Sunday, March 02, 2008

Singapore Style Mahjong: Pinghu

I had earlier discussed some features of Singapore Style mahjong in the previous post Mahjong, Singapore Style, namely, the use of animal tiles and immediate payouts in some situations. A third feature I consider to be important in Singapore Style mahjong is the pinghu hand (平和 Mandarin: pínghú, Cantonese: pengwoo, Japanese: pinfu). This pinghu hand is somewhat different from pinghu hands in other variants, such as Japanese riichi maajan and Cantonese/Hong Kong Old Style mahjong (HKOS), and this feature of Singapore Style mahjong will be discussed in some detail in this post, with reference to the other variants, and with some speculation on the development of this hand.

This hand is a difficult hand to learn for beginners to Singapore Style mahjong, despite its usefulness in the Singaporean game. The English name of All Sequences, or All Chows, suggests all that is needed to complete this hand is complete of four three-tile sequences and a matching pair. However, this is not the case, and the English name is just a convenient term to describe the general application of this hand. There are certain conditions required before the hand can counted as a pinghu hand in Singapore Style mahjong.

Making a pinghu hand in Singapore Style mahjong
Basically, the hand is composed of four three-tile sets of sequences or runs (顺子 Mandarin: shùnzĭ). Such sequences can be exposed or concealed; there is no requirement to have all sequences concealed like in Japanese riichi maajan. In order to declare a win with the pinghu hand, there are two main conditions: the hand has to have a multiple wait, and the eyes have to be tiles that are not a potential double.

The multiple wait refers to the number of different tiles that the hand is waiting for. This multiple wait has to be for tiles from the same suit, and can only be for two or three different tiles due to the nature of this hand. If the hand is only waiting for a unique tile (that is, only one tile can complete the hand, whether this is a closed wait, an edge wait, or a single wait), and the player wins on a discard, the hand would not be counted as pinghu. The exception to this is if the winning tile is self-drawn. However, this is not applicable to a situation where the player has a hand where he had melded four sequences leaving a concealed single tile, since this clearly does not allow a multiple wait. The reason why a player can win a self-drawn pinghu when waiting for a single tile, and not when he has only one tile left in the concealed portion of his hand, is that there are no specific rules about checking the winning tile, to see if it completes a unique wait or a multiple wait.

The eyes are the remaining pair in the hand, and have to be tiles that are not potential doubles. If these tiles can be melded as a pung, this pung should not give the player a double; this typically means that among the Honour tiles, only tiles of winds that are not the seat wind or the round wind can be used as the eyes in the pinghu hand.

Given that the pinghu hand has to be completed in a particular way, players of Singapore Style mahjong have to learn the rules correctly, although many beginners do not learn the pinghu hand correctly. These players are then most like to commit fouls when playing, a supposed one-double pinghu hand turning out to be a no-double chicken hand (the Singaporean game is usually played with a one-double minimum for winning), often an expensive mistake since the errant player has to pay the other players as a penalty.

Origin of the Singapore Style pinghu (with some speculation)
The pinghu hand is not simply a hand that has four sequences and any pair. There are certain conditions required while making the hand for it to be considered as pinghu and not any chicken hand. The Chinese term for this hand, 平和 (Mandarin: pínghé but usually pronounced as pínghú; literally a "flat or even" win), seems to indicate that this hand is very ordinary and has no value. This may seem strange to Singaporean players since the pinghu hand is worth at least one double in Singapore Style mahjong! However, we have to look at the history of mahjong development.

The style of play which predominated at the turn of the 20th century is known as Chinese Classical, and the point-scoring is more complicated than in most modern variants. Essentially, points were awarded pungs, kongs and bonus tiles (flowers etc.) as well as to pairs of certain tiles, as well as for declaring a win, or winning with a unique wait, and this counts as the basic score. Doubles are used to progressively multiply the basic score to obtain the final score. Riichi maajan retains this scoring of basic points (fu in riichi maajan) to some extent whereas variants such as HKOS and Singapore Style removed the need for such point-scoring, keeping only the doubling.

