Luck and Skill in Mah Jong

Mah Jong is an extremely versatile game and is well suited for all kinds of players. It is easy to learn and an excellent parlor game, which can be played by people of all ages. It can be played as a sheer game of luck without paying much attention to defense. To intellectually and philosophically oriented players it offers a puzzle, solving of which requires mastering of all details of the rules and scoring and ability to adapt quickly to changing conditions of luck and to find a balance between offensive and defensive strategies. Finally, players seeking thrill and excitement soon notice that Mah Jong requires a keen psychological eye, ability to make quick and bold decisions, and can result in high profits or great losses just in a turn of a tile.

The nature of the game is determined by the rules, scoring and payment method. The classical rules are well balanced and suit all kinds of players: the default European Classical rules with simplified scoring are a recommended choice for novice players, while the Chinese Classical rules with Flowers and Seasons, increased possibility to score well with concealed hands and with the Limit set at 1,000 points (rather than 500 points as in European Classical rules) offer more possibilities for both intellectually and gambling oriented players.

The players looking primarily for intellectual challenge are likely to find their favorite amongst the modern pattern-centered rules (Chinese New Style, Chinese Official, Alan's Zung Jung or Wilmington 12-Tiles Rules) while players inclined to gambling will definitely find the modern Japanese rules the most interesting version of the game. The players who prefer to combine these two elements, are recommended to try Japanese Classical, Japanese Transitional, IMS or MMM rules. Finally the players who enjoy tile-matching games, collecting beautiful, high-scoring hands and games which require a good memory, might choose e.g. American Modern or French rules.

How much luck is involved?

As the total number of tiles in a Mah Jong set is 144 (or 136, if Flowers and Seasons are omitted), and a complete hand is formed of four sets and a pair, it is clear that the number of possible winning hands is huge. Though the tiles received in the dealt hand are important for determining the initial goal, it is not so rare that a player ends up winning with a hand where more than half of the tiles of the completed sets have been picked from the Wall or from other players' discards.

It is also true that a novice player may be lucky enough to beat expert players. Even in the classical rules a player may win the complete game by just one lucky hand though not necessarily with a Limit hand (a special hand that normally automatically scores the maximum points). It is important to note that big profits are often a result of a) collecting an average winning hand combined with bonuses for extra tiles (like Flowers, Seasons and Dora tiles), and/or b) using the classical payoff scheme, according to which all losers pay double if the winning player is East. The so called Limit hands are rare in other than American and French rules (the American rules use jokers and Charleston to help players collect big hands, and the French rules allow partially melded irregular winning hands).

Though the meaning of luck in Mah Jong is undeniably great, it would be a serious mistake to think that Mah Jong is a sheer game of fortune. In the long run a skillful player is guaranteed to win, and a player relying solely on luck will find that the game becomes sooner or later utterly frustrating not so much because he has lost his luck, but because experienced players constantly ruin his ambitious attempts for high-scoring hands either by going out on quick and easy hands or by seeming to know the tiles he needs to complete his hand, and then strike with one or two high-scoring hands without giving a clue.

Skill in Mah Jong cannot be compared with skill required in purely intellectual games like chess or go. The Japanese word 'ojozu' (often translated as 'skillful') means "one who knows how to adapt to his luck", and describes accurately the kind of talent required from a good Mah Jong player. This does not involve an attempt to control or force the luck (which is an endeavor based ultimately on superstition), but an attempt to control the likelihood of having luck on one's side and ability to exploit it to the full, once this goal is achieved.

Becoming a skillful player

A.D. Millington lays out the following four stages for becoming a skillful player: 1) Learning the rules and scoring, 2) Study of the principles of probability for collecting different combinations, 3) Learning defensive strategies and development of psychological eye in order get an idea of goals of the opponents, and 4) Learning bluffing skills in order to confuse and mislead opponents. 

Few examples of the contents of each of the four stages are given below.

a) Learning the rules and scoring

As mentioned above, the nature of the game is greatly affected by the selected rules, acknowledged scoring patterns and their scoring values, and the payoff scheme used.

