Aesthetic Criteria for Hand-Building Mahjong: Three Elements and Four Dimensions

Pattern Selection in Hand-Building Mahjong: Beauty or Difficulty? argued that beauty should be central to selecting patterns, and that difficulty without beauty should not be rewarded. This excludes small patterns such as Concealed Hand, riichi, edge, closed, and pair waits, and Fully Concealed Hand, which produce overrewarding and imbalanced values in various rulesets. Using Four Seas patterns, this article continues the discussion: what exactly constitutes a pattern's beauty, and how should we judge it?

Concealed pungs and concealed kongs

Continuing the discussion of beauty and difficulty, consider concealed pungs and kongs. Their difference from exposed pungs and kongs is whether the three or four tiles were all drawn privately. Concealment is itself a difficulty-based pattern, while the tile arrangements of concealed and exposed sets are identical. Concealed pungs and kongs are therefore also purely difficulty-based patterns and should not be included in hand-building mahjong.

Concealed pungs and kongs belong to the oldest minipoint system of classical mahjong: an exposed pung of simples scores two points, a concealed pung four, an exposed kong eight, and a concealed kong sixteen. Pungs and kongs are easier than chows; classical minipoint scoring is a system that rewards difficulty. Aesthetically, there is no difference between exposed and concealed pungs, or between exposed and concealed kongs. Some might say that winning with Four Concealed Pungs is beautiful. But even with Four Concealed Pungs, the tiles must all be turned face up at the win. How is the arrangement then different from ordinary All Pungs? Four Concealed Pungs is therefore fundamentally difficulty-based. Riichi additionally distinguishes the double-yakuman Four Concealed Pungs on a Pair Wait: Four Concealed Pungs plus Single Wait, or one difficulty-based pattern added to another.

Among modern competitive rules, only Chinese Official Mahjong retains the full range of concealed-pung and concealed-kong patterns, but combinations of exposed and concealed kongs have long been contentious in its scoring. Zung Jung and riichi do not have a separate concealed-kong pattern, treating exposed and concealed kongs together as kongs, which is a step forward. Yet both retain concealed-pung patterns. Choosing between concealed pungs and kongs—especially when pursuing the yakuman Four Concealed Pungs—greatly weakens kongs. A kong, which has one of the strongest justifications as a pattern, becomes something riichi players forgo to preserve concealed pungs. The solution is simply to remove concealed-pung and concealed-kong rewards: these difficulty-based patterns do not belong in hand-building mahjong.

Three aesthetic elements and four dimensions

Mahjong tiles have three elements: suit, meld structure, and rank. These are also the three elements of their beauty.

• Suit comprises the three numbered suits and honors.
• Meld structure comprises chows, pungs, and pairs.
• Rank runs from one to nine.

These elements already appear in classical patterns: Full Flush scores three fan, All Pungs four minipoints, and terminal pungs and kongs receive double points. This suggests that earlier players already recognized mahjong's beauty, and that the perception has remained consistent over time. Full Flush, Half Flush, and All Pungs still occupy central positions in competitive and regional rules.

The main-route patterns selected for the Four Seas Casual Edition belong to the families with the strongest historical foundations, tile-structure justifications, and prevalence across rules. They also best express the beauty of tile arrangements. From them, we can see that beauty arises from combinations of suit, meld structure, and rank along four dimensions: identity, symmetry, completeness, and continuity.

More specifically:

• Identity, or consistency: Among whole-hand patterns, Pure One-Suit and Mixed One-Suit express consistency of suit. All Sequences, All Triplets, and Seven Pairs express consistency of structure: four chows, four pungs, or seven pairs. Outside Hands, in which every pung, chow, and pair includes a terminal, expresses consistency of rank. Identity is the strongest aesthetic dimension; among the three elements, the order of aesthetic strength is suit > meld structure > rank. Among combination patterns, Two Identical Sequences belongs to the identical-chow family: its suit, structure, and ranks all match. This also explains why its higher pattern, Four Identical Sequences, is unrivaled in both beauty and difficulty. Pure Straight requires three chows of one suit, while Three Similar Sequences requires three chows with identical ranks. These are all forms of identity.
• Symmetry: In the Casual Edition this chiefly concerns ranks. Pure Straight contains ranks one through nine, forming a symmetry. Outside Hands permits only 123 and 789 chows, and 111 and 999 pungs, which are also symmetric across the ranks one through nine.
• Completeness: This means collecting the different elements. Three Similar Sequences contains all three suits; Pure Straight contains every rank from one to nine.
• Continuity: Suit and meld structure are categorical variables, so continuity applies only to rank, as in Half Straight and Pure Straight. A chow itself also consists of three consecutive ranks.

Aesthetic dimension	Suit	Meld structure	Rank
Identity	Pure One-Suit, Mixed One-Suit, one-suit families	All Sequences, All Triplets, Seven Pairs	Outside Hands, Two Identical Sequences, Three Similar Sequences
Symmetry			Outside Hands, Pure Straight
Completeness	Three-suit families		Pure Straight
Continuity			Half Straight, Pure Straight

Although all four dimensions—identity, symmetry, completeness, and continuity—appear in the Four Seas Casual Edition, the Intermediate and Advanced Editions contain more patterns expressing the beauty of suit, structure, and rank along these dimensions. New patterns are, in fact, selected according to these aesthetic categories and criteria.

Pattern aesthetics in the Four Seas Advanced Edition

Aesthetic dimension	Suit	Meld structure	Rank
Identity	One-suit families	All Sequences, All Triplets, Seven Pairs	Outside Hands, Every Set Contains One Rank, matching-rank pungs and chows
Symmetry	Mirrored Sequences, Mirrored Triplets, Mirrored Sequences and Triplets	Two Identical Sequences Twice, Two Shifted Sequences Twice, Half Straight Twice, Two Consecutive Triplets Twice	Straight families, Outside Hands, Every Set Contains One Rank
Completeness	Three-suit families, All Types, dragon, wind, and seven-honor families	Thirteen Orphans	Straight families, Nine Gates
Continuity			Shifted chows, consecutive pungs, straight families, Seven Consecutive Pairs

Non-aesthetic elements

Many modern patterns were invented without reference to the aesthetic qualities of suit, meld structure, and rank described above. Prominent examples adopted by Chinese Official Mahjong are All Green, whose tiles have only green markings, and Reversible Tiles, whose markings are vertically symmetric. Changing the colors or designs on the tiles would invalidate these patterns. Similar examples include Red Peacock and All Black.

Other patterns require particular tiles. A 2–5–8 Pair requires a pair of specified ranks; Catch Five requires a 4-character and 6-character closed wait won specifically on the 5-character. Some requirements refer to the tile illustrations: Fishing for the Golden Tortoise is a pair wait on the 7-bamboo; The Peacock Flies Southeast requires pungs of 1-bamboo, East, and South; Two Dragons Playing with a Pearl consists of two Half Straights and a pair of 1-dots. Wind, Flowers, Snow, and Moon requires four pungs: 1-dots for the moon, 5-dots for flowers, any wind, and White Dragons for snow. Others rely on wordplay. A Roaming Dragon Plays with a Phoenix requires a Pure Straight, plus West and 1-bamboo as a pung and a pair; the Chinese words for West and “play,” and the name of the bird depicted on 1-bamboo, provide the allusions. Prosperity All the Way requires one set each of ranks one, six, and eight in the same suit, whose Chinese names form a similar-sounding auspicious phrase.

These patterns fall outside the proposed categories and criteria of structural beauty. Most specify particular tiles, allow few combinations, and are difficult to remember. Hand-building mahjong should not include them.