Thus, in Chinese Classical mahjong, a 'No-Score' hand can score one double for pinghu. This hand does not have any pungs or kongs, or pairs that can score basic points. This can be viewed as some form of consolation, since there are hardly any basic points to double (except for points scored for winning, and for points for bonus tiles, and a few other situations), unlike hands with pungs and kongs. The pinghu hand in Singapore Style mahjong can be analysed as a development of this Chinese Classical pinghu hand. This is the reason why the eyes cannot have tiles that are a potential double, since in Chinese Classical, such pairs (of tiles such as Dragons, Round Wind, and/or Seat Wind) score basic points.

Why the hand has to have a multiple wait is more of a mystery. According to Millington's description [1], his pinghu hand allows single waits ("filling the only place"). Of course, this may not be a standardised way to play a pinghu hand. Perhaps some players have a different view of what 'no-score' means, and this could mean points for 'filling the only place' should have been excluded as well and players therefore did not allow single waits for pinghu. In riichi maajan, this is taken even further: the winning tile cannot be for completing a pair, even if there is a multiple wait. Thus, in a sequence of 1d-2d-3d-4d, 1d and 4d can be valid waits for Singapore Style pinghu, but not for riichi maajan, as this counted as a single wait (nobetan "stretched single"). Completing the pair ("fishing the eyes") does earn some basic points according to Millington, and is considered a different situation from 'filling the only place'. The Singapore Style pinghu hand is likely to be a development from Chinese Classical, but in a way that is not exactly faithful to Millington's version.

Interestingly, the Singapore Style pinghu hand differs from other pinghu hands. In Chinese Classical mahjong, the pinghu hand is awarded one double. The pinghu hand is also awarded one double in riichi maajan and in HKOS. The Singapore Style pinghu scores one double only if the player has bonus tiles, and four if there are no bonus tiles (both flowers and animals). Given that the usual limit in Singapore Style mahjong is five doubles, a four-double pinghu hand is thus quite high-scoring. However, it is usually not easy to win a pinghu hand without drawing a bonus tile, and since there are twelve such bonus tiles in Singapore Style mahjong, the chances of drawing a bonus tile are higher.

As the structure of the pinghu hand in modern play has some precedents in Chinese Classical mahjong, the scoring for pinghu in Singapore Style mahjong could perhaps be attributed to the 'no-score' principle as well. The 'no-score' of the pinghu hand in Chinese Classical only encompasses points for pungs, kongs, and pairs of certain tiles; points for self-draw, "filling the only place", "fishing the eyes", "drawing the final tile", and bonus tiles, are allowed. The pinghu in Singapore Style mahjong seems to have gone one extra step: disallowing bonus tiles, thus reducing the basic points (that would have been counted in Chinese Classical), and in turn allow this hand to score more doubles.

Four-double pinghu and its consequence on play
The pinghu hand is generally easy to make, and a pinghu-based strategy is rather viable in Singapore Style mahjong. Players usually assess their hands at the start, to see if their hands has a good chance for a four-double pinghu, provided they do not already have drawn bonus tiles. If they did not draw any bonus tiles, and quite a few have already been exposed by the other players, they have a good chance at completing the pinghu without any bonus tiles. Once such a decision is made, players may break up pairs of Honour tiles with potential for doubles (such as Dragon tiles) and give up the chance to obtain doubles through making pungs of such tiles, since there is a more valuable hand if they pursue the four-double pinghu.

Even if they did draw a bonus tile, there is a good chance that the bonus tile carries some double (one-third of bonus tiles are animal tiles, which are worth one double for any player). This is why pinghu hands are quite common in the Singaporean game.