E.g., if the East winner pays and receives double, it is clear that this must be taken into account. The dealer himself must be careful not to aim too high, since failing would mean that he pays double, and also that he loses the deal and the continued chance for having advantage of the East position. Likewise, the other players must be able to play defensively, if it seems that East is likely to win on a big hand.

When using Japanese rules, special attention must be paid to the defensive strategy (as the discarder of the winning tile must pay for all losers); also, the Japanese versions of Mah Jong often use rules like Riichi and Sacred Discard, learning of which is essential in order to have any chance for success. In addition, it is important to note that certain patterns earn an extra bonus only if they appear in a concealed hand. As modern Japanese versions require the winning hand to be worth at least 1 han, players not paying attention to scoring assignments might easily try to go out on a hand that does not meet this requirement, and accordingly must pay severe penalties.

When pattern-centered rules like Chinese New Style are used, the prerequisite for winning is to learn all patterns and their scoring and ability to quickly recognize chances for achieving them. The key to success in pattern-centered games lies in the player's ability to improve his hand with changes not requiring too much effort, and continuing doing that up to the point the hand is complete. A player who relies solely on collecting traditional patterns (like One Suit with Honors, Pung hand, etc.) is unlikely to succeed.

Players familiar with classical Chinese or Western rules only should note that in all modern Asian versions of Mah Jong only the winner is paid for the final score of his hand. This is a fundamental change, which must be taken into account when planning the goal of the hand. As there is no reward for "nearly winning the deal", and as most of the modern Asian rules penalize somehow the discarder of the winning tile, some of the strategic advice given in the books restricted to the classical rules are not applicable in modern games, or at least must be adjusted to take into account the differences in the payoff scheme. 

This is especially true for recommendations given for collecting high-scoring triplet-based hands. In modern Asian games the threshold for basing the winning plan on collecting these kinds of hands should be higher than in classical games, not only because there are no payments between the losers (should the hand fail), but also because a triplet-based hand is far less flexible than one containing Chows or mixed sets. Collecting a triplet-based hand easily leads to a situation where the player cannot afford to pay attention to discards (without sacrificing his winning plan) and accordingly must take a risk of becoming the discarder of the winning tile. In addition, the modern Chinese rules have abandoned point-scoring for basic sets (Pungs and Kongs) so there is no bonus for collecting solitary triplets from Terminals or ordinary Honors.

b) Study of the principles of probability

As for the probability of achieving different winning hands and combinations, it should be noted that due to the great number of variables involved in the game of Mah Jong, it is impossible to present mathematically precise calculations or statistics, and even if it were, they would not guarantee success. It can even be said that if all four players are equally skillful, the player who wins the game is the one who plays most boldly in the gray area where statistics and laws of probability do not directly encourage going for a mid-difficult or big hand. This may involve only one deal per player during the complete game while the rest of the deals are played by conforming to the most probable: going out quickly with easy hands, occasionally trying average hands like One Suit with Honors, playing for a draw in case the dealt hand is extremely poor, etc. This strategy is likely to guarantee that other players' profits stay rather low, while at the same time easy, Chow-based hands allow effective defense without the need to play exclusively for a draw.

Though mathematical calculations are not as useful in Mah Jong  as in games like poker, few general remarks are worth noting. The most probable winning hand is one that consists of at least one combination of Chows, not only because sequential pairs (e.g., 4-5) can be completed from both ends (with two different tiles), but also because Chows and sequential pairs when collected from the same suit form clusters, where the number of possible completing tiles is greatly increased. The classical example of the ideal winning hand (though extremely rare) is a hand called Nine Gates, which consists of a concealed calling hand containing 1-1-1-2-3-4-5-6-7-8-9-9-9 of the same suit. This hand can be completed with any of the nine suit tiles, and if it is assumed that all possible winning tiles are still available, it provides 23 chances to go out. 

This example illustrates also the fact that the probability for a multiple chance winning hand is decreased for each set that is completed by claiming another player's discard, because there are less possibilities for re-arranging the remaining tiles in hand to adapt to changing conditions. Each melded set also reveals more of the winning plan of the claiming player and accordingly helps other players to avoid dangerous discards. 

