Shimada's "Problems In Composing Igo Rules"

Chapter VI

Problems In Composing Igo Rules

1. Origin of Problems and their Development.

Apart from earlier periods in history, the first time that there was a problem with the Rules of Go was in a game in the fall of l928, at the Nihon Kiin (Japan Go Society), between Mr. Kensaku Sekoshi [? SEGOE Kensaku] and Shigeyuki Takahashi. While the pattern was being developed, as shown in Diagram 1 (a so-called "Mannen ko" -- "Thousand year ko" or "eternal ko"), both had played on "dame" ("useless points"). There were no more "dame", and it was White's turn to play. Then many people, including both players, gave their opinions, but the game's result was judged, politically, as "both Black and White win".

Whenever a problem occurs, the people concerned are summoned, and they discuss it and make a decision. This method is common, and necessary, in baseball and sumo games, but Go is not the same as these. In Go everything that happens is clear and exact, and no umpire is necessary at all, so that if the rules are concise, no problem need arise. Normally, the reason that this sort of problem arises, is that the rules of Go have not been codified. Because the problem has been under consideration since 1928 and has not yet been settled, it is certain that codification must be extremely difficult. But, inasmuch as the "primitive system of Go" [defined in Chapter 2] can be regularised with astonishing simplicity, if we cannot compose the rules of Igo, we must have been playing this perfect game imperfectly.

Diagram 1

Mr Hajime Yasunaga is the only person who has constantly made efforts to solve this problem of codification. In 1929, in the magazine "Kido" ("The Way of Go") his article -- "The Basis of Rationalization of Igo" -- was published. It must be the first document concerning this problem. An article appearing in [a later edition of] the same magazine, was entitled "The Draft of an Igo Constitution", and was also written by him. This is what he wrote:

The Draft of an Igo Constitution

Article 1: Board: it shall be a plane with 19 parallel lines drawn each way, [both] vertically and horizontally.

Article 2: Stones: players shall indicate their moves on the board with stones of two colours.

Article 3: There are two players, and each shall possess stones of [one colour].

Article 4: Each player shall have the right to move by turns.

[page 91]

Article 5: When a final "liberty" ("katsuro" in Japanese) is taken/occupied by the other player's stone then that first player's stone shall be removed from the board.

Article 6: No stone shall be placed "in check" on its final "liberty" without causing the removal of the opponent's stone. [? means "suicide" not allowed]

A "liberty" for one stone means a possible move to any of [up to] four neighbouring points connected by a line.

This applies correspondingly to two, or more, stones.

Article 7: The repetition of the same pattern shall be prohibited unless the right to an alternate move is disregarded. ["ko" rule ?]

Article 8: The end: if the right to an alternate move is abandoned three times successively [i.e there ar e3 consecutive "passes"].

Article 9: At the end, the following methods shall be used for judging [the result/score].

Living ("sei" in Japanese)

1. Stones which cannot be taken away from the board, or which can protect themselves from being taken away, shall be called "living".
2. Those stones which are not living shall be taken away from the board at the end of a game.

Captured Territory ["ji" in Japanese]:

A territory on a board which is enclosed by independent and living stones shall be called captured territory. In this case, one point shall be one point of captured territory.

Enclosure:

1. By "To enclose one point" we mean that on its nearest [maximum] four points ("liberties") [connected by] lines we find the same coloured stone. This also applies to the enclosure of two or more points.
2. Stones which are taken away from the board [i.e. captured] shall be deducted from that player's points.
3. The difference between the territories thus obtained shall be used for judging, and the player who has earned the larger territory shall win by the difference.

In October, 1940, just before the Pacific War broke out, a report entitled "Rationalization of Go," by an American [see a later edition (which includes the 1940 one?) -- Olmstead JMH and Robinson KD, 1941 -- Craig Hutchinson's reference "Ol41"], gave us a chance to discuss the rules of Go. Again, I tried to revise Yasunaga's plan after I had discussed it with him very carefully. My efforts came to fruit in the article "A Tentative Plan for the Rules of Go" (in an earlier edition of this book).

