Selecting Patterns for Hand-Building Mahjong: Beauty or Difficulty?

Is Zung Jung Hand-Building Mahjong? argued that hand-building rules should encourage beautiful, difficult, large hands rather than continual small-hand racing. Such rules should first provide many buildable patterns with different forms of beauty and a rich range of construction routes, so as many initial hands as possible have something to pursue. Here we consider which patterns are worth building and should be included.

Since the explosion of patterns in New Style mahjong, regional traditions have produced hundreds of them. Sheng Qi's 1999 book Mahjong Studies alone records 391. Guangdong and Hong Kong New Style patterns, historical Japanese yaku, and newly invented patterns can all supply ideas. But more patterns do not automatically make a better ruleset. Historically, selection has chiefly rested on two criteria: beauty and difficulty.

Beauty and difficulty

Beauty is expressed by the fourteen tiles in the completed hand. Strictly speaking, it is subjective, but there are broadly shared standards. Classical mahjong centered on minipoints for pungs and kongs, yet also rewarded large hands with uniform suits or structures, such as Full Flush and All Pungs. Their presence in many rulesets today shows that common standards of hand aesthetics exist.

Beauty and difficulty often correspond: a more beautiful hand imposes more restrictions and is generally harder. But they can diverge. Pure Straight and Pure Shifted Chows both involve three chows in one suit. Pure Straight contains the complete sequence of nine ranks, from one to nine, and is naturally more beautiful; Pure Shifted Chows requires repeated tiles and is therefore harder.

Beauty and difficulty are sometimes connected, but not always. The beauty of a hand is independent of how it is constructed or won. Normal operations such as chows and pungs do not affect it, and a self-drawn Pure Straight is no more beautiful than one won on a discard. Aesthetic patterns necessarily entail some difficulty because their suits and ranks restrict the available tile types and combinations. Repeated-chow patterns such as Pure Double Chow, and Little or Big Three Dragons, are difficult because they require repeated copies of tiles.

Difficulty, however, includes not only the constraints inherent in beauty, but also additional restrictions on construction and winning. Concealment disallows chows, pungs, and kongs during play; self-draw requires the final tile to come from one's own draw. These restrictions naturally make winning harder. Edge and closed waits constrain the winning tile's position within a chow, while a pair wait requires a single kind of tile to complete the pair. All have low tile efficiency and thus greater difficulty. Last Tile, heavenly and earthly wins, and wins on the final draw or discard similarly reward circumstances unrelated to the hand's appearance. Below, patterns defined by appearance will be called aesthetic patterns, while those defined by construction or winning difficulty unrelated to appearance will be called non-aesthetic patterns.

Beauty or difficulty?

Which criterion should hand-building mahjong use—beauty, difficulty, or both? In my view, pattern selection should chiefly consider beauty, rather than difficulty with no aesthetic content.

A beautiful structure necessarily carries difficulty because it limits tile types and quantities: Full Flush uses only one suit, while All Pungs requires four pungs and a pair. This difficulty arising from beauty can be called aesthetic difficulty. Pattern values should be based on that difficulty, with harder patterns receiving higher scores.

The reverse does not follow: a difficult achievement need not be beautiful. Winning quickly is harder, so a hypothetical ruleset could award three fan for a win within three turns, two within five, and one within seven. Such rewards correspond to difficulty, but not to appearance: the hand could be the simplest basic winning structure. This can be called non-aesthetic difficulty. However hard it may be, it conflicts with the purpose of hand-building mahjong and does not deserve a reward.

Some non-aesthetic patterns are entirely luck-driven: winning on the last draw, the last discard, a replacement tile after a kong, or by robbing a kong, as well as heavenly and earthly wins. Robbing a Kong's old Chinese name, “Golden Rooster Seizes the Food,” has four characters, like the other three circumstantial names; restoring it would make their form consistent. These achievements are passive accidents of luck beyond a player's deliberate control and can be called chance-based scoring patterns. Their probabilities are very low: heavenly and earthly wins occur once in several hundred thousand hands, and each of the other four less than one percent of the time. Self-draw is also purely chance-based, but far more common, at about one quarter. Its close connection with payment systems deserves a separate discussion.

Other non-aesthetic patterns are difficult but can be deliberately pursued: edge, closed, and pair waits; Concealed Hand; riichi; Last Tile; and Melded Hand. A player may avoid calls to obtain the concealment reward, or pass a possible win until only the last copy remains to obtain Last Tile. These deliberately buildable achievements with difficulty but no aesthetic content can be called difficulty-based patterns.

Hand-building mahjong should mainly include aesthetic patterns, selectively include chance-based patterns, and exclude pure difficulty-based patterns. For hand-building mahjong, beauty is the criterion for selecting patterns; difficulty is the basis for assigning their values.

Pure difficulty-based patterns are the source of overrewarding

A close look at the difficulty-based patterns listed above shows that they are precisely the patterns most often overrewarded across mahjong rulesets. New Style overrewards edge, closed, and pair waits and Fully Concealed Hand; Japanese classical mahjong and Zung Jung overreward concealment. All Chows and All Simples, by contrast, are aesthetic patterns, not difficulty-based ones. Riichi overrewards riichi and concealment, while Chinese Official Mahjong overrewards a broad range including Concealed Hand and Fully Concealed Hand. Most are small, very frequent patterns. Heavenly and earthly wins and the four rare circumstantial patterns do not suffer from overprevalence because they occur so infrequently.

Why does difficulty-based scoring lead to overrewarding? Precisely because it is unrelated to appearance. Even the simplest appearance-based patterns constrain tile suits, structures, or ranks and exclude certain other patterns. Seat Wind Pung or One Kong constrains one meld, or three tiles in the former case; Mixed Double Chow and Pure Double Chow constrain two melds, or six tiles. Mixed Double Chow cannot coexist with Half Flush, and a kong cannot coexist with All Chows. In other words, aesthetic patterns impose mutual constraints and exclusions.

By contrast, pure difficulty-based patterns are independent of one another and can accumulate. Imagine a ruleset allowing Concealed Hand, Fully Concealed Hand, riichi, Last Tile, and Single Wait to combine. Their accumulated difficulty and value might be considerable, yet the actual tile structure could be a Chicken Hand. Such accumulation can easily inflate scores and upset balance. This resembles treating dora as a non-aesthetic pattern and obtaining a mangan hand through riichi and five dora.

These patterns can also be deliberately pursued. Where the winning requirement is easy to meet, actively constructing them becomes the optimal way to race for a win, explaining why concealed riichi accounts for more than forty percent of Japanese wins. In higher-threshold combination systems such as Chinese Official Mahjong, these low-difficulty, small patterns repeatedly appear in the combinations used to qualify. Earlier analyses often blamed an excess of small patterns in general, but the real problem is pure difficulty-based ones such as concealment and pair waits, rather than small aesthetic patterns such as All Chows, All Simples, and Mixed Double Chow.

Another problem is that deliberately pursuing these small difficulty-based patterns conflicts with basic tile logic. A player may pass a ready-made win to pursue Last Tile, or decline a self-drawn winner and discard it in order to claim a discard win for Melded Hand. Such choices add variety, but the costs of contradicting basic play outweigh the benefits. Chinese Official Mahjong's lack of a same-turn passing prohibition largely accommodates patterns such as Last Tile and Melded Hand, but a side effect is an excessively offensive game that neglects defense.

To conclude, beauty should be central to pattern selection in hand-building mahjong. Difficulty without beauty should not be rewarded: difficulty-based patterns are the source of overrewarding in many rulesets. Purely luck-based patterns, being rare and entirely passive, can be included to make the game more entertaining.