Some Fundamentals of Mahjong

Points on Choosing a Set and a Style of Play

By R. F. Foster

ONE of the first essentials for the enjoyment of Mah-Jong is a good set of tiles. Many prefer those of Chinese manufacture on account of their smoothness, a certain warmth to the touch and the atmosphere that attaches to objects from the East. Tiles of domestic manufacture have the advantage of being more uniform and more easily replaced if lost or broken. Their thinness is no longer an objection, now that racks are so generally used.

The Chinese tiles vary in both width and length. The three varieties found are here shown in exact size.

The one at the left is known as the standard, and eighteen tiles of this size will be exactly the length of a standard rack. Players who use them will obviate the necessity of counting the tiles when building the walls. Those who play the three-hand game a good deal prefer the smaller sizes, since the walls are not so long.

The Chinese are a nation of carvers, and they make many sets that are works of art. But the customs officials refuse to pose as judges of art, and so they appraise the tiles by the thickness of the bone in proportion to the bamboo back. There are three standard thicknesses in common use – 3, 5, and 7 millimeters respectively.

It follows naturally that the best workmanship is put upon the thicker bone. The carving is more uniform, the circles are better aligned and the English numerals are all of the same size and design. The better sets are hand-painted, but the cheaper are often only stained. To the unpractised eye the difference is not apparent, but, when one comes to wash the tiles, it will be found out. An important point is the mortise that holds bone and wood together. A good sharp mortise is invariably a mark of the better class of tiles. In the cheaper sets this mortise is merely an insert, and the tiles frequently come apart.

Some players, beginners especially, demand large black numerals on the tiles. These are to be found only in cheaper and medium sets. In the vary best sets, in which the ordinary concentric circles are replaced by delicately carved apple-blossoms, the numerals are usually small and light in color, so as not to mar the artistic effect. Some sets are so elaborately decorated that they are impractical for play, the designs being so crowded, especially in the Bamboo suit, that it is difficult to distinguish the denomination of the tile.

In a good set, the tiles are of uniform whiteness, but since some importers are in the habit of going over the tiles before selling them, and filling up any dark lines in the face of the bone, it is difficult to discover these defects until repeated shuffling has worn off the filling. Sets that are unnaturally white should be regarded with suspicion, and tested with a damp cloth. One should never buy a set without turning all the tiles out on the counter, face down, in order to be sure that the backs are evenly matched in shade and free from any of the dark streaks that are frequently found in bamboo. These enable a player to identify certain tiles in the walls, during the play, or in an opponent’s rack. It is practically impossible to get what an expert would call a perfect set, because, in spite of the greatest care in selection, there are always some tiles, perhaps only one or two, that have slightly beveled edges on the bone face, or some other trivial flaw.

The tiles are sold in all sorts of boxes. Most of these boxes are now made in this country. Those with drawers built to hold 36 tiles each, are the most convenient. Thus the suits can be separated, and each of the players can pack a different drawer in putting the set back in place.

In what follows, it is assumed that readers of ASIA know the elementary details of the game; the comparative values of various kinds of incomplete sequences; the value of one concealed Kong as compared to four grounded sets; and all that may easily be found in any good book of rules.

The object in Mahjong is to win more points than your opponents and incidentally to get some amusement or excitement while doing so. There are three ways to win at this game. One is to get a hand completed for a Woo, or Mah-Jong, before any other player does so, in order to win something from everyone and pay nobody. Another is to get together valuable counting combinations, so as to win something from the others who failed to Woo, when you fail to do so yourself. Another is to cut your losses by careful discarding, so as not to enhance the scores of other players with whom you will have to settle later. Incidentally, careful discarding in the end play may draw the game and save you considerable loss.

In your attempts to attain to any of these objects, the kind of hand you hope to build up is called your objective. This may be largely or entirely controlled by the style of game that you agree to play, because it has lately become the fashion to prefer excitement and high stakes to intellectual enjoyment. The present craze is to get high-counting hands, and, in order to get them, players frequently agree to put certain restrictions on the game, so as to prevent the probability of an early Woo. The object is to gain sufficient time and opportunity to get these big hands together. Skill and judgement are largely replaced by luck, and the luck must be given ample time to materialize.

