John Fairbairn wrote:
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Doesn't "group tax" mean that you pay a penalty for having more groups?
This is another case of a modern term not properly reflecting the ancient one, which was "two overflowing".
The currently definitive text on rules history is 围棋规则演变史 (History of the evolution of weiqi rules) by Chen Zuyuan (ISBN 978-7-80740-147-6).
It's a rather long book, and the relevant portion is on page 80, referring to the Dunhuang Go Classic. I did summarise the main arguments in New In Go. For those that haven't got that, one of the main points is that Japanese scoring and Tang counting are not quite the same thing.
Since I am going to dispute Chen below, let me say that I agree with that statement.
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It can be shown, by textual exegesis, that Tang counting requires both sides to play an equal number of moves (which is why I presume Bill is stressing prisoner return).
That is what the texts say, but the game records do not conform to that. It may well be, as you have suggested, that different forms of the game coexisted in China in ancient times.
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By a more complicated route it can be demonstrated that "two overflowing" refers to what we, not they, called group tax, but it was not clear cut to ancient Chinese what it meant, and had to be spelt out by Liu Zhongfu in the 12th century.
Chen indeed infers the group tax from the "principle" of "two overflowing", but does not really spell out how he gets there. More when I quote him below.
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Bill's claim (if I understood him aright) that group tax is a natural way for go to evolve may, therefore, be on slightly shaky ground.
What I show is that a group tax is not evidence of stone scoring, even though in modern times there has not been a group tax with territory scoring. I do show that there is a possible form of go which naturally leads to territory scoring with a group tax. Whether it was an older form of go is a question that we cannot answer. But it could have been.
Now to Chen. He provides the following interpretation of "two overflowing" or "both overflowing". All of his quotes are from GoGoD.
Chen Zuyuan wrote:
Obviously, “overflowing” is an ancient go term. It means that stones have been placed everywhere they can on the board, and the next one will overflow, so that the game is over. “Two [or both] overflowing” means that both Black and White are "complete, with no overflowing". Therefore, the meaning of the sentence is: “Both sides place stones on the board until there is no place left to play, then stop, and the player with more stones is the winner.” This is stones scoring.
Note that he is careful to say, "no place left to play", even though there is no evidence at all that the board was filled by actual play. But if the board was simply filled we would have modern area scoring without a group tax. And it is plain that ancient games had a group tax. So the group tax aspect of "overflowing" is something that Chen derives from ancient practice, not from the text per se. I think that he is right, but I want to point out that the group tax is not inherent in the text. I also think that he is right that vicarious play is the reason for the group tax. Nearly every version of go rules that I know of that are or were actually used involve vicarious play in one way or other.
Chen Zuyuan wrote:
Of course, we are more concerned about the information of rules in C&IP. After "complete, with no overflowing" the book continues, "At the end of the game, Black and White need not fill up the board; the side with more empty territory is the winner." It does not mention "equal stones" here, but this premise is certainly implied, because it can be taken for granted and therefore omitted.
C&IP stands for "Carefree and Innocent Pastime Collection", written circa 1100. Chen touched on the "equal stones" criterion. It is used today in the AGA rules, via pass stones. (Thanks in part to yours truly.) But I submit that that premise is not certainly implied. It is only implied if territory is counted as a shortcut for stone scoring, i. e., if a form of
equivalence scoring was in use. That may be so, but is not certainly so. (Note: Chen does not use the term, equivalence scoring, although he describes it.)
Later on Chen discusses Jia Xuan's game, which was played around 960. Here is the game record from GoGoD.
Chen notes that White wins by 8 points according to the game record, and that that implies a group tax. The score is Black 51, White 43, which, as Chen has already noted, is a feature of territory counting. The dame have not been filled, which Chen has also noted is a feature of territory counting. Equivalence scoring requires that each side has filled in the same number of stones. Now, there is a seki at the end of the game, but there are two (unfilled) dame in the seki, so the parity of the net score is unaffected. It must be odd by stone scoring. Instead, the net score is even, consistent with territory scoring with the group tax. Besides, C&IP says that you count territory. How does Chen deal with the even result?
