Designing Four Seas Intermediate, Part I: Scoring Patterns

See Four Seas Mahjong (Intermediate Edition): Entertaining Hand-Building Rules and Four Seas Mahjong Intermediate Edition: Rules Explained.

Four Seas Intermediate bridges the beginner-oriented Basic Edition and the hand-building-focused Standard Edition. This transitional edition was not originally planned. However, moving from the Basic Edition's eighteen patterns and ten-point minimum to the Standard Edition's one hundred patterns and progressively higher winning requirements introduces eighty-two more patterns. Players need an intermediate step.

After several revisions, the Intermediate Edition expands on Basic along two dimensions: pattern difficulty and the breadth of hand-building routes.

In difficulty, Basic tops out at Pure One-Suit, worth sixty points. Intermediate raises the ceiling to the 160 points of Big Three Dragons and Thirteen Orphans. It adds higher patterns, worth no more than 160, to families already present in Basic, including Two Identical Sequences Twice and Three Identical Sequences. Four Seas treats a family of patterns with a shared structural justification as the unit of hand-building. Once players understand a lower pattern, its higher forms are easy to understand and remember.

In breadth, Intermediate adds common whole-hand families—All Types, Every Set Contains One Rank, and All Unrelated—and relatively accessible chow combinations, such as Half Straight Twice, Mirrored Sequences, Three Shifted Sequences / Two Shifted Sequences Twice, and Assorted Straight. Although thirty-one patterns are added, they introduce only seven or eight new families, consistent with Miller's law.

Intermediate covers the principal whole-hand and chow-combination families. With appropriate winning requirements, it is itself a complete, varied ruleset devoted to hand-building.

Four Seas Mahjong Intermediate Edition 3.1

Class	Category	Subcategory	5	10	20	30	40	60	80	120	160
Suit					All Types	Mixed One-Suit		Pure One-Suit
Pattern		basic	All Sequences			All Triplets		Seven Pairs
		special				All Unrelated	Seven All Unrelated	Five Honors and Knitted Straight			Thirteen Orphans
Number	terminal		All Simples			Mixed Outside Hand	Pure Outside Hand		All Terminals and Honors
	linked				Mixed Linked		All Linked		All Symmetric
Quad	Quad			One Quad		Two Quads				Three Quads
Honor	Dragon			Value Honor					Little Three Dragons		Big Three Dragons
	wind					Little Three Winds			Big Three Winds
One-Suit	identical Seq			Two Identical Sequences					Two Identical Sequences Twice	Three Identical Sequences
	shifted seq		Two Shifted Sequences					Three Shifted Sequences			Four Shifted Sequences
	shifted seq							Two Shifted Sequences Twice
	straight	symmetric	Two Terminal Sequences				Pure Straight			Golden Bridge
	straight	consec seq	Half Straight				Half Straight Twice	Mirrored Half Straight
Three-Suit	identical Seq		Two Similar Sequences			Three Similar Sequences	Mirrored Sequences
	consec seq				Assorted Straight
chance	turn				Last Tile Draw			Blessing of Man		Blessing of Earth	Blessing of Heaven
	turn				Last Tile Claim
	Kong				Robbing a Kong
	Kong				Win by Kong Replacement

Winning requirement	Self-draw	Discard win
Beginner	10	10
Standard	10	20

Four Seas payment system; hand score H, payment threshold 50

Outcome	Winner	Discarder	Each other player
Self-draw	+6H	—	−2H (all three opponents)
Discard win, H ≤ 50	+4H	−2H	−H
Discard win, H > 50	+4H	−(4H − 100)	−50

I. Scoring patterns

A hand-building ruleset naturally benefits from many buildable patterns. Chinese Official Mahjong's outstanding strength is the richness and variety of its patterns. With Basic already serving beginners, Intermediate can explore historical and contemporary patterns from many traditions: Chinese Official, Zung Jung, Guangdong Old and New Style, historical Japanese yaku, Taiwanese mahjong, and original designs. The guiding principle is that beauty is the criterion for selecting patterns; difficulty is the basis for assigning their values. Any pattern meeting the criteria in Selecting Patterns for Hand-Building Mahjong: Beauty or Difficulty? and Aesthetic Criteria for Hand-Building Mahjong can be considered: beauty in suit, meld structure, and rank through identity, symmetry, completeness, and continuity. The newly selected families are examined below.