Players pursuing four-double pinghu are considered dangerous, and players sitting above them may play defensively, by discarding carefully to prevent chows (there is no restriction of exposed chows in Singapore Style, unlike in Japanese riichi maajan), that is, until the four-double pinghu player draws a bonus tile which reduces the danger immediately (a four-double hand to a one- or two-double hand).

The pinghu hand can be seen as a basic hand, yet it is one of the more difficult hands to learn for beginners. In the typical Singaporean game, where there is a one-double minimum for winning, the pinghu hand is commonly used to obtain the minimum, especially for players who dislike to depend on luck to obtain doubles through drawing bonus tiles. Moreover, the high score of pinghu when a player has no bonus tiles is an incentive to attempt this hand, despite the possibility of drawing a bonus tile later in the game that will reduce the score.

I hope that I have thrown some light on the pinghu hand in the context of Singapore Style mahjong through this discussion. Does this pique your interest in Singapore Style mahjong?

1. A.D. Millington, 1993, The Complete Book of Mah-Jongg, Weidenfeld & Nicolson.


YS said...

I am not sure when the pinghu has become a 4 doubles hand. It used to be worth only 3.5 doubles. As late as the early 1990s, it was still worth 3.5 doubles. I used to play a Singapore style DOS computer game from 1989 to early 1990s, and the pinghu was also worth 3.5 doubles only. To me 3.5 doubles is more logical. A pinghu is a more difficult formation to make than Pung Pung and Half Suit (worth 2 doubles), but a simpler formation to make than Pure Suit (4 doubles), therefore the number of doubles should like in between. It should not be worth 4 doubles because it is easier to form than the Pure Suit. For this reason, I find that doubles counting in Hong Kong mahjong is more logical.

EP said...

How does one compute 3.5 doubles? For a base stake of $0.50, 3 doubles will score $4/$8 and 4 doubles will score $8/$16. So, is 3.5 doubles scoring $6/$12?

Actually, when I started playing mahjong seriously in 1991/1992, we were already scoring 4 doubles for a flowerless pinghu.

I think in terms of simplicity, half-doubles are complications. Normal doubles are easy to compute, but half-doubles do not seem to be. Most mahjong players would therefore probably make the scoring of a flowerless pinghu a round number to make such computation easier. Also, if a flowerless pinghu is considered to be halfway in difficulty between All Pungs ('Pung Pung') and Mixed Suit ('Half Suit'), then should the scoring not be 3 doubles instead, rather than a complicated 3.5 doubles?

Perhaps Hong Kong Style mahjong doubles scoring may seem more logical in some aspects, but I believe that the Singapore Style scoring also makes sense, in some ways. It feels rather balanced for a style that is so heavy on luck and randomness (look at the 4 animal tiles for extra doubles!).

YS said...

It's actually quite simple to compute 3.5 doubles. It's not exactly 3.5 (as in exactly the middle between 3 and 4 doubles) but we use .5 to denote that it is somewhere between 3 and 4.

A flowerless pinghu is computed as 10 times the amount of the base rate. So if the base rate is 0.50/1.00, the flowerless pinghu will be worth 5.00/10.00. This amount will lie somewhere between 3 and 4 doubles.

Base rate (chicken win): 0.50/1.00
1 double: 1.00/2.00
2 doubles: 2.00/4.00
3 doubles: 4.00/8.00
3.5 doubles: 5.00/10.00
4 doubles: 8.00/16.00
5 doubles: 16.00/32.00

You can test with any base rate, and you'll see that the x10 rate will always be between 3 and 4 doubles.

One interesting point that you may like to note. For a 4-double pinghu, if it happens to be a Pure Suit, then the total doubles would be 4 + 4 = 8. Based on the table below. This would be worth 128.00/256.00.