In this plan the terms used were complicated, and I myself was dissatisfied. Besides this, since the war, I thought of a board position that was not covered by this plan. After the war, the pamphlet entitled "The Structure of Go" [Olmstead JMH and Robinson Karl D, 1946, Craig Hutchinson's reference "Ro46"], was sent to me by the American again (see Chapter 4) [where it is discussed in detail]. It may have served to stimulate the "Nihon Kiin" (Japan Go Society) to organize a Rule Establishment Committee, and lay down "Go Rules of Japan Go Society". These rules cannot be called new ones -- I attended the committee -- but they were nothing but comments on the conventional rules of Go. Since then, Americans have continued their study of the rules, and the Nihon Kiin has expressed its interest in their studies. Some problems have still remained unsettled.

2: The Characteristics of The End of a Game and Calculation in Go.

[page 93]

As I stated above [a previous chapter, where he distinguishes between Go, primitive Go, and Igo -- in his terminology, Igo is the game we all now play], in the simple patterns of Go, a game is a struggle between Black and White for existence on the board. It is at the end that both players admit neither the necessity nor the possibility of any further move. Judging is done on the basis of the number of Black and White stones left on the board at the end of the game. There is no reason for difficulty, and the judging is a comparison of two whole numbers.

But in Igo, the situation is different and not so simple. For instance, the concepts "living stones", "seki" (literally means "blocked"), and "dead stones", seem so simple to players that they have become standard, but they are no longer clear theoretically, and there are some patterns in which it is difficult to make a decision. And also in a game there is occasionally a disagreement on "teire" ("a [remoulding] move"). What are the causes of these problems? I will explain them in the next section.

What is the end of a Go game? One of the remarkable characteristics of Go is that one ends a game with "dame" (literally "useless" points). The players declare the game is ended -- they do not mean to claim that "there is nowhere to play the stone", but that "the next move does not affect the result of the game". It is time to end the game if both players admit [agree] that the result will not be changed by further moves. Since ending a game in this way should be backed up by the skill of the players, in a sense, the game-end is at the mercy of their subjective judgement. But, it is a well-known fact that judging can be fully objective among Go players. It is worthwhile to note that "proficiency" is considered prior to the end of a game; there is Go prior to the rules; the players intuit Go prior to Igo.

At first there is Go, and Igo is nothing but one of its forms. This fact cannot be ignored when we think of "the rules of Igo".

I hear someone saying "it is difficult to learn Go". Why? The beginner has the rules explained by means of made-up Igo, and therefore intuition to Go is poor. And when he begins to understand the meaning of the learned rules, and their propriety, his intuition develops. I think each of you -- readers -- has had such an experience.

Generally, the players tend to avoid an unnecessary move although it may be inevitable. This tendency is especially strong in Igo, and the stronger the tendency becomes, the more skilful the players become. Because of this, untouched territories at the end are "dame" in a bad sense. "There is no 'dame' among poor players". This statement is good irony.

"The beauty of dame".

This is a witty remark which Yasunaga used to make. No unnecessary move is made, and therefore "dame" remain at the end. There is a beauty where "dame" is left for itself. This beauty is a remarkable characteristic at the end. This cannot be seen either in traditional Chinese Go or in primitive Go. The Nihon Kiin (Japanese Go Society), admitting some irrationalities in calculation of Go, still dares not to give up this "dame" -- only because of its beauty. In a game of Go, the end is announced; the numbers which affect the judging are already clear, but for convenience of calculation, the dame is arranged by placing stones, and all the Black and White stones on the board are sorted into groups of living stones, seki, and dead stones. The next step is that all the dead stones are taken away from the board, and Black (White) dead stones are subtracted from the points in territories enclosed by Black (White) living stones. According to the difference of the numbers of points between Black and White, judging is to be made.

At this moment, the important thing is that a "captured territory" in Igo is the territory which is enclosed only by living stones, and the territory in seki is not "captured territory". Seki are the stones which exist being with Black and White stones, and we do not maintain that the territory surrounded by these stones belongs to either side; this perhaps is a Japanese point of view. On the contrary, Americans have studied this particular point. We Japanese must study it too.

Anyway, Black and White stones at the end of the actual game of Go, have to be sorted into one of the three categories: living, seki, and dead stones. This discrimination relies on the possibilities (potentiality) of the art of Go. This also proves that Go is prior to its rules. Then the problem are "What is a living stone?" and "What is seki?". They are very difficult - the only extremely difficult problems in Go.

3. Living and dead stones; four stones in a corner ["bent 4 in the corner"].

Every player of Go has a clear idea of living and dead stones, or seki. This idea has been learned from his past experiences -- games and study -- and is not taught by others or through books. Some people disagree with me, saying "Everybody has been taught 'A stone with two eyes is living.'" But it takes us long experience to learn what stones on the board have two eyes, and nobody has ever been taught the definitions of eye and seki accurately. Let us think about the problem which seems to us the simplest -- "A stone with two eyes". Living stones posess two eyes perfectly. What is an eye? An eye is a spot which is enclosed by a series of stones.

