“Mahjong” End Games

Asia, September 1924

By R. F. Foster, Copyright, 1924, by R. F. Foster

When you begin to play Mahjong, you have the prospect of a certain average number of draws from the Wall, say fifteen or twenty. But if you have to make a new plan after having used up a dozen of those opportunities, you have not much chance to carry it through. In the clearing of suits, what has gone before has not only wasted time, but has loaded your hand up with a lot of tiles that you will have to get rid of and that are just the tiles the others are waiting for. But in the cleared-suit game the shortness of time and the smaller number of opportunities to draw from the Wall are not so important as the number of wanted tiles that are still in the Wall or that will surely be discarded if others draw them. For this reason you will find it advantageous to have a suit to yourself, if you can manage it, and not to decide too soon what suit you will go for, since, once you ground a set, you cannot change your plan.

The middle game decides the end game every time. It sometimes happens that the developments of the middle game are such that, although you may have a suit to yourself, that suit is not coming your way. The discards are not made from the right quarter to suit your Chows, or the tiles you want are discarded before you are ready to use them. In many cases it will pay you to give up a suit that you might have had to yourself, and to go for a suit that you have to share with another player. This happens often.

In the one-double game and especially in cleared suits, the real play, with the greatest opportunity for skill, is in the first and the last few moves. The ending in the cleared-suit game seems generally to be regarded as a matter of you luck in getting what you want before the others get what they are after. Yet there is really no luck about the ending if you are well versed in the defensive game and have observed the discards carefully, so as to infer correctly what you have to hope for and what there is to be afraid of. In playing cleared suits, you have usually only one opponent that you can help or harm, since you are out of the tiles that another wants. If you start your practice at end play by paying strict attention to one player only, you will soon realize that the difference between thinking of nothing but your own hand and watching another’s hand as well is the difference between winning games and throwing them away.

It is practically impossible to separate any advice on end-game play from the facts upon which that play is based, because all end play is based on the middle game and the information it offered about what was going to happen later. If one thinks of it for a moment, any given player makes an average of fifteen to eighteen discards in each game. Since each of these means something, the lot of them, taken together, must mean a great deal; yet to the average player they mean so little that he notices them only as interfering with or helping his own game.

If you will take the trouble to sort out the four hands that are illustrated in this article, putting the tiles in the proper racks for E, S, W and N, and will pick out the tiles indicated as drawn from the Wall by simply taking them out of the drawer in which the set lies, one at a time, as they are wanted, you should have no difficulty in following every step in the play and the reasons for it, whether you study a single hand by itself or all four together. The hands are from actual play and illustrate several of the fine points of the end game, as developed from the middle game. The holders of the hands were playing cleared suits, with East the Dominating Wind.

I have found it necessary, to facilitate in this article or in others the study of Mah Jong play step by step, to invent some system of notation, similar to that used in bridge and chess. I have decided on the following as probably as good as any; The initials, B, C and D are used for Bamboos, Characters and Dots, followed by the Numerical value; EW stands for East Wind and GD for Green Dragon, etc.; each horizontal line, numbered by an Arabic numeral at the left, represents the play once round the table. The word “Chow” or “Pung” shows that the last discard was used by the player in question, and the tile immediately following the word “Pung” or “Chow” is his discard. If a tile is indicated as drawn and immediately repeated, the meaning is that it was discarded again, without being taken in hand. The left-hand column shows the tile drawn; the right hand, the discard. For example, “EW-B6” means that the player drew an E Wind and discarded a 6 of Bamboos.

East begins by discarding the 9 of Dots. His first discard is not from his shortest suit. If he began with the Bamboos, he might have to shift to the Dots on his third discard and might thus disclose his objective too early in the game. Since it is advisable to conceal this as long as practical and there is no doubt about the suit E will try for, it does not matter which of the two suits he gets rid of first. W, who has no doubt about the suit he will clear, takes the first Chow that offers, without waiting for Pungs, as many players would do with such a hand.

This discard by N shows that he is still undecided about which suit to play for, with two probably almost equal in length, or that he is waiting to see what S is going to do before he shows his own hand. Both W and E have declared their objective.

N’s immediate discard of the Wind he has just drawn shows that he is still unwilling to decide and strengthens the impression that his suits are about equal. The importance of this inference will be pointed out in the end game. If S should happen to disclose that he was playing for Characters, N might reap a decided advantage from having the Dot suit to himself.

N is not going to wait any longer for S, but determines to try for the Bamboo suit, in spite of his unfavorable position with regard to W. His advantage is that he is able to Pung something.