1. All Unrelated and All Types

Both All Unrelated and All Types provide options for very poor starting hands.

Like Thirteen Orphans, All Unrelated is a largely luck-driven pattern with little skill involved, and is overvalued in Chinese Official Mahjong. Four Seas neither encourages nor penalizes purely luck-driven patterns. All Unrelated offers a route for an otherwise hopeless hand. Because it must be concealed and cannot combine with other patterns, Four Seas assigns it twenty points, enough to qualify for a win. [In the latest version 2.0, its value was raised to thirty points.]

All Types is a traditional pattern expressing the completeness of the five tile groups. It accommodates some hands unsuited to other main routes. However, its six points in Chinese Official Mahjong, plus one for a terminal or honor pung, are excessive: any additional point qualifies, making it the second most prevalent pattern. Four Seas assigns All Types ten points, requiring a ten-point Value Honor to qualify and discouraging automatic pursuit of All Types. Together, All Types and Value Honor form a qualifying main route, but total only twenty points; Mixed One-Suit, Mixed Outside Hand, Mixed Linked, and other routes offer higher scoring opportunities. [In the latest version 2.0, All Types was raised to twenty points and qualifies on its own.]

This also brings us to Mixed Shifted Chows, Chinese Official Mahjong's most prevalent pattern. Four Seas excludes it for two reasons. First, it is easier than the two-meld Pure Double Chow, in the sense of allowing more combinations. Since Two Identical Sequences is worth ten points, Mixed Shifted Chows might deserve only five. Second, Mixed Shifted Chows can transform into or combine with Mixed Triple Chow, Mixed Straight, Pure Shifted Chows, Pure Straight, and other chow patterns. It is the core of Chinese Official hand-building. The problem is that this core offers less beauty than Pure Double Chow. If construction must revolve around such an overprevalent pattern, it would be better to omit it. Mixed Shifted Chows is the largest problem in Chinese Official pattern design, explaining why some expert games prohibit it and why sixteen-point-minimum games have emerged.

3. The linked-rank family

Every Set Contains One Rank, also called All Linked or Mantingfang, is a traditional pattern found in Guangdong New Style and “Nothing Is Too Unusual.” Chinese Official Mahjong's All Fives is a special case; the linked-rank definition generalizes the family. Zung Jung considers its justification weaker than that of Outside Hands. Terminals do have a distinctive difficulty, but requiring a common rank in every set naturally generalizes the outside-hand concept and shares its aesthetic qualities.

Aesthetic Criteria for Hand-Building Mahjong discusses the identity of rank and symmetry across ranks one through nine in Outside Hands. Linked hands likewise require every chow, pung, and pair to contain one rank. Although three chow forms are possible, those forms are symmetric around the chosen rank. A rank-four linked hand, for example, permits 234, 345, and 456 chows, 444 pungs, and a 44 pair. All contain four, and the chow forms are symmetric around four. In a sense, linked hands offer greater beauty than outside hands.