The sentence looks complete. But, there is the following discordant example. In Diagram 2, White stones are called, "living with a false eye" or "living with two head" [also "double-headed dragon"]. The two eyes are not false, but perfect. Each eye is a spot which is enclosed by a series of three stones. Speaking of the Black stones in Diagram 2, their two eyes are not completely enclosed by a series of stones. Previously, I almost gave up trying to regularise "an eye" directly, because it is very hard to do. But after the war, I was much surprised to see the definition of this "eye" made clear by Robinson and Olmstead in their research. Although it is done beautifully -- as I had guessed before -- their definition required long sentences. (see Chapter 4, p 69)

Diagram 2

[page 97]

In Go we play stones one by one, and stones with two eyes can never to be captured. This is the original reason for saying that a living stone has two eyes. I take this statement and adapt it for definition as follows: "However many times the opponent plays his stones, the stone which cannot be captured shall be a deemed to be living stone with two eyes". It seems conservative, and somewhat indirect, but I think this is the best, and wisest, definition ever made. The purpose in defining this "living stone with two eyes" is very clear. Thus, the only remaining problem is how to regularise it in the best terms. That is a matter of skill in the use of words. If we think of this "living stone with two eyes" and "seki" at the same time, the situation is much more complicated. As to the question about what a living stone is together with "seki", the simplest answer is "uncapturable stone". It is obvious that this definition is not sufficient according to Diagram 3. Two marked Black stones in Diagram 3(a), and one marked White stone in Diagram 3(b), are living stones in a position to be taken off. According to the Yasunaga draft, these stones are taken into account, and "The stone which is capable of protecting itself against being taken away from the board" is regarded as a "living stone". According to this, the problem in Diagram 3 can be solved, because the stones can be protected by playing other stones.

[page 98]

Diagrams 3a and 3b

Diagrams 4a and 4b

In regard to the rules on life or death of stones -- [consider] "bent four in a corner". A good example is the White stones in the corner in Diagram 4. White has no chance to place stones but Black can obtain a "ko" by playing 1 in Diagram 4(a) followed by 2 at A to give Diagram 4(b), and a "ko" after Black captures White's 4 at "A". There is another way to finish up this game without "ko". The White stones become unconditionally dead if black stones outside are living. The reasons are as follows:

1. "Kozukushi": the White stones can be captured if all the stones for "eternal alternation" are captured [? i.e. if all "ko" threats have been prevented]
2. The possession of "the right to play" [being the one who can play first, sensibly?]: White has no chance in this game. The right to play is only with Black.

(1) may be called the basic reason, because it was the original reason that the stones for "eternal alternation" cannot always be taken away by placing stones. Generally, seki contains stones which cannot be captured [unless the opponent ignores a move]. For instance, in Diagram 5, White "2 - 1" for "eternal alternation" cannot be taken away.

Diagram 5

[page 100]

(2) was taken up at first in the Yasunaga draft, but it cannot be compatible. In Diagram 6, it is obviously seki, but the three White stones and Black stones inside have no reliable stones and are in a position to be taken away at any time. Speaking of the possession of the right, they are in the same position as White in Diagram 4.

Diagram 6

[and there's an SGF file as well.]

We take the meaning of the word "right", not as right referring to the stones on the board, but to the place where the stones are played.

The White stones in Diagram 4 are placed in Black's territory, and on the contrary, the Black and White stones in Diagram 6 exist where they should exist. Such explanation also can be made too, and Diagram 6 can be applicable to it, but still there is a counterexample to it.

Diagram 7

[and there's an SGF file as well.]

[page 100]

Diagram 7 is called "Hanezaki", and is seki as a whole. Three Black stones marked [triangle] have no reliable stones and also lie in the territory of White's existence.

In Diagram 7, if White takes all three marked Black stones, the next time four White stones will be captured and White will lose. Anyway, in this situation the first player to move will be defeated.

We have thought over "four stones in a corner" from various angles, but we fail to find any adequate reason for the unconditional death of those stones. If we move and capture them, it will lead to "eternal alternation". In this situation, it is not reasonable to sentence all these stones to unconditional death. It may be natural that we have not found any evidence for the sentence [of death].

