Two Tensions in Hand-Building Mahjong, Part I: Building Hands and Racing to Win

Pattern Selection in Hand-Building Mahjong argued that patterns should be selected for the beauty of their tile arrangements, rather than difficulty unrelated to beauty. This principle excludes small, purely difficulty-based patterns such as Concealed Hand and riichi, removing major sources of overrewarding in various rulesets. Yet Zung Jung has already excluded these difficulty-based patterns, apart from concealment, and eliminated their overrewarding, while most wins still consist of small patterns such as All Chows, All Simples, and Concealed Hand. Avoiding small-hand racing therefore requires additional measures, including a higher minimum score for winning and a larger selection of patterns. This brings us to the first tension in hand-building mahjong: building hands versus racing to win.

Building hands and racing to win

Although the concept of hand-building in A Historical View of Zung Jung Mahjong differs somewhat from its everyday meaning, the book repeatedly emphasizes that Zung Jung is hand-building mahjong rather than racing mahjong. It does not clearly define racing mahjong. As the name suggests, racing mahjong should mean pursuing the fastest, easiest winning patterns without regard to their aesthetic qualities. Japanese classical mahjong races for Concealed Hand, All Chows, and All Simples; Japanese riichi races for riichi, value honors, and All Simples; Chinese Official Mahjong races to meet its eight-point minimum. Existing rules contain incentives for racing, including base points, overrewarded small patterns, and imbalanced pattern values. Yet even after removing these factors, Zung Jung still has a seventy-percent predominance of Concealed Hand, All Chows, and All Simples. Is Zung Jung Hand-Building Mahjong? discusses this in detail.

Most present-day rules end a hand when one player wins. A player must first win, and only then does the value of the patterns determine the score. Throughout construction, players continually choose between a quick, small win and a larger hand with a higher reward. Each decision must consider not only one's own hand but also the opponents' chances of winning and the sizes of their hands, so that the expected scores of the alternatives can be compared. In a formula, let SW be the score received for winning, PW the probability of winning, SL the average payment when losing, and PL the probability of losing. The expected score of a choice is G = SW × PW − SL × PL. Compared with winning a small hand, building a large hand generally takes more turns: SW rises and PW falls, while SL rises slightly and PL also rises. The increase in SW must therefore compensate for the adverse effects of the other three variables. Players need to estimate all four from the situation at the table.

The best strategy in Zung Jung is to assess the initial hand and the first few draws: pursue a main-route hand if one is available; otherwise, race for a small concealed, all-chow, or all-simple win. Small patterns such as All Chows and All Simples are in an entirely different range of difficulty from main-route patterns such as Half Flush and Mixed Triple Chow. Pursuing the latter greatly reduces PW and correspondingly increases the probability of losing. Even if the payment on a loss remains almost unchanged because everyone else is also pursuing small hands, a poor starting hand means that the larger winning score cannot compensate for the decline in winning probability.

Minimum winning requirements

How can this tension be resolved? To prevent small hands from winning before large hands can be completed, many rules impose a minimum winning requirement: three fan in Guangdong Old Style, for example, or eight points in Chinese Official Mahjong. Zung Jung opposes such a requirement on the following grounds:

“If the aim is an ideal hand-building mahjong ruleset, a minimum winning requirement restricts players' strategic freedom. It forces them to build a hand regardless of their starting materials or the threat posed by opponents, thereby weakening the game's skill component.” Furthermore, “Ideal hand-building mahjong does not require hand-building in every hand. It gives players strategic freedom, allowing them to judge from their tiles and the situation whether to build a hand or race to win.”

This idea of freedom in hand-building has some merit. In practice, however, the World Series of Mahjong was compelled to adopt a five-point minimum, and even with that requirement, Zung Jung remains dominated by small-hand racing.

A minimum score slows the pace of winning, prevents isolated small patterns from winning too easily, and increases the chances of completing large hands. Choosing that minimum is crucial. If it is too low, as in riichi and Zung Jung, any scoring pattern qualifies. Chicken Hands are excluded, but small patterns such as concealment, All Chows, All Simples, and riichi become the main racing targets. If the minimum is too high, it creates the restriction on freedom described above. Suppose Zung Jung required twenty-five points to win. Because its small patterns are few and worth little, players would essentially have to pursue a handful of main-route patterns. This resembles Shanghai mahjong's Full Flush, Half Flush, and All Pungs routes, Guangdong Old Style's three-fan minimum, and the sixteen-fan variant of Chinese Official Mahjong: only a few main routes generally qualify. Because these routes depend heavily on the initial tiles, forcing players to build large hands regardless of what they hold restricts their freedom and makes small patterns worthless.

A minimum also creates another issue: small patterns below the threshold that can be combined to qualify have a major influence on both the rules and strategy. Chinese Official Mahjong is often criticized for the predominance of Mixed Shifted Chows and All Types. These relatively easy patterns, which offer little beauty, receive six points and can readily bring a hand up to the minimum. In terms of the number of combinations, Mixed Shifted Chows, involving three chows, is easier to construct than the one-point Pure Double Chow, involving two. It also readily develops into Mixed Triple Chow, Mixed Straight, Pure Shifted Chows, and other patterns. The inclusion and valuation of these two patterns profoundly influence how Chinese Official Mahjong is played and how much depth it offers.

Thus, hand-building mahjong needs a reasonable minimum winning requirement. The height of that threshold and the selection of small patterns around and below it must be scientifically designed and tested in practice.

Are hand-building and racing really contradictory?

Building large hands and racing for small wins appear to conflict, but “large” and “small” are relative. If Zung Jung has no minimum, everyone races for Chicken Hands, and All Chows and All Simples look somewhat more beautiful by comparison. At a five-point minimum, All Chows and All Simples become the small racing patterns, making larger patterns such as Half Flush and Mixed Triple Chow difficult to complete. Suppose the minimum were thirty points. Small hands would no longer qualify, so players would have to build main-route patterns such as Half Flush and Mixed Triple Chow. Yet they would still race for these hands, preventing still larger patterns such as Full Flush and Little Three Dragons from being completed.

Large and small hands are relative, and so is hand-building. Whatever the minimum, hands just above it will always be the easiest to complete and the ones everyone races to win. This follows from mahjong's winning mechanism. Variants such as Blood Battle to the End and Blood Flow Like a River alter that basic mechanism, but are outside this discussion. All mainstream mahjong rules today involve racing; there is nothing inherently wrong with having one winner in a hand.

Hand-building mahjong can also be racing mahjong. Its design should encourage players to build hands while racing to win, so that racing in accordance with hand-building principles yields the greatest return. While players pursue victory, their completed patterns should express the beauty of large hands, and their offensive and defensive choices should show their understanding of hand-building and the situation. That is the kind of ruleset we should aim for.