Observe that W has no fear of N’s going out yet, because W knows that, if N had about equal suits when he discarded those two Winds, one after the other, he must still have a Dot left. The two last discards by E, his own Wind and a RD, mark him as having already cleared his hand of all but the Character suit. So he is evidently playing for three doubles. His draws are very lucky.

Note that N is careful to get rid of the Character before the Dot. The reason for this is that E has not yet grounded three sets; but if N discards the Dot, it might easily happen that E would get down a third set before N had another opportunity to discard, and then the discard of the C1 might be dangerous.

This is the beginning of the end play and the critical point of the hand. It is now clear to N that W cannot have any Pair or Winds or Dragons, because of his discards. All those that he has not discarded are already grounded. Therefore the remainder of W’s concealed hand must be all Bamboos. From the Bamboos that W has passed up and those in N’s hand, it is easy to infer that among those in W’s hand are at least one B1 and one B2, perhaps with a pair of 5’s, 7’s or 8’s. It is practically impossible for W to have any sequence in Bamboos.

The average player in N’s position, upon drawing the fourth B3, would complete his Kong and draw a loose tile before discarding. This would be, for several reasons, a very bad play. In the first place it is very important in the end game to clear the hand as completely as possible, for fear some player will go out. Completing the Kong is worth little compared with securing the three doubles for a cleared suit, and N plays correctly in keeping the B3 and discarding the D3. He is sure W could use that B3. If N completes the Kong first, his had will be worth just 4 points, no doubles. He will give W an extra double for robbing the Kong and will have to pay him 240 points. Then he will have to pay E 120 and S 12, a total of 372, which is about 200 more than the game finally costs him.

It will be seen that so far S has been playing a defensive game. He has not yet declared his suit, having grounded nothing but the three Dominating Winds. S has been defending himself against E, who is always a player to be watched, because he must be paid double if he wins. S knows that E has only one chance to go out, and that is that he holds two Pairs, one of which is a Pair of 7’s. S arrives at this conclusion by a careful study of E’s discards. Neither of E’s Pairs can be 3’s; but they might be 2’s, 4’s, 6’s or 7’s. If the situation is examined carefully, it will be seen that it is impossible for E ever to get a third 2, 4 or 6. The only chance left to him is the 7’s. S’s scheme is to play so that he can use a 7 just as well as E could. He can discard safely against E as often as necessary to prevent him from getting a three-double hand on a Woo.

E’s only chance is to draw himself out by discarding what he has and trying something else, but of course he does not know that. He does not even know for certain whether S is playing for Dots or Characters, and the natural inference would be that he had the Dots (since he had that suit to himself) up to the time he discarded three of them. There are a great many Dots to come, and some players are very foxy about their discards when they have tiles to spare.

Turning our attention to W, we find that he knows himself unable to win the game unless he gets the fourth B3. This is impossible so long as N holds on to that tile; but of course W does not know that N has it and would naturally expect him to make a Kong with it if he had. W cannot risk discarding the B2, for fear of putting N out with three doubles, if N should happen to be holding up the fourth B3 with a B1.

N, on his part, is in a tight place and knows it. He knows that W cannot win so long as he is depending on the B3 to complete his hand, and there is no other sequence that W can have. But N is not much better off himself. It is impossible for him to get a B4 to complete that sequence, 3, 4, 5. If he draws the B1 or B2, he can let the B5 go and have a chance to complete the 1, 2, 3 sequence; but if he draws a 5 or a 9, or even a 6, 7 or 8, he will have to discard it again or face certain death by giving up that B3.

The actual ending of the game went this way, the N and W players having nothing to do with the fight between E and S, since they were powerless to interfere in the Dot and Character suits.

South announced “Mah Jong.”

S had studied E’s hand with care, so as to pick the right sequence to lay down when he took the C5. Also he must be ready to use one of those missing 7’s if it came along, being very confident that it was of no use to E. At the same time he had to keep those dangerous 2’s for his “Eyes” and to lock up both the 4’s in sequences.

The result of this careful play on S’s part was that he won 416 points, in spite of all E’s luck in the draw. N lost 184, W 120 and E 112, after settling all their differences. N had only 4 points to be doubled three times; E had 8. The winner, S, got 2 for filling the only place in addition to the usual 20 for Mah Jong and 4 for the Wind set, with two doubles, for Dominating Wind and a cleared suit.

It may be remarked in passing that this is no game for those who have adopted the American fad of turning all the discards face down as soon as they are made, a custom unheard of in China. Mahjong is quite difficult enough without that. No one can recollect thirty or forty discards in their exact order and remember by whom each one was made and at the same time recall how many of five or six different tiles have been discarded, when there was nothing at the time of those discards to indicate that they would ever be of the slightest importance.