4. Unsuccessful Revised Plan.

If we deny the conventional law by which "four stones in a corner" is sentenced to unconditional death, what we should do? Our idea is based on "It is unreasonable that the stone which we cannot capture without any sacrifice is sentenced to be unconditionally dead stone". Placing any stone on the board in order to capture other stones is itself a sacrifice (according to the present law). It is impossible technically to regularise the situation by the necessity, and lack of necessity, for placing stones in this case. Therefore, the idea ought to be expressed as follows: "All dead stones shall be captured by placing stones". This idea maintains that we will go back to the primitive pattern of Go, and it is not inconsistent with our first opinion. From this standpoint, I tried to revise the Yasunaga plan twice. I tried to provide reasonable rules, while adapting the present conventional law to them, but I failed again.

The definition of "living stone" is as follows in the first revised plan:

"Living stones" shall be defined as follows:

(a). White stones cannot be taken away by Black's successive placing of stones when he chooses.

(b). Although Black has the first move, the white stones can be corresponded to (a).

(c). Besides the above cases, the White stones can prevent themselves from being taken away by White's first move.

(d). Besides the above cases, the stones can be connected with the stones in (c).

The stones in (a) and (b) shall be called "independent living stones" and (c) and (d) shall be called "seki".

(a) means "living stones with two eyes" (defined above). In (d) the word, "connected" is used. I was not satisfied with this word, because its meaning is vague, but I found the basic defect in (b) later. Please see Diagram 8.

Diagram 8

[and there's an SGF file as well.]

[page 103]

This is a pattern of seki outside of "hanezaki", and as a whole it is a seki. But according to (b), there is no chance on the part of Black, but strange cases appear where these two [marked, White] stones are "independent living stones". As another example, there is Diagram 9.

Diagram 9

[and there's an SGF file as well.]

[page 103]

The characteristics of this diagram are:

1. If White starts first, he will lose.
2. Black can capture White stones on either side [but not both].
3. But [some of] the White stones will be "live" if the stones on the other side are captured.

The "three stones in the corner" become "living" according to (b): the White stones in both sides do not fall under any articles; as a result, they are sentenced to be "dead stones", but while the White stones are captured on one side, the White stones on other side become "living"; then this fact makes it unreasonable that the White stones on both sides shall be "dead", in this case. Even only these two examples required changes in my revised plan. The second revised plan was "The Plan for Regulation of Go" (1943).

More detailed, longer sentences were used for the definition of "living stones". I thought I had been successful with this plan at that time but I was not actually. I do not like to write complicated, long sentences. Now I have noticed a curious thing about my plan -- that is, "I have repeated the same thing". I should have noticed it earlier.

Once I made a definition of "living stones", I tried to find an objection to it.

I am afraid that I have described this vicious circle several times, and now I have no courage to do it once more.

Go is infinite in the sense that an arbitrarily large board is imaginable. We cannot foresee what will happen next on this board. The definition is certainly dangerous to make; e.g. "The stones which meet such and such requirements shall be 'living stones' and otherwise they shall be 'dead stone'". And furthermore, it will be presumptuous on my part. Now I have changed my idea -- obviously my attitude is now different from what it was before.

We should forego the conventional law on "the stones in a corner" in order to rationalise the rules of Igo in Japan. What will happen then? Let us study the matter in the next section.

The next diagrams are concerned with "four stones in a corner", and similar relations.

The next two diagrams concern "four stones in a corner" and similar matters. If I were to say that these stones are "unconditionally dead", then people, at present, may not agree with me.

[p 105]

In Diagram 10a, if [asWhite] you start to attack, you will do so according to the order in Diagram 10b.

Diagrams 10 a, and 10 b

[and there's an SGF file as well.]

In Diagram 11, if Black starts to attack, what will happen? Does White agree to the death sentence on all his stones?

Diagram 11

[and there's an SGF file as well.]

[page 105]

5. Other Problems.

The rules, including the definition of "living", and "dead" stones, are unsettled and hazardous. This is the conclusion of last section: the "dead" stones shall be taken away by placing stones. Theoretically, this is a return to the primitive Go. But if we revise some parts in calculation of primitive Go, it may be possible to make the most of the conventional law of Igo. I think there is no other stone unturned, besides this.

In order to develop this way, it is necessary to study the causes of the problems happening at the end of a game, The problems are:

1. "Four stones in a corner", and similar matters.
2. Necessity of "teire" [re-moulding -- see later].
3. "Three points without capture", and similar matters.
4. Unusual situations at the end of a game.

