Scoring in wéiqí

Olli Salmi
14.9.2008

It is well known that scoring in the game of go is different in China and Japan. In China the so called area counting is used while Japan uses territory counting. In area counting you score for both the points occupied and the points surrounded, in territory counting only for the points surrounded minus the stones taken by the opponents. However, it should also be well known that both systems give the same final score if both players have made the same number of moves. This is elementary mathematics. When all the prisoners in territory counting have been placed on the board, both players have an equal number of stones on the board. Then the difference between the territories is equal to the difference between areas. At the end of the count all played stones are on the board to make the subtraction easy. Captured stones are kept as counters to keep track of the number of moves made. They are not a special bonus or loot or booty as beginners tend to believe.

If one of the players has passed, the number of his moves and his stones on the board at the count is smaller than the opponent’s so he gains a point for every pass when compared to the area score. This is the essential difference between Chinese and Japanese scoring: in Japan you gain a point for passing but in China you do not. The method of counting is a superficial difference.

Since it is possible to get the Chinese score with both area and territory counting, it should be possible to get the Japanese score with area counting. To do this you put a stone aside – in a virtual neutral point – when you pass and require that both players play an equal number of moves.

I will try to prove it here because I have not seen it proven anywhere. I have sent the proof to Matti Siivola on 21.6.2006 and to Robert Jasiek on 19.8.2006. They have not refuted or confirmed it. Modified from Ikeda 5.2.
http://gobase.org/studying/rules/ikeda/

A_i stones on the board (i = 1, 2, A₁ Black's stones)
B_i stones removed by capture
C_i surrounded territory
territory score = (C₁ − B₁) − (C₂ − B₂)
area score = (A₁ + C₁) − (A₂ + C₂)

Now we should find the territory without using the term B_i.

M_i number of turns
P_i number of passes
M_i = A_i + B_i + P_i
B_i = M_i − A_i − P_i
territory = C_i − B_i = C_i − (M_i − A_i − P_i) = C_i − M_i + A_i + P_i

If both players have used the same number of turns (M₁ = M₂), territory score = (C₁ − M₁ + A₁ + P₁) − (C₂ − M₂ + A₂ + P₂) = (C₁ + A₁ + P₁) − (C₂ + A₂ + P₂)
If black has the last move (M₂ = M₁ − 1), territory score = (C₁ − M₁ + A₁ + P₁) − (C₂ − (M₁ − 1) + A₂ + P₂) = (C₁ + A₁ + P₁)-(C₂ + A₂ + P₂ + 1)
This means that White has to move last or pass.
Q.E.D.

When the points are counted, a player gets one point for each stone put aside. They can be placed on the board in neutral points. You can make room for them by removing an equal number of black and white stones along the boundary between them, but since it is the difference in points that counts, this is not necessary.

With this scoring it is natural that you do not want to play inside your own territory (real or imagined): playing on the board does not increase your area but playing into the lid increases your points. It is also unnecessary to fill in the neutral points because you can get an equal amount by passing. This would mean that they should be divided equally between the players like empty points in seki are divided under Chinese scoring. Only one player’s points need to be counted and compared with 180½. The pieces can be suitably arranged as long as they are not moved from the surrounded territory into the outside or vice versa.

Sometimes there are points in seki which can be filled by only one player (one-sided dame). In Chinese scoring you get a point for them but in Japanese they can be countered by passing so there is no net gain and moving into these points is waste.

Although territory counting is faster than area counting (http://www.figg.org/cgi-bin/view.cgi?id=2280&dName=soci), tradtional Japanese scoring is clumsier than Chinese scoring because you need special rules to take care of the situations that both sides can claim to win. With Chinese scoring the game can always be continued without loss of points.