6 doubles: 32.00/64.00
7 doubles: 64.00/128.00
8 doubles: 128.00/256.00

Now if the pinghu is 3.5 doubles, and if it is also a Pure Suit, then the total doubles would be 3.5 + 4 = 7.5. So how to calculate 7.5 doubles? Simple, we use the rate for 3.5 doubles which we calculate above, and doubles it 4 times (same as we would double a 4-double pinghu 4 times if it is also Pure Suit):

4.5 doubles: 10.00/20.00
5.5 doubles: 20.00/40.00
6.5 doubles: 40.00/80.00
7.5 doubles: 80.00/160.00

Again, notice that the rate for 7.5 doubles lies between that of 7 and 8 doubles.

EP said...

YS, thank you for the information and clarification! It's most interesting! I have not met anyone using this particular system of scoring, so it is new, valuable information to me.

So, yes, your "3.5" doubles is calculated that way. Since it is 10× the base, it will always fall in between 3 doubles (8× the base) and 4 doubles (16× the base). However, it does come much closer to 3 doubles than 4 doubles. I still wonder why you score 3.5 doubles for the flowerless pinghu though, instead of just 3 doubles. Is there any particular justification in choosing a higher score than 3 doubles (for example, in terms of difficulty)?

Given your explanation of how 3.5 doubles work, I can guess at why the flowerless pinghu is scored as 4 doubles. Basically, it has to do with simplification of scoring. I am not sure if you used to score mahjong the old 'classical' way, by assigning points to pairs, pungs and kongs, before applying doubles to get the final score. The loss of such a scoring system is very likely due to Singapore players simplifying the procedures of scoring. Everything then just boils down to a few numbers: 1, 2, 4, 8, 16, and 32 in a 0.5/1 base 5-double limit setting.

YS said...

I don't have an answer to you question on why the flowerless pinghu's points is above 3 doubles, and not simply just 3 doubles. To me, I just followed the rules. It seems that this rule was not made up by my friends. I was also introduced to an MS-DOS based computer mahjong game based on the Singapore style during 1989, and the points for flowerless pinghu was also 10x base rates. Obviously this computer game was developed in Singapore, and it further reinforced my view that the 3.5 doubles was not something made up by my friends, but really does exist.

I am not sure what you meant by the 'classical' way of scoring. Perhaps you can give an example. I am interested to know.

EP said...

I am not doubting that the rule exists. The questions of interest to me are: why? and how many people actually use them?

The problem with Singapore Style mahjong is the high incidence of house rules. Since there is no governing body, house rules proliferate. It is generally fine when a group of people play only amongst themselves using such house rules and do not play with other people using other house rules. The problem arises when mixing of groups of players with different house rules come together to play. In a way, evolution occurs, compromises are made and rules that are more general/common are set, with all players happy in end.

The classical way of scoring has been dropped, generally, in Singapore, with everyone using more simplified rules in scoring (reflecting a trend in Hong Kong Style). However, this classical way of scoring continues to be used in Europe.

For the example, I am using the scoring as explained by Ting in his book Ting's Basic Mahjong (1980), on a version of Singapore mahjong using classical scoring but also using animal tiles.

Basic Point Scoring:
Exposed Pung of simple tiles (2–8): 2
Concealed Pung of simple tiles (2–8): 4

Exposed Pung of terminals or honours: 4
Concealed Pung of terminals or honours: 8

Exposed Kong of simple tiles (2–8): 8
Concealed Kong of simple tiles (2–8): 16

Exposed Kong of terminals or honours: 16
Concealed Kong of terminals or honours: 32

Pair of dragons, seat wind, or round wind: 2

Self-drawn: 2

Calling for unique (1-sided) wait: 2

Flower or Animal: 4

Winning a hand: 30

The procedure of scoring: for each player, after a player wins, adds up all the possible points from the tile combinations in his hands, and apply doubles to see the final score.