Let us study 2, 3 and 4.

Necessity, or lack of necessity, of Teire [remoulding].

Diagram 12

According to conventional law, it sometimes become controversial. In Dia. 12, after White has captured a Black stone at "a", because of the fact that White has the majority of the chances for "eternal alternation", can White capture the arrested single Black stone? There may be arguments pro and con. From the standpoint of the conventional law -- individual stones shall be investigated and categorised as "live" or "dead". Actually, if a [White] player holds out until "dame" is "teire", he can win by one stone, that is to say, it results in the same situation as "lack of necessity."

[There is some original text that has not been translated. It refers to Diagrams 13a - 13c.]

[page 107]

Diagram 13

Three Points Without Capture, and Similar Matters.

[page 107]

Diagram 14 a

In Dia. 14 a is a so called "three points without capture". If Black plays first, at "a", and captures four White stones, then what follows is shown first in Dia 14(b), and then in Dia 14(c). After Dia 14(c), Black can capture the single stone -- White 3. Black has captured five stones, and lost three, and as a result, Black has lost two stones [? compared with assuming that White stones are dead]. However, if White plays 5 in Dia 14(b), at "a" instead, then White can hold out [and play a "ko"], so it may be reasonable that Black loses by two stones.

Diagrams 14 b, and 14 c

Returning to Dia 14(a) -- if White has the first move, and plays at "a", then Black re-captures, and we have the sequence in Dia 14(e). As far as White 2, Black has gained five, and lost two [sic!], stones. Black can also turn the situation into "eternal alternation" by Black 3 -- as a result, it can be said that Black can win by three stones. Consequently, in this situation, it is advantageous to give the first move to the opponent. According to the present law, neither contests the other under this situation, and it judged that Black wins by three points.

Diagram 14e

I am not familiar with what has been said about "three points without capture". This peculiar agreement has been made as a convenience only for this situation. I think there is no authority for this. Until a game ends, neither moves, but the game must be judged somehow, and in this situation one Black, and four White stones, are supposed to be captured, and therefore, Black may as well he said to win by three stones.

[page 108]

In Dias 15(a), 15(b) and 15(c), the situations are slightly different from one another. However, needless to say, to decide by so many uncaptured stones is not good, and too complicated. The agreement should be abandoned.

Diagram 15 a, 15 b, and 15 c

[and there some corresponding SGF files: Diagram 15 a, Diagram 15 b, and Diagram 15 c]

In the primitive Go laws -- dead stones are actually taken away, and all the stones, on the board are living -- before the end of a game, Black must have the first move in this situation and no controversy arises.

The Extraordinary Situation at the End.

This problem happens because of the contradiction between the final results and the banning of repetition of the same pattern (the agreement in "eternal alternation"). It is found, not only in traditional Go, but also in Igo. We can say that it is almost impossible for such a situation to happen in a game, but as long as such an occurrence can be imagined, we have to provide a rule for it.

In the process of a game -- under the prohibition of repetition of the same pattern -- all is simple and clear. There is no room for any difficulty. But a board is limited in size, and the result of a game has to be judged. Until the time of the end, the game continues and the players can place stones on the board until the end of a game. But at the moment of the end, they simply cannot change the situation on the board. The numbers of "dead" and "living" stones which the players have captured in the process of a game are different from what they should have been. This phenomenon takes place in connection with the "prohibition of the repetition of the same pattern". This prohibitive rule is "develop a game by placing stones in other part of the board". Here a contradiction is found if the players say that there is no other part for stones. Let me take up one example. From the viewpoint of simplification of the rules of Igo, one of the primitive Go rules is very noteworthy. It says, "If both players pass twice successively, it is the time of the end of a game", and at this moment the player whose number of stones is larger than other's is the winner of this game". According to this article, the following situation is imaginable.

[page 110]

Diagram 16

In Diagram 16, for simplicity's sake, I make use of a miniature board. If Black plays at 1, then White takes "eternal alternation" by playing "a", then Black has no place for stones, so he passes, and White passes next. According to the [rules of] primitive Go, this is the end. And White wins by two stones; the two "stones in a corner" are "living" [maybe this just means that all White stones in the bottom left are alive?]. In this case, Black is prohibited from capturing White's stone at "a", so the situation will not change if "they can pass three times". This unusual situation has been discussed since the early days, and therefore, the Yasunaga draft adhered to it. Yasunaga says about it "When a player passes, the situation before the pass shall be allowed to be restored. After three successive passes, the game shall end". According to this, when Black and White pass in Diagram 16, Black can capture White's "a" next. This situation can be solved in the normal way. But this article may as well recognise infinite circulation [an infinite cycle of moves]. Because of this I did not adopt this article for my revised plan.