In deciding on the style of game that shall be played, players have three varieties to choose from:

  1. The original game, as played by the Chinese. This is to get together four sets and a pair, no matter what those sets are or how they were obtained. This is usually called a straight game.
  2. The one-double game, in which it is agreed that no player can Woo without at least one double in his hand. Those who do not Woo are allowed to count anything they have, just as in the straight game, whether they have a double or not.
  3. The cleared-suit game, in which no player can Woo that has more than one suit in his hand. That is, if he has any Bamboos, he must have no Characters nor Dots; but he may have Winds and Dragons with any suit.

No. 1 offers five principal objectives to the player, with the privilege of shifting at any stage of the play, according to his judgement of what is going on around him and what he gets from the Wall or the discards. His objective will depend on whether he imagines it will be more profitable to try to Woo, to get a big count, to block another player, to put the small hand out or to draw the game. He may run the gamut of all five of these objectives in a single hand, or he may find it unnecessary to pay any attention to more than one, or perhaps two, of them.

No. 2 requires of the player some judgement at the start in deciding whether or not to take the first thing that can be used, or to pass it up and wait until the objectives of the others players, especially of the one on each side, are disclosed. In the end game there is some very careful discarding, but between these two extremes there is usually nothing but the monotony of drawing and discarding.

There are only three ways to get the necessary double for this form of the game: Dragons, cleared suits and all-count hands. The Dragons are pure luck; the all-count hands are not only rare, but usually disappointing if they do not Woo, and they interfere with the easier process of getting a double through a cleared suit. The result is that a very little experience leads you to concentrate all your attention on clearing a suit, keeping all Winds and Dragons until the suit is cleared.

Two consequences naturally follow this policy. After the first one or two draws and discards, it is impossible to postpone longer the selection of the suit to play for, and just as soon as a set is grounded or you discard two different suits, your objective is disclosed to your opponents, because, after grounding that set, you cannot change to any other suit. The other consequence is that, in holding up a mixture of Winds and Dragons in order to get rid of suits you do not want, you are left at the end game with a supply of very dangerous discards. On looking over the “dead” tiles, you will find that others have been keeping the same thing, and it then becomes a gamble as to who shall take that has the power, and who shall keep that can. This is sometimes rather exciting, but there is not much skill in it. You are continually ruining your own hand to avoid giving up a tile that you imagine will put another player out, only to find that it was of no use to anyone.

It must be remembered that in this form of the game any doubles that accrue through the holding of Flowers or Seasons do not qualify for a Woo, but simply add to the other doubles already in hand. It may also be noticed that those who do not Woo can count all they have, with or without doubles.

No. 3 is simply a further limitation of No. 2, restricting the required double to one thing, the cleared suit. No matter how many other doubles there may be in the hand, if it contains more than one suit, it cannot Woo. Consequently, having once grounded a set, you can do nothing but trust to luck to clear the hand of everything else, in the face of the opposition of three players who know your objective from the start and will do all they can to prevent your gaining it. You must not only clear your hand of all but one suit, but you must get together a sufficient number of sets in that suit to complete the hand for a Woo, or you will find that it is of little value. Many cleared hands, with 13 tiles of one suit that do not Woo, can claim three doubles, with nothing in them to double.

The reason that players agree to enforce the restrictions requiring one double, or a cleared suit, to Woo, is that they know their style of game cannot win against the straight Chinese game, unless the limit is raised to such a point that one or two big hands in the course of an evening will offset all the small losses.

Some persons will tell you that the straight game, which admits of “dogging” hands, is a losing game. If so, they should be glad to play against it; but they know perfectly well that they cannot beat that game by waiting for big hands unless the limit is very high. The average hand in the straight game is worth about 74; in the one-double game, 166. The experiment of one playing the straight game against three who were determined to have a double has been tried out at length several times, and the straight Chinese game always won. It is a peculiarly defensive game, and gets into safe harbor when it sees trouble ahead.

