Game players often like to discuss the 'luck vs. skill' issue. Some players prefer games with little or no luck, while some players feel that games without a healthy dose of luck are too 'dry' and boring for them. In a contribution to MahjongNews.Com, mahjong scholar Alan Kwan is going to explore deeper than the surface and discuss in fine details what is really meant by 'skill' and 'luck. Some of the issues apply to gaming in general, not just to mahjong alone.

Skill: "competition factor" or "intellectual playability"?

When people say 'skill vs. luck', they usually mean by "skill" actually the game's "competition factor", which is the weight of skill towards the outcome of the game. Logically, this is the factor which is the direct antithesis of the luck factor: a game with a high competition factor must naturally has a low luck factor, and vice versa. Some players define it to be the number of "levels" of ranking which players can be seperated into, where a player one level higher than his opponent should achieve a certain winning percentage.

However, I do not think that this "competition factor" is the main reason why most lovers of strategy games play those games. If it were, since the skill factor of any game (which has any skill element at all) can be increased by raising the number of games in a match (it is a well-known mathematical fact that a best-two-of-three match has a higher competition factor than a single game, and so on), we would conclude that most game-playing would be conducted as rather long matches spanning a large number of games, but that is far from what we observe in practice, especially in casual gaming. (In some German games multiple rounds are played; but that is more to give meaning to the scoring, as in Lost Cities and Galloping Pigs, or to balance unequal sides, as in Lord of the Rings: Confrontation, than merely to increase the competition factor.) It is true that the competition factor is a useful quality, and we do sometimes want to determine the better player; most gaming tournaments do involve repeated games for this reason. However, my feeling is that the "holy grail" which strategy game players seek after goes beyond just the competition factor; it is a more sophiscated quality which I call "intellectual playability".

Intellectual playability consists of multiple facets and is harder to define than the competition factor; it includes the factors which intellectually stimulates the player when he plays (and studies) the game. In a nutshell, it is about having the right mix of strategic complexity and coherence. Strategic complexity (not to be confused with rules complexity) is about providing interesting strategic decisions to the player; the decisions should come at a good density, and there should be a good amount of variety in the decision-making situations so that they remain interesting. Ideally, there should be some freedom in the decisions too. Coherence is the quality that enables the player to formulate playing strategy in concrete, conceptual terms, instead of having to resort to brute-force game-tree tracing all the way till the conclusion of the game for every move. For example, Go playing by humans is as much about knowing the concepts of territory, live and death, connectivity, etc. as calculating many moves in advance. A game with very low coherence is probably more interesting for academic study than for practical play.

Against the competition factor, any luck factor is clearly its antithesis. But when we turn our attention to intellectual playability, the "luck" factor can either work for or against it. If the luck factor is excessive, it makes the decisions immaterial, and hence uninteresting; in this sense, there is a certain correlation between the competition factor and intellectual playability. But a suitable dosage of random elements in a game can serve to enhance its strategic complexity, both by increasing the complexity of the decisions themselves (the player has to consider the consequences of different results from the random elements), and by expanding the variety of the decision-making situations the player has to face. Backgammon is a good example.

Luck elements also serve some purpose besides enhancing the strategic complexity. It can increase the excitement level of the game. The very fact that it lowers the competition factor, hence giving some chance for the less skilled player to win, is also a desirable quality in some cases - because players like to win. Sometimes a novice player loses interest in playing the game (or at least, in playing against the same opponent) when he feels that he can't win against a strong opponent. However, excessive luck can make the game seem silly and unsatisfying.

So how does that relate to mahjong?

Mahjong is a strange beast because there are so many different versions being played, and its luck and skill factors can vary a lot depending on which version. Thus, it is inappropriate to just make summarily statements about luck vs. skill in "mahjong" without specifying which version. Here, I will discuss in depth how the rules (mostly, the scoring rules) can change the skill and luck factors.

