Self-Draw Inflation

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Created on Monday, 18 May 2009 11:52

Last Updated on Wednesday, 28 November 2012 18:00

Written by Alan Kwan

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Zung Jung: a Perspective of Mahjong History

 Some modern scoring systems give a hand a much greater reward - up to tripling the normal value - just for winning on a self-drawn tile. This is particularly common in modern Chinese mahjong, including also non-mainland-China versions such as Hong Kong Old Style and Taiwanese mahjong, and also MCR. Despite its prevalence, I consider this an improper "excessive inflation" element (self-draw inflation). Let us investigate its origins. As I believe that self-draw inflation originated in Hong Kong Old Style, and got propagated to other Chinese versions (and eventually MCR) from there, we will look at how it crept into Old Style.

The one Faan for Self-Draw in Old Style came from mis-propagation

Hong Kong Old Style has inherited pretty much the same pattern list as Chinese Classical (the versions with triplet-point counting which preceded Old Style), but there is one noticeable exception: any hand which wins on a self-drawn tile receives one Faan.

While there is a reward for "Self-Draw" in Classical mahjong, said reward has always been a mere 2 points (the smallest score unit in that system, amounting to an increase of 20% or less in the total hand value; note that these are quite different from the "points" in MCR); any inflation of such in Classical mahjong is unheard of. In comparison, other 2-point patterns in Classical mahjong, namely edge/gap/eye/2-pair call, have never received any inflation either in Classical mahjong, and were dropped off during the transition to Old Style. This should be no surprise: compared to the 4-point patterns, the 2-point patterns are a lot easier and deserve no higher value.

Let us look at the odds: each round, the three opponents discard one tile each, while the player draws one tile; hence, in theory, a self-draw win would occur one-quarter of the time among all winning hands. (In practice, the opponents will try to avoid dangerous discards, so among skilled players, the ratio of self-draw wins will be even higher.) In contrast, for "Win on Kong" (initially a 4-point pattern), one gets only a one-shot 1/17 chance (assuming a two-way call) when he declares a kong while calling. The experienced mahjong players among our readers will certainly have an idea in mind about their relative frequencies in practice. Therefore, it would be hard to justify the claim that the one Faan for "Self-Draw" in Old Style has simply come from inflation of its 2-point value in Chinese Classical. Rather, I have found two possible conjectures for the true origin of that one Faan.

The first possibility is that, the one Faan is a mis-propagated (i.e. incorrectly propagated) form of the Late Classical pattern "Totally Concealed Hand". We should notice that, in the historical propagation of mahjong among the Chinese, it has been a tiny minority (perhaps less than 1%) who have learned the game by reading a book; most have learned through oral instruction. We can imagine the scene where a player, with a concealed hand, exclaimed in delight when he won on self-draw, and claimed an additional Faan apparently for drawing the lucky tile (in fact, for Totally Concealed). Meanwhile, a novice spectator (who lacked a clear understanding of the rules) misunderstood the Faan to be awarded for Self-Draw itself, missing the subtle point that only a concealed hand should enjoy that privilege.

On another note, Modern Japanese mahjong terminology sometimes refers to a Totally Concealed hand (門前清自摸和) as just "Self-Draw win" (自摸和), as every tile in the winning hand has been drawn from the wall; it could be possible that similar terminology had been used occasionally in China, causing confusion to the novice. "Totally Concealed" is a rather common pattern in Late Classical, but it has vanished in (standard) Old Style; it seems a plausible explanation that this is due to its being mis-propagated in another form, namely "Self-Draw".

The other possibility is the confusion caused by someone trying to explain the doubled payment for self-draw in the Old Style "Discarder-Doubling" payoff scheme by calling it a "Faan". This confused the novice, who misunderstood the Faan to be in addition to the doubled payment.

Without any official regulating body to correct the mistake, the novice's misunderstanding could be allowed to mis-propagate far and wide, eventually becoming the standard rule in Old Style.