The fact that triplets especially triplets of Honors, as these cannot be re-arranged as sequences are more difficult to collect, also explains why experienced players often discard solitary Honors and Terminals at the start of the deal (i.e., when it is most unlikely that they will be claimed). Novice players, on the other hand, tend to keep all Honors in hope of collecting at least one triplet of them, and often also achieve this goal, but end up having several uncompleted Honors in hand when another player declares out on a much less ambitious hand.

The novice players also tend to exaggerate the meaning of the Limit hands. An experienced player knows that these hands (excepting ones based on seven pairs, and some of the less rare ones, like Thirteen Orphans or All Green) are extremely rare (without assisting devices like jokers or Charleston) and require an exceptionally good dealt hand, and that even if the probabilities are good, it may be wise to settle with the second best plan.

c) Learning of defensive strategies

In Mah Jong the defense is often also the best offense.

First, it is crucial to pay attention to other players' discards and melds simply to see that one's own plans are not ruined by the unavailability of possible completing tiles.

Secondly, the player must observe other players' actions in order to not make dangerous discards himself (this is especially true in the Japanese Mah Jong): experienced players often shape their hand by following the flow of discards (discarding tiles that have already been discarded by other players, or used in melds), sometimes even if this requires discarding some favorable tiles. This can be afforded especially if the hand is still concealed and composed mainly of sequences, since there are good possibilities to alter slightly the winning plan and rebuild the hand.

Thirdly, an experienced player knows when the situation calls for a defensive quick and easy winning hand (offensive defense), playing for a draw (passive defense), or whether it requires obstructing one player from achieving a high-scoring hand by assisting other players to go out on a low-scoring hand (active defense).

One of the most difficult of all skills required from a good player is the ability to give up collecting a promising hand (e.g. One suit with Honors with two Dragon triplets with only two suit tiles missing from a complete hand) and change attack to pure defense (involving e.g. breaking the Dragon triplets). This is a hard step, but one that is worth taking in certain situations (e.g., if East seems to be about to complete an equally well-scoring hand, especially on the last round). These kinds of abrupt changes in strategy are common especially in Japanese Mah Jong, where one bad discard can easily cost a player several thousands of points.

However, defensive strategy should be seen as an integral part of the whole: a player who is excessively defensive and timid in taking advantage of luck when it is on his side, is not likely to win the game.

d) Learning bluffing skills

The last stage (though only partially applicable in the context of games played on the computer) developing the psychological skills in order to fool opponents and conversely the ability to see through other player's attempts at the same is something that can be learned only after years of practicing. In addition to dissimulation carried out by physical means (facial expressions, arrangement of tiles in a way that disguises the true intention, etc.), this might mean e.g. discarding a couple of "good" but replaceable tiles in order to suggest disinterest in the kinds of tiles discarded, while in fact they are still part of the winning plan (this kind of a situation might arise e.g. if the player collects One suit only: isolated tiles of the correct suit can be sacrificed especially in exchange of Honor tiles picked from the Wall this way the player can downsize his goal to One suit with Honors, if it seems that a pure suit hand cannot be collected).


In conclusion it can be said that the hallmark of an expert player is above all flexibility, ability to adapt to changing conditions of luck and quickly find a balance between contradictive impulses. This includes both the regular game play with steady improvement of the hand, and more critical situations, where an average hand suddenly improves greatly because of few successive lucky draws from the Wall, or when one of the other players seems to be able to collect a high-scoring hand.

In the first case (with no visible threat in sight), an experienced player resists the temptation to collect the easiest or quickest possible winning hand, and instead chooses to improve his hand and maximize his scores by trying to include patterns, which can be achieved relatively easily. This normally means that a player is very careful in claiming a tile discarded by another player, even if it fits in his winning plan, since a melded set often makes the hand less flexible.

In the second case, where the situation calls for a fundamental change in strategy, a skillful player is able to abandon his original plan and play according to the requirements of the new situation. In the positive case (suddenly improved hand) this might mean aggressive playing, which utilizes every chance to complete the needed sets, without paying much attention to one's own discards, and in the negative case (threat of another player going out on a valuable hand) it might mean an attempt to go out on a quick and easy hand, breaking completed sets in order to make safe discards, or feeding a less dangerous player with tiles that allow him to go out on a low-scoring hand.

*Related topics
Historical overview
Symbolism of Mah Jong