Chen Zuyuan wrote:
The dame comprise 13 moves (marked X {in Chen's diagram of the end of play}). Black would make the last move. So how can there be equal Black and White stones? A natural idea is White will make an additional move, that is, minus 1 point, as in AGA rules. As a result White would lose by 9. But the result is still 8, as in present Japanese rules. How can that be? A reasonable assumption is: If Black makes the last move, in order to have equal stones for each side, Black will remove his last stone. Once territory counting is adopted, dame are naturally not played. People tend to simplify habitually, so the last dame will be ignored.
At last Chen alludes to equivalence scoring in the AGA rules. He also provides a rationale for Black not playing the last dame. However, in that case we have territory scoring, not equivalence scoring. Chen does not make the case, but there is a modern example of territory scoring deriving from area scoring in a similar fashion, by use of the Taiwan rule. See
http://senseis.xmp.net/?TaiwanRules .
Chen claims that, "On the surface, the go rules of the Chinese Tang Dynasty were territory scoring. Essentially they were territory counting, but actually a method of stones scoring with "two overflowing"." Unfortunately, he gives no evidence for that claim whatsoever.
The Dunhuang Go Classic refers to stone counting, not territory counting. Chen claims that the C&IP describes a form of equivalence scoring, but, despite the fact that it contains the phrase, "complete, with no overflowing," the C&IP clearly states: ""At the end of the game, Black and White need not fill up the board; the side with more empty territory is the winner." But to have equivalence scoring, the dame must be filled and White must play the last stone. If the C&IP gives a fuller description of equivalence scoring, Chen does not state it.
As Chen points out, there are four complete game records in the C&IP. Three of them have odd net scores, and could be examples of either territory scoring or equivalence scoring. The fourth, Jia Xuan's game, is not an example of equivalence scoring, a fact that Chen admits. He explains the fact that it uses territory scoring, not just territory counting, by appealing to the principle of an even number of stones. But that is turnabout. He first invoked that principle to explain equivalence scoring, and now he uses it to justify territory scoring. What is the difference?
The difference is that, by having the second player (White in this case) fill the last dame, so that one dame may remain unfilled, Chen is appealing to a principle of the same number of plays, not necessarily the same number of stones. In practice, under territory scoring the dame are filled before counting, anyway, except for dame in seki. Now, it is true that the game records state the same number of plays by each player, even if there are an odd number of plays actually in the record. That might indicate equivalence scoring, but only if the number of plays is enough to fill all the dame. In none of the game records is that the case. Why the players are said to make the same number of plays is unknown. As Chen shows, having the same number of plays by each player is not enough to distinguish equivalence scoring from territory scoring.
Chen's story is this. Ancient go, as the Dunhuang Classic indicates, used stone scoring with a group tax. From this a form of go arose that used equivalence scoring, counting territory and prisoners instead of stones on the board, but having a group tax. From this form of go territory scoring with a group tax arose. This form of go was adopted in Japan. Presumably stone scoring continued unchanged in China into the 20th century, the two different forms of go coexisting for some time in China. This is a plausible story, but Chen gives no evidence for the existence of a form of go with equivalence scoring.
IMO, one reason for this story is that Chen does not associate a group tax with territory scoring, but with stone scoring. That was the case in the 19th century. Japanese territory scoring had no group tax at that time, but Chinese stone scoring did. Thus, in his view, territory scoring with a group tax must have evolved from stone scoring.
However, I have shown how territory scoring with a group tax can evolve from a different form of go, not from stone scoring. The group tax actually depends upon vicarious play. In both stones scoring and territory scoring play could continue until a player would have to fill an eye that is necessary for life (or a dame in seki). But that would be tedious, and instead the necessary eyes are simply not counted in the final score.
My story has both stone scoring and territory scoring coexisting, both with a group tax, without either one deriving from the other. (Both are forms of no pass go, BTW. The pass is a modern invention.) I show one possible form of go from which territory scoring could have evolved.
Both Chen's story and mine have forms of go for which no direct evidence exists. But I think that the four complete game records in the C&IP are examples of territory scoring with a group tax.
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Bill Spight
we have reached a scorable board. The players could agree to stop play and count the score. Black has no safe moves. White has three safe moves. Net score: White wins by 3. That is the same score as we get if we count the Black points of territory (4) and subtract 2 points for each Black group to get 0, and then if we count the White points of territory (5) and then subtract 2 points for the White group to get 3.