The harmful side effect of "Discarder-Doubling" payoff scheme aggravates self-draw inflation

According to the Old Style "Discarder-Doubling" payoff scheme, on a self-draw win the winner assumes the privilege of East and collects double from each opponent, for a total income of sixfold the basic value. When winning on discard, the discarder pays double while the two others pay single, for a total of fourfold the basic value. Taking ratios, the payoff scheme gives self-draw 1.5 times (6:4) the income of winning on discard; in combination with "Self-Draw" as a one-Faan pattern, a self-draw win triples the income.

But it should be noted that the doubled payment for self-draw in that scheme is merely a straight inheritance of East's doubled income from the Classical "East-Doubling" scheme; rather than being the expression of any intent to reward the self-draw, it is merely a "makeshift" method (i.e. not really the best method, but only the best method among the ones available) employed probably because the mahjong masses of the time (because of limited wisdom and mathematical proficiency) could not think of a better method, such as the "Zung Jung Discarder-Doubling Scheme" (i.e. for a self-draw win, the three players split the fourfold payment equally).

Is the makeshift method a good one? In the original East-Doubling scheme, the spotlight is shone upon the East seat; East not only enjoys double income, but also risks double losses. An important strategy aspect in Classical mahjong is for the three other players to join forces (to some extent) against the East player. Shifting the emphasis from the East seat to the self-draw has neither any grounds nor any advantages; the intent of the Discarder-Doubling scheme is to punish the discarder, while the emphasis on self-draw is nothing but a "harmful side effect". In fact, while the doubled payment for self-draw is imitating the external form of the original East-Doubling scheme, the internal nature is very different: not only does it introduce a heavy luck element, but also it violates the principles of pattern-building mahjong (i.e. a hand's value should closely reflect its "beauty" and difficulty), since the "beauty" of the hand feels nowhere near tripled just by self-drawing the winning tile. In a sense, self-draw inflation lessens the punishment on the discarder, and contradicts the very intent and purpose of the Discarder-Doubling scheme.

Some may say that, "Self-Draw" does deserve triple income since it occurs (in theory) one quarter of the time. If such argument were to be accepted, we should also be obliged to reward "Final Draw" or "Win on Kong" by a hundred times, and "Blessing of Heaven" by 300,000 times! If we are to follow the same scale as other "Incidental Bonus" rewards, a pattern with 1/4 occurrence does not deserve triple reward, not even 1.5 times reward.

It's broken, so let's fix it

Originating from Old Style, self-draw inflation has been propagated all over China and has permeated many modern versions; the "false Discarder-Pay-All" scheme (discarder pays single, but everyone pays single when self-draw) used in Taiwanese mahjong and MCR is just a yet more distorted interpretation of both the "triple total income" effect of self-draw in Old Style and the "everyone pays discarder's amount" method derived from the makeshift method in the Discarder-Doubling scheme. In the minds of many Chinese players, self-draw inflation has even become a "natural standard" of mahjong, not supposed to be questioned or challenged. But the truth is that self-draw inflation is an error, a combined result of a harmful side effect and mis-propagation, and should be corrected this moment. It is not even an intended effect, despite that many Chinese players (not knowing its true roots) believe otherwise and even try to defend its "intent". Even if my conjectures are inaccurate, and the one Faan for Self-Draw in Old Style has actually originated through inflation of its 2-point value in Chinese Classical, an Incidental Bonus pattern of such high value yet with such high frequency is a violation of mathematical principles, and should be abolished.

Concerning this issue, Zung Jung has established the "Fixed Income Principle" (i.e. the value of a hand should be determined by the patterns in it, not by where the winning tile comes from), not just as a rule, but as a steadfast principle. Giving for self-draw any greater reward than its Classical counterpart violates this principle, and does not just introduce a flaw, but totally breaks the entire scoring system - no matter how intricately crafted and balanced the rest of the system is.

In MCR terms, adding 1 point for "Self-Draw" as a pattern is acceptable, but the effective tripling of the hand's pattern value in the payoff scheme must be abolished.

• Author's note: this is a chapter from my book Zung Jung: a Perspective of Mahjong History, edited for the current context. The work of translating the book from Chinese to English is currently under progress. Further news about the book will later be announced on the Zung Jung official website.

• © 2009 Alan KWAN Shiu Ho. All Rights Reserved. Usage by Mahjong News granted by author's permission; no unauthorized duplication allowed.