Aesthetics	Suit	Meld structure	Rank
Identity	One-suit families	All Sequences, All Triplets, Seven Pairs	Outside Hands, Every Set Contains One Rank, matching chows
Symmetry	Mirrored Sequences	Two Identical Sequences Twice, Two Shifted Sequences Twice, Half Straight Twice	Straight families, Outside Hands, Every Set Contains One Rank
Completeness	Three-suit families, All Types	Thirteen Orphans	Straight families
Continuity			Shifted chows, straight families

Chinese Official Mahjong selects only All Fives from this family. It also includes Upper, Middle, and Lower Tiles, and their lower patterns Upper Four and Lower Four, which overlap substantially with linked hands. This raises questions: why restrict ranks to 123 or 456 rather than 234 or 678? Why 1234 or 6789 rather than 3456 or 4567? The large/middle/small terminology also feels strongly associated with gambling; these patterns clearly derive from betting on high and low dice results. Some designers consequently replace them with three or four consecutive-rank bands without fixing their positions. Yet restricting tiles to a range of three or four ranks does not, in itself, fit the four aesthetic dimensions of identity, symmetry, completeness, and continuity. Lower Four can include 123 dots and 444 characters, for example: the suits are unrelated, the structures differ, and the ranks do not match. Many people therefore find little beauty in the Upper, Middle, and Lower Tiles family.

Four Seas instead selects the more beautiful linked-rank family and introduces Mixed Linked as an easier version of All Linked. All Linked is difficult. Although nine ranks are possible, any one rank-specific version is considerably harder than Pure Outside Hand, ranking below only Pure One-Suit. There are only twelve copies of any rank across the three suits. Four melds and a pair all containing that rank require at least six of those copies. Pure Outside Hand, by comparison, needs six tiles from the twenty-four copies of ranks one and nine, making it much easier. All Fives accounts for only 0.17 percent of Chinese Official wins. Even allowing nine target ranks gives All Linked a theoretical rate below 1.5 percent. Its low visibility is closely connected with its difficulty.

Because All Linked is hard, Mixed Linked can be introduced in the same relationship as Mixed One-Suit to Pure One-Suit, or Mixed Outside Hand to Pure Outside Hand. Four Seas requires every numbered meld or pair to contain the chosen rank, while the remaining sets may be honors. As in Mixed One-Suit, honors can replace a rank-based set, greatly relaxing the construction constraints. The resulting reduction in difficulty warrants only the twenty points needed to qualify. The simplest Mixed Linked hand needs four chows, in any suits, all containing the same rank; the available tiles span five consecutive ranks. This accommodates what would be Mixed Shifted Chows in Chinese Official Mahjong and can combine with Two Identical or Shifted Sequences, Three Similar Sequences, Three Shifted Sequences, Mirrored Sequences, and even Two Identical or Shifted Sequences Twice. It cannot combine with Half Straight, consecutive pungs, or Assorted Straight, but can combine with Mixed Outside Hand or Mixed One-Suit. It can also retain a two-sided wait. Mixed Linked can therefore become a main-route pattern, making the linked family practically buildable. An initial concentration around one rank suggests this route, while also giving defenders clues.

After introducing Mixed Linked, I discovered that it was not a Four Seas invention: it already exists in Hong Kong-style Taiwanese mahjong. With sixteen-tile hands, All Linked is still harder there, so introducing a mixed version is a natural step.

All Symmetric is an original Four Seas pattern above All Linked. For a chosen rank from two through eight, it permits only the chow centered on that rank, its pung, and its pair. There is no rank-one or rank-nine version. It is the fullest expression of symmetry around one rank. It can combine with Three Similar Sequences, Two Identical Sequences, Two Identical Sequences Twice, Three Identical Sequences, Mirrored Sequences, Little Three Similar Triplets, and other patterns, potentially reaching the two-hundred-point limit.

5. Identical and shifted chows

Two Shifted Sequences also comes from Guangdong New Style. It is the natural lower pattern of Three Shifted Sequences: two same-suit chows shifted by one rank. Less beautiful than Two Identical Sequences, it usually receives fewer points and less attention. Its distinctive feature is the ability to transform into Two Identical Sequences: in a typical two-sided wait, one end produces identical chows and the other shifted chows. Similarly, Three Shifted and Three Identical Sequences, or Two Shifted and Two Identical Sequences Twice, differ by only two tiles and can transform into or support one another. Shifted chows can thus be viewed as a lower form of identical chows, both being same-suit combinations with identical or nearby ranks.