This strikes at once at the great objection to the cleared-suit game, and in slightly lesser degree to the one-double game. The player who is in hard luck has no defense. He cannot get from under. His only escape is to Woo, and, in the case of many hands, to Woo is impossible from the start of the play, for two reasons. In the first place there is the determined opposition of the other players. In the second place, there is not enough time. It is not necessary here to go into the mathematics of the chances for a hand that starts with nothing to end with a Woo. In the straight game it can do so in several different ways, and the worst-looking hands sometimes win out and escape the big fellows, for the simple reason that the sets can be got together quickly, since any sort of set will do.

Even in the straight game there are certain types of hands that have not even an average chance. So clearly do the Chinese recognize this hopelessness in certain original hands that they give that player a right to demand a new deal if he holds nine Honors, without a pair in his hand. No. 1 is a specimen of a hand without even an average chance of success. The odds against completing such a hand under the restriction of a double or a cleared suit are 10,648 to 1, which is only a little larger than the odds against finding four Dragons of the same color in the original 13 tiles, the odds against which are 6,361 to 1.

No. 1

In the one-double game, there are numerous hand sin which there is no chance for a double except by clearing a suit, and if the hand fails to Woo, the cleared suit is of no value unless there are high-scoring sets in it, or something on the outside, such as Seasons. But in the one-double game you may make some allowance for luck. Any poker-player will tell you that there are days when it is “all in the draw” and other days when it is “all in the deal.” The same thing is true of Mah-Jong. Sometimes one is continually lucky in the first 13 tiles. At another time one seems able to fill anything from an interior sequence to a Kong. On one’s best days, it is both.

If you are superstitious and know when you are “in the vein,” you may start with a very unpromising hand and, in the course of the play, may be fortunate enough to draw three Dragons, or three of your own Wind or the Dominating Wind. These will inevitably have to be obtained from the Wall, because, as already pointed out, Dragons and Winds are about the last things that players discard in this form of the game. By the time they do discard them, if you can use them, the rest of your hand must be ready for them, because by that time the game is about to end. Take such a hand as No. 2. East Wind dominates and your are North, playing the one-double game.

No. 2

If you are going to gamble on your luck in drawing from the Wall, you have two chances for a double and two more of either East or North Wind. You might add a third chance – to draw three Dragons. In any case, you are assuming that a cleared suit will not be necessary for the double. Then you should play the straight game, taking anything that comes along that will make up a set, whether it is a Pung or a Chow, in “Bams” or in “Crackers.” Your aim must be to get your hand in shape to receive the finishing touch of a lucky draw in the way of a double. That is, you build up your hand as if there were no such thing as a restriction upon it for a Woo, or as if your already had the required double concealed. If you are so fortunate as to draw what you hope for, the conditions imposed by the one-double game are fulfilled.

Of course, the moment you lay down two different suits, your adversaries see your game. If you are playing the cleared-suit game, they know you have abandoned all hope of a Woo and are going for counts to offset your losses. There are many hands in which you may take a chance on getting out with no sequences. Even if you do not win, you will have something to deduct from the scores of the two others that do not Woo either. Take such a hand as No. 3, when you are East and Dominating Wind both.

No. 3

A concealed Kong (of One Dots) is worth as much as four ordinary sets grounded and doubled. To try for a double or a cleared suit in a hand like this is very much like attempting to make a silk purse out of a sow’s ear. You know that if you do not Woo on any hand, you will have to pay the winner an average of 166 points; double if either of you is East. Then you should abandon the Woo, but save your counters.

In the one-double game, the probabilities are, mathematically, that you will start with a pair of some doubling combination, such as two Dragons of the same color or two Winds that are either you own or Dominating, only once in 23 deals. But this figure is for a specifically named double, such as Red Dragons. In play with a Dominating Wind double, there are five separate sets of three tiles that will give you a double: three kinds of Dragons, and two kinds of Winds. Therefore your chance to start with a pair of some one of these is one-fifth of the 22 to 1 chance, or about 4 to 1. Take hand No. 4.

No. 4

Having got your starter, a pair of a doubling combination, two Green Dragons, you still have choice of trusting to luck to get the third and “dogging” the hand right from the jump; or clearing the “Bams,” so as to have another string to your bow; or playing for all counts. The decision once made, you cannot change your objective unless you return to the straight game, and gamble on getting the third Green Dragon.