (usually the highest-scoring element), although it isn't strictly necessary to declare what your main scoring element is - it's just a starting point.

Step 2. Then combine any other scoring elements which are not inevitably included in that main scoring element. (Note: one way to look at it is to combine elements in decreasing numbers of sets. In practice, you can usually add any and all scoring elements that use all the sets, all the tiles, or four sets first, then add two- or three-set scoring elements. Lastly, you would add scoring elements based on concealment and/or how the winning tile had been obtained.)

Step 3. Be mindful of the "combine-just-once" principle. Having combined sets to form your main scoring element, any sets not used in that main element may be combined only once, with no more than one set that has already been used to form the main element, to form additional scoring elements. The player is permitted to try differently ordering the combinations to achieve extra points, but it rarely works out that higher scores can be obtained by doing so. There are other prohibited combinations as well. Examples are given below.

In following the steps above, certain rules apply. The following is based on the Chinese-language book, CHINESE MAHJONG COMPETITION RULES ("CMCR"), published by People's Sports Publishing House in 1998 (ISBN 7-5009-1630-2/G - 1529). Pages 29-30.

10.1.5. Principles for Scoring the Hand
The scoring of a completed hand is based on the table of scoring elements provided in the rule book. When a player completes the hand, the player shall identify the primary scoring element first, then add other scoring elements that are not inevitably related to, or derived from, the primary scoring element or one another. In calculating the hand's score, the following principles must be observed.

10.1.5.1. Prohibition against implied inclusions
When a high-scoring pattern cannot be made without also making a lesser pattern, you cannot claim both the high-scoring pattern and the low-scoring pattern. Sometimes referred to as the "non-repeating principle" or the "non-implied principle."

10.1.5.2. Prohibition against separation
Once some sets have been combined to create a particular scoring element, you may not "separate" the tiles of those sets and re-organize them into other sets to form a different scoring element. Sometimes referred to as the "non-separation principle."

10.1.5.3. Prohibition against identical patterns
Once you've used a set to form a particular 2- or 3-set pattern, you can't use the same set to form an identical pattern with another set. Sometimes referred to as the "non-identical principle."

10.1.5.4. Freedom of choice principle
If a set can be used to form a low-scoring pattern or a high-scoring pattern, you are free to claim the higher-scoring pattern. Sometimes referred to as the "high-versus-low principle."

10.1.5.5. Prohibition against repetitive set usage ("combine-just-once") Once two or three sets have been combined for a scoring pattern, any other remaining sets in the hand may be combined only once with an already-scored set, when creating additional scoring patterns. Sometimes referred to as the "assessment-once principle." Note that this principle especially affects combinations of chows-based patterns.

Examples

10.1.5.1. Prohibition against implied inclusions. When a particular scoring combination cannot possibly be made without also including another (lesser, inevitable) scoring element, the lesser element is said to be "implied," thus it is not permitted to combine the two (to add extra points). For instance, the hand "All Even" cannot be made with chows or terminals or honors (it can only be made with pungs of even numbered suit tiles), therefore it is not permitted to combine the points for "All Even" and the points for "All Pungs" or "All Simples" or "No Honors. "All Even" is worth 24 points; the points for those other attributes are "implied" (already included) in the 24 points.

For another example, it would not be permitted to combine both "half flush" (also called "clean") and "one voided suit."

10.1.5.2. Prohibition against separation. If you have 111222333 in one suit, you can either call that three pungs or three chows. You can't claim points for calling it chows, then claim additional points for calling it pungs.

10.1.5.3. Prohibition against identical patterns. For instance, if you have 123B 456B 456B, you can't say that's two short straights (using the 123B twice to form two identical patterns).

Another example.





This hand is All Chows and All Simples. All of the sets in the hand work together to create these two scoring patterns, and it is permitted to combine them when adding the score.

In addition, the 234B 345C 456D comprises Mixed Shifted Chows. The winner might wish to claim that the remaining chow, 567B, should be combined with the 345C 456D to make a second Mixed Shifted Chows scoring pattern, but the non-identical rule prohibits doing this because it uses one of the sets in the first Mixed Shifted to make a second Mixed Shifted. However, the 567B can be combined with the 234B to make a Short Straight, because the set hasn't been used for Short Straight already.

Last example.





This only earns you Mixed Shifted Pungs once. You cannot take the fourth pung and combine it with one(s) you already "used up" to make a second Mixed Shifted Pungs. To use a set from the first combination to create a combo of the same type would violate the non-identical rule. (Note: The holder of this example hand can take consolation from the fact that this hand is All Pungs - and, if the pair is simples as shown, All Simples).

10.1.5.4. Freedom of choice principle. For instance, if you have 123 456 789 all in one suit, it makes sense to claim Pure Straight (kwa leung in Chinese - Pure Dragon), rather than Short Straight. You can't have both, so claim the more valuable.

10.1.5.5. Prohibition against repetitive set usage ("combine-just-once"). While the above four principles are well understood and accepted by new players, this rule (which I used to call "the exclusionary rule") is sometimes a source of vexation and confusion. Consider this Mixed Straight hand:





The 123B 456C 789D can be combined to make a Mixed Straight (8 points). That leaves the 789C to be used together with something else in the hand - you can use it just once, EITHER to create Short Straight (456789C) OR to create Mixed Double (789D 789C) - but not both, for an additional point.

Note that in this example, the pair is made of honors. That means the hand does not earn another 2 points for All Chows (more properly, "Pin Hu"). There may be other points for the final wait or for concealment.

Note further that Example 6 on page 13 of the Competition Mahjong Official International Rulebook (Takeshobo, 2002, ISBN 4-8124-0944-6) is erroneous in permitting both short straight and mixed double chow in a mixed straight hand.

Also, let's consider an example hand in which numerous two-set patterns may be found.



There are several ways the patterns might be combined. All result in the same score.

   234C 567C are combined to form a Short Straight. 234D can be combined with 234C to make a Mixed Double Chow. Then the remaining 567D may be combined either with 234D to make a second Short Straight or with 567C to make a second Mixed Double Chow.

   234C 234D are combined to form Mixed Double Chow. 567C may be combined with 234C to form a Short Straight. Then the remaining 567D may be combined either with 567C to form a second Mixed Double Chow or with 234D to make a second Short Straight.

   234C 567C are combined to form Short Straight. 234D 567D are combined to form a second Short Straight. Because of the wording of the Combine-Just-Once rule, you might be challenged if you then try to use one already-used set with another already-used set to form a Mixed Double Chow. Thus it might be your best bet to go with A or B instead.

Scoring the above hand, you get All Chows (2) and All Simples (2), then you can add any three of these four: Mixed Double Chow (1), Mixed Double Chow (1), Short Straight (1), and Short Straight (1). That makes only seven points - not enough to go out. You'll need to self-pick, go out on a unique wait, keep your hand concealed, or win on the last tile of its kind in order to get at least one more point to meet the minimum.

To recap: start by choosing your Primary Scoring Element, usually the highest-scoring element (often encompassing all the tiles or sets of the hand), as a starting point.