For example, Player A (sitting in West) may have:
Exposed: F1,F2,Cat RRR GGG WWWW
Concealed: B1B2B3 D2
Winning on: D2

He scores a total of 68 points (12 from flowers/animals, 8 from the exposed pungs of Red and Green Dragons, 16 from the exposed kong of West Wind, 2 from the single wait, and 30 from winning. He also scores 4 doubles (1 from the cat, 2 from the Dragons, and 1 from the Seat Wind). His final score is 68×2×2×2×2 = 1088 points!

As you can see, it is a very complicated (and time-consuming) process just to score a hand (and all hands, winning or not, are scored!). This slow and troublesome procedure is probably why scoring became simplified, by eliminating point-scoring of tiles and just applying doubles directly to a base stake.

YS said...

That's interesting! I didn't know that there is such a way of scoring. I only know about applying the doubles directly to the base stake. But are you sure that in Singapore, there had being a time when there were actually people who used this classical way of scoring? This system seems quite foreign to me.

EP said...

Yes, there is such a way of scoring! As written in my original post and my earlier comment, this classical scoring is still used, predominantly in Europe, but also in Japan in riichi-dora mahjong (but also with a lot of changes in its development).

To us Singaporeans, this system does seem foreign, since we are no longer exposed to it. Even the older Singaporeans (who may have learnt and used this classical system) have abandoned it and so we no longer see this in use. Of course, not all older Singaporean players learnt mahjong that long along and so may not have used it at all. I know of it because some older players I have spoken to mentioned using this system, including my mother and friends of her generation. Ting's Basic Mahjong also confirms this: since this book was written in 1980 from the perspective of a Singaporean playing Singapore Style mahjong, it must be reflective certain trends and common practices back in the 1970s. Singapore Style mahjong probably then developed in a very different direction since.

Anonymous said...

3.5 doubles for Ping Hu was in fact quite common in the 80s and perhaps much earlier.

4 doubles for Ping Hu is actually quite a recent event, perhaps to avoid argument by fixing it 4 doubles where it will be less arbitrary.

EP said...

Anonymous, thank you for your comment, and I apologise for the delay in publishing the comment and replying to it.

I frankly doubt 3.5 doubles for pinghu was all that common before the 1980s.

Like I mentioned in an earlier comment, Ting's Basic Mahjong (published in 1980) still uses the old method of scoring. Ting only adds animals to the bonus tiles, which is the difference between this form of mahjong (which may be now characterisable as 'Singapore Style') and more traditional forms of mahjong (e.g., such as those played in Europe using Chinese rules unchanged since the 1930s). Pinghu in his book is still only 1 double.

The problem in researching the truth of this particular practice would be the unreliable memories of old players and the lack of true documentation, so I fall back on Ting (1980).

Gary Moh said...

Hi Ed,

Firstly there are two type of Ping Hu in SG Mahjong.

Ping Hu with Flower/Animal tile only give you one double in SG and it is called Little/Smelly Ping Hu(小平胡/臭平胡).

Those w/o Flower/Animal tile are 3.5~4 doubles is simply called Ping Hu(平胡).

I was playing with the above rules when I was young in the 80s, and my parent play with such rules as well even earlier.

Here the wiki on SG rules that say the same thing as well.

EP said...

Dear Gary,

Technically, there is only one type of pinghu in Singapore Style mahjong, but how it is scored differs under different situations. This is because the conditions and restrictions for making pinghu with or without bonus tiles are the same. Only the values differ when there are flowers/animals or when there are none.

Of course, if you want to see these as two types of pinghu, you can. It is how you want to use it that affects whether it is two types or just one type of scoring element.

I find it extremely clumsy to refer to both patterns when it is actually only one in technical discussions. It is simply 'pinghu' when referring to the general strategy of using chow sets all the way, regardless of whether a player has bonus tiles or not.

Also, I find that students often confuse the two, simply because they treat it as two patterns when it is really just one. Whatever the value, the conditions and restrictions for making a hand pinghu are the same. By thinking of them as two patterns, but not grasping that they are exactly the same except for value in the presence of bonus tiles, they create a mental obstacle for themselves.