One way to score mahjong is to apply uniform scoring: every hand scores the same fixed value regardless of its contents. Since luck always plays its part when trying to complete a high-scoring hand (in a typical scoring system), uniform scoring minimizes the luck factor and maximizes the competition factor. The player cannot gain a big advantage by luckily winning a few big hands, so it is consistency in overall performance which counts. Despite this strength, uniform scoring is rarely played in practice (except as the very first games when teaching a novice), because it sacrifices a lot of the strategic complexity of pattern-building mahjong; the game can be rather monotonous and dry.

Even with uniform scoring, mahjong has inherently a substantial luck factor in its tile-drawing mechanism. This puts an upper bound on the competition factor of the game; I would even say that, if the competition factor is all we are pursuing, it would be more efficient to simply abandon mahjong and move to another game. Fortunately, mahjong gives us a reason to stay by offering its own blend of intellectual playability. In its basic playing rules, mahjong offers a game with good strategic complexity (although that can be greatly enhanced if pattern-centered scoring is adopted), and also a highly coherent game with rather simple rules. A large part of that coherence lies in the game's winning condition, namely the regular hand (four sets plus a pair). Hence, in my humble opinion, some western versions which depart too much from the regular hand should really be considered a different game; NMJL Mahjong (USA) is no more Mahjong than Hearts is Bridge. Indeed, most Chinese players (if they know NMJL) would conclude that, the only reason anyone is playing that is because they don't know better.

Most scoring systems reward the hand based on a measure of its contents. Ideally, a hand's value should precisely reflect its beauty and difficulty; this is what I refer to as the ideal of pattern-building mahjong. The reason beauty (consistency, sameness, and systematism demonstrated by the hand) should be rewarded is to optimize the coherence factor, the same reason as why the regular hand should be the core of the game. A well-designed pattern-centered scoring system greatly enhances the variety in the situations one will face, and also adds a healthy dose of freedom in the strategy. For this reason, the balance is very important: if some easy patterns get assigned too high a value, they will be attempted all the time while the less favored patterns will be ignored, and this hurts the variety and the freedom, resulting in a monotonous game. With a well-balanced pattern-centered scoring system, the large gain in intellectual playability is well worth the small trade-off in the competition factor.

Unfortunately, most existing scoring systems tend to excessively reward certain elements: certain elements get large rewards far more than justified by their difficulty (frequency). The most conspicuous example is the 'self-draw inflation' in modern Chinese mahjong (which is discussed in another article of mine). In the case of more player-controllable factors such as the 'concealment inflation' in modern Japanese mahjong (riichi), the imbalance causes the player to form "peculiar", monotonous habits which eventually undermines the strategic complexity of the game. But when the inflated element is totally or mostly luck-based, such as self-draw inflation, the competition factor is sabotaged with little to no gain in intellectual playability. In either case, the intellectual playability of the game suffers, often greatly, in comparison to the ideal pattern-building mahjong.

In the worst case, we have the version which appeared recently in Hong Kong mahjong parlours, which applies nearly uniform scoring but also includes several atrocious inflation elements, including tripling self-draw inflation. This version offers neither the strategic complexity of pattern-building mahjong nor the competition factor of true uniform scoring; it is merely a gambling game played for gambling excitement.

Conclusion

While mahjong's competition factor can be maximized by adopting uniform scoring, it is better to optimize the intellectual playability with pattern-building mahjong. However, excessive rewards for luck-based elements hurts the competition factor without benefiting the intellectual playability; those should be avoided.

My points are summarized in the following table:

As a final note, Chinese Official mahjong (MCR) is not pattern-building mahjong. The ideal pattern-building mahjong should be focused on the regular hand, and the hand value should reflect precisely its beauty and difficulty; but Chinese Official has a high minimum requirement so that most regular hands cannot win, and the huge basic points and the self-draw inflation largely overshadows the points from the patterns. Chinese Official, despite using a large number of scoring patterns, is a peculiar form of speed mahjong with a high minimum requirement, with relatively flat hand values (beyond the minimum requirement) but with self-draw inflation. With the winning hand defined more by the scoring patterns than by the regular hand, the game loses a fair amount of its original coherence, as well as most of its supposed rules simplicity.

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