This family is difficult. Even its easiest main patterns, Three Shifted Sequences and Two Shifted Sequences Twice, score sixty points. The four identical/shifted patterns can be treated as one main route, but even collectively they are much harder than other routes.

6. The straight family

Two Terminal Sequences, Pure Straight, Golden Bridge, and the Standard Edition's Pure Terminal Sequences form a family of same-suit chow patterns symmetric across ranks one through nine. Their relationships are:

Two Terminal Sequences → (+456) → Pure Straight → (+357) → Golden Bridge → (+1289−46) → Pure Terminal Sequences

Half Straight Twice appears in many traditional patterns, but usually with a fixed pair: Two Dragons Playing with a Phoenix requires 1-bamboo, Two Dragons Seizing a Pearl requires 1-dots, and Two Dragons Embracing a Pillar requires 2-bamboo. Half Straight Twice removes the fixed-pair restriction while retaining the combination of two half straights, generalizing these patterns into a new main route.

II. Main-route pattern families

Four Seas Intermediate now includes all the whole-hand and chow-combination families, described as six chow routes, three pung routes, and six whole-hand routes: fifteen in total. The mnemonic is:

“一对幺、五不带” — six whole-hand families.

“三龙般、六花镜” — six chow families.

“杠元风” — three pung families: kongs, dragons, and winds.

Type	Route	Main patterns	Introduced in
Whole hand	One suit	Pure One-Suit	Basic
Whole hand	Triplets	All Triplets, Seven Pairs	Basic
Whole hand	Outside hands	Mixed Outside Hand, Pure Outside Hand, All Terminals and Honors	Basic
Whole hand	All Types	All Types	Added in Intermediate
Whole hand	Unrelated hands	All Unrelated, Thirteen Orphans	Added in Intermediate
Whole hand	Linked hands	Mixed Linked, All Linked, All Symmetric	Added in Intermediate
Chows	Pure Straight	Pure Straight	Basic
Chows	Identical chows	Three Identical Sequences, Two Identical Sequences Twice	Basic
Chows	Three Similar Sequences	Three Similar Sequences	Basic
Chows	Half Straight	Half Straight Twice, Mirrored Half Straight	Added in Intermediate
Chows	Shifted chows	Three Shifted Sequences, Two Shifted Sequences Twice	Added in Intermediate
Chows	Mirrored Sequences	Mirrored Sequences	Added in Intermediate
Chows	Assorted Straight	Assorted Straight	Added in Intermediate
Pungs	Kongs	Two Quads, Three Quads	Basic
Pungs	Dragons	Little Three Dragons, Big Three Dragons	Basic
Pungs	Winds	Little Three Winds, Big Three Winds	Basic

The edition column replaces the original chart's colors: yellow identifies routes already introduced in Basic, while green identifies additions in Intermediate.

Nine routes—those represented by “一对幺、三龙般” and kongs, dragons, and winds—were already introduced in Basic. Intermediate adds six more.

Among whole-hand families, one-suit hands and All Types concern suit; All Triplets / Seven Pairs and All Unrelated concern structure; and Outside Hands and linked-rank hands concern rank. This balances mahjong's three aesthetic elements.

Among chow combinations, one-suit routes include Pure Straight and the shifted/identical-chow family; two-suit routes include Half Straight Twice and Mirrored Sequences; and three-suit routes include Three Similar Sequences and Assorted Straight. This balances the three forms of suit combination.

Compared with Chinese Official Mahjong, Four Seas replaces the less aesthetic Upper/Middle/Lower Tiles family with linked patterns, removes the overprevalent Mixed Shifted Chows, and adds two-suit combinations: Half Straight Twice, Mirrored Sequences, and Two Identical or Shifted Sequences Twice. This expands the routes available while giving two-suit hands more opportunities to develop.