The modern Chinese rules are not traditional in China. They were formed under Japanese influence during the first half of the 20th century. The original Chinese rule was that no points were awarded for the eyes that were necessary for a group to live. Two points were deducted for each live group. This is known as 还棋头 huán qítóu ‘returning the group heads’ in China, usually group tax in English. The logic is quite clear. You got a point for every stone that was or could be on the board at the end of the game (stone count). These are eminently unproblematic and conceptually elegant rules, ur-rules. There is no need to define territory. Seki is nicely taken care of. The score can be calculated before all the possible stones have been placed on the board, by territory, which was the custom in Tang and Song dynasties, or by area, which was the rule in Ming and Qing dynasties. In the former case both players would have to move the same number of moves. You need to pay group tax, unless you play the game to the end and count the live stones, in which case the group tax is automatic.

According to the available evidence this way of scoring was used throughout Chinese history until the first half of the 20th century, when Japanese go entered the country (Hé Yúnbō 2001). The modern Chinese scoring is a compromise between original Chinese scoring and Japanese scoring.

Under modern Chinese scoring all possible stones could also be placed on the board, but under Japanese rules it makes no sense. Arrea counting and territory counting are abbreviated procedures for the full stone count, but n Japan territory counting started a kife of its own.

Group tax is still advocated by some Chinese sites. The other feature of the original Chinese rules, the shìzǐ 势子, ‘power stones’, was still in use in 1973 when a Chinese fellow student at the Peking Language Institute attempted to use them. He took them immediately away when he saw my astonishment. Power stones were not used with handicaps. According to the Qing dynasty game records that I have seen (Liú Shànchéng 1985), the handicap stones were placed in the same way as in Japan, except for a three-stone handicap, which had the third stone placed in the centre point. I do not know the source or trustworthiness of the claim that the placement of handicap stones is or was free in China.

Why is Japanese scoring different? When the game was adopted in Japan, it looks as if phenomenon was taken as essence: the game was introduced in the superficial form of territory counting, not as the real game with underlying stone count. No motivation was seen for group tax and equal number of moves so these were abolished, while the rules for seki were kept as they were with no points for eventual territory. It is of course also possible that the Japanese knowingly changed the rules to reward passing, but then seki is illogical. In any case, the result was a game which could not always end gracefully by itself, so arbitrary rules for some situations were needed.

Summary.

The difference in Japanese and Chinese scoring in wéiqí is usually described as a question of territory counting vs. area counting. However, these counting methods are equivalent if passes are taken care of. The real difference is that Japanese scoring gives a point for each pass. Any eventual rues debate should be about this.

The reason for this difference may be a misunderstanding when the game was introduced in Japan. The territory scoring that was prevalent in China at the time of the introduction was taken as the real essence of the game and the underlying stone count was not understood.

PS.
I take this oportunity to propose an etymology for the strange term liberty, which in Chinese is 气 qì ‘breath’ and in Japanese 呼吸点 kokkyuuden ‘breathing space’ or 活路 katsuro ‘escape route’. The first to use this term may be Emanuel Lasker in Brettspiele der Völker (1931), but he uses it in singular: a stone has Freiheit 3, ‘liberty 3’ if it has three adjacent empty points. This usage rings a bell: I suggest that liberty is an inaccurate translation for German Freiheit, Freiheitsgrad ‘degree of freedom’, which in physics means ‘any one of a limited number of ways a point or body may move’. There is no doubt that this is what Emanuel Lasker had in mind, but it seems that the original translator of the term into English (Edward Lasker?) did not know this term in English and used an inaccurate translation.

Hé Yúnbō: Wéiqí yǔ Zhōngguó wénhuà 何云波: 围棋与中国文化 (2001) [He Yunbo: Weiqi and Chinese Culture]
Lasker, Edward: Go and Go-moku (1934) (2nd ed. 1960)
Lasker, Emanuel: Brettspiele der Völker (1931)
Liú Shànchéng (ed.): Zhōngguó wéiqí (2 vols.) 刘善承：中国围棋 (1985) [China Weiqi]