CMCR: Article 10 Principles vs. Exclusionary Rule
by Cofa Tsui (March 2005)
This message serves the following purposes:
1. To introduce the original and complete meaning of Article 10 of the Chinese Mahjong Contest Rules in English. Article 10 provides complete rules for assessing the basic score of a winning hand.
2. To review the "Exclusionary Rule" introduced by Tom Sloper.
Article 10 of the Chinese Mahjong Contest Rules provides the principles for assessing the basic score of a winning hand ("Article 10 Principles"). The original rule is reproduced below. Note that the English translation is by the author of this message and shall not be treated as the official translation.
1. Scoring of a hand
(5) Principles in assessing the basic score
The scoring of a winning hand shall base on the "Table Of Value Of The Score Elements" provided in "These Rules". When a hand is won, the player shall identify the main score element of the hand in accordance with the "Table Of Value Of The Score Elements", *and assess the total score of the hand by combining all score elements that are not inevitably linked to one another*. When assessing the scores, one shall also observe the following principles.
1. Principle of non repetitive
If a score element, due to the conditions of its formation, would inevitably imply also the formation of other score elements, then the other score elements shall not be scored.
2. Principle of non separation
Once a score element is identified, the pieces of itself cannot be separated to create yet another element for additional score.
3. Principle of non identical
Pieces that have been used to form a score element cannot be combined with other set of pieces to form another identical element for additional scores.
4. Principle of selecting the higher score
If two sets or more of pieces can form two score elements or more but only one element can be scored, the player can select the element with the higher score.
5. Principle of assessing once
For a set *that has not been combined* [in an element], it can only be assessed once with *the corresponding set that has already been combined* [in other element].
In the above quote of the original rules, the *emphasis* is added by this author for purposes of easy reference. Texts within the square brackets "[...]" are added to express the author's understanding of the Chinese wording. In addition, for the purposes of easy reference, in the following discussions "article" and "sub-article" shall mean the corresponding rule article of the Chinese Mahjong Contest Rules ("CMCR" for short).
The "Exclusionary Rule" introduced by Tom Sloper may be found at his website, http://www.sloperama.com/mjfaq/mjfaq22.htm, and is repeated below for easy reference:
"ONCE TWO OR THREE SETS HAVE BEEN COMBINED FOR A SCORING PATTERN, ANY OTHER SETS IN THE HAND MAY BE COMBINED WITH AT MOST ONE OF THE ALREADY-SCORED SETS, WHEN CREATING ADDITIONAL TWO- OR THREE-SET PATTERNS."
I could not find this "Exclusionary Rule" throughout the original Chinese Mahjong Contest Rules (ISBN 7-5009-1630-2/G - 1529, published in Chinese in 1998.). In his website Tom said "it is assumed that this rule is documented in the 2002 book 'Chinese Mahjong Contest Rules: Questions and Answers' (ISBN 7-80602-511-1)." I do not have this 2nd booklet. I do not believe this 2nd booklet has the status of modifying the original CMCR. Therefore the reasoning used to explain the sample hands provided herein is based on the original CMCR only, unless expressly stated otherwise.
Upon comparing Tom's Exclusionary Rule and Article 10 of CMCR, I found that the Exclusionary Rule is very similar to sub-article 10.1(5)5. However, the Exclusionary Rule is not a complete rule as far as assessing the basic score of a winning hand is concerned. In contrast, use of the Exclusionary Rule alone to assess a winning hand could produce different results than if the assessment is based on the complete rules of Article 10.
In particular, I believe the wording "ANY OTHER SETS IN THE HAND MAY BE COMBINED WITH AT MOST ONE OF THE ALREADY-SCORED SETS" of the Exclusionary Rule is questionable and is in contrary to the wording of "assess the total score of the hand by combining all score elements that are not inevitably linked to one another" of sub-article 10.1(5).
The sample hands that follow are provided in Tom's website, and are hereby reviewed with the comparison of both rules of Article 10 and Tom's Exclusionary Rule.
123B 456C 789D 789C EE
Tom said: "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."
Explanation based on CMCR: Only one more additional element can be claimed because of sub-article 10.1(5)5, the principle of assessing once.
234B 345C 456D 567B 88C
Tom said: "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 Exclusionary Rule prohibits doing this because it uses more than 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 that combination only uses one set from the Mixed Shifted pattern."
Explanation based on CMCR: 567B cannot be combined with the 345C 456D to make a second Mixed Shifted Chows because by doing so it will violate the principle of non identical of sub-article 10.1(5)3.
234C 567C 234D 567D 88B
Tom said (in summary and with respect to the first 4 sets of the hand): Only 3 out of the following 4 combinations can be claimed:
Explanation based on CMCR: The first step in assessing the hand is "by combining all score elements that are not inevitably linked to one another" - refer to sub-article 10.1(5). With this first step all of the above 4 combinations are formed. The second step is to reduce the number of valid elements by applying various principles of Article 10. However, there is no valid principle from Article 10 that would reduce the number of combinations. Hence all of the 4 combinations may be claimed.
222B 333C 444D 555B 77D
Tom said: "This only earns you Mixed Shifted Pungs once. You cannot take the fourth pung and combine it with two you already "used up" to make a second Mixed Shifted Pungs. To use two sets from the first combination would violate the exclusionary rule. The holder of this hand can take consolation from the fact that this hand is All Pungs (and, if the pair is simples as shown, All Simples)."
Explanation based on CMCR: A second Mixed Shifted Pungs cannot be claimed because of the principle of non identical of sub-article 10.1(5)3.
Example 5 (Not in Tom's website)
222B 333B 444B
Can we claim the following combinations?
222B 333B 444B
234B 234B 234B
234B 234B (234B not claimed)
To my understanding, Tom's Exclusionary Rule will not be able to handle this problem as it does not seem to involve "ANY OTHER SETS IN THE HAND".
Explanation based on CMCR: (a) Only either 222B 333B 444B or 234B 234B 234B can be claimed as by the rule definition they are implied in each other. (b) Once either 222B 333B 444B or 234B 234B 234B is created, it cannot be separated and re-mixed to form another new element - Refer to sub-article 10.1(5)2, principle of non separation. (c) The element of 234B 234B will most likely be ignored due to sub-article 10.1(5)4, principle of selecting the higher score.
Example 6 (Not in Tom's website)
222B 333B 444B 555B
To my understanding, since question of this example will inevitably involve more than three combined sets, this will be a situation Tom's Exclusionary Rule cannot handle. ("ONCE TWO OR THREE SETS HAVE BEEN COMBINED FOR A SCORING PATTERN...")
In a simple way to explain the entire Article 10, I suggest that the correct process of assessing a winning hand may be summarized into two steps (steps that are not simple, though):
1. To find out ALL possible score elements of the hand;
2. To reduce the number of valid elements by applying various principles of Article 10.
In reality, with due amount of practice, you'll be able to exclude most implied elements in just step 1.
by Cofa Tsui
Copyright 2005 Cofa Tsui. All rights reserved. Feel free to quote and use in other communications with proper credit.