[page 111]

Diagram 17

Diagram 17 is a so-called "long eternal alternation" ("mannen ko" in Japanese, "mannen" means "thousand years" in English). If we follow the sequence -- White captures at "a", Black pass, White pass, Black captures the single stone, White pass, Black pass -- then long, and infinite, circulations [cycles of moves] take place. (The player who stops placing stones will win-- at Black 4, or White 7, either of the players may stop -- so it is not a good example). In my old edition there is one of Robinson's rules: "The repetition of the same pattern just after a pass is permissible, but the third repetition is not allowed. Three successive passes end a game". According to this article, there no infinite circulation, but the following example is imaginable.

Diagram 18 a

In Diagram 18 a, when there are no dame and chances for "eternal alternation" ["kozai" in Japanese. "zai" means "material in English]. After White 1, and Black 2 at "a", Diagram 18(a) becomes Diagram 18(b).

Diagram 18 b

Then White 3 causes seki according to the present, and the primitive Go, rules. According to Robinson's rules, when Black 4 passes, White then unexpectedly plays 5 at "a". This is the repetition of the same pattern, but because the previous turn was a pass, it is permissible, and White 3 and 5 cannot be captured because of the repetition of the same pattern. These Black stones ought to be "dead".

This unexpected situation is caused because of the limited size of the board. In order to explain one unexpected situation, one has to make a new rule, and on account of this new rule, a new unexpected situation comes up. This may be called a vicious circle, as may the definition of "life of stone."

Whatever way we may develop in order to define the "end of a game", we can not prove that any unusual situation will not arise. But in reality, there is little possibility of this kind of situation. And therefore, I would like to adopt the simplest provision: "A game ends right after each player passes successively". One might combine Robinson's rule and Yasunaga's plan: "The repetition of the same pattern is permissible, if a pass is done between the patterns. But the third repetition is not allowed. A game ends with successive three passes". This rule is very effective, but still it is not sufficient to prove the impossibility of unexpected situations.

6. One Point of View.

I would like to submit one plan in order to settle the problem. Inasmuch as my plan, in the old edition of this book, resulted in failure, it is my duty, in this new edition, to make a suggestion for a solution of the problem, regardless of the value of my new plan.

Let me first clarify my purposes and position.

1. The rules shall be perfect; "perfect" shall be the objective judgement and prevent all troubles in a game.
2. The freedom of placing stones shall be guaranteed.
3. In many cases, the judgement based on the conventional and new rules shall be expected to coincide with each other as much as possible.
4. The conventional rule on "four stones in a corner" shall not be recognised.
5. "Three points without capture" shall not he permissible.
6. The possibility of "uncaptured" three stones at the end of a game shall not matter. This type of pattern very seldom occurs at the end of a game.

Among the above items: (3) was discussed in the previous section; (5) very seldom takes place in a game, and if it does, it will be settled smoothly. (3) and (4) seem, to be a contradiction, but actually the conventional law seldom comes into force for "four stones in a corner". "Four stones in a corner" occurs very often in a game, but naturally disappears in offensive moves, and does not usually remain until the end of a game. Seki is rare too -- we understand that possibility of seki is very small according to the statistics.

The conventional law comes into strong force for the coexistence of "seki" and "four stones in a corner" at the end. This does not happen very often. (4) means the return to the primitive pattern, and it seems a big problem, but actually it is not, and it is reasonable for rationalising Go. Thinking of a Go game, let us provide rules for it, one by one. Please read the following section, in regard to the exact definitions of rules and their statutes. There is no trouble for the board and Go stones. Concerning "alternate turns," it would be most desirable that turn be subject to the players choice: he can start to move anywhere and can pass at any time. Therefore, let me provide the article as follows:

As the result of a move, a new pattern should be created on the board as a whole. So that, it must be better to include in this article a byelaw to prohibit the repetition of the same pattern. Then a turn is entirely subject to the players, and a suicide move is permissible (see p. 13). Under the prohibition of the repetition of the same pattern, no problem occurs in the middle of the game -- at the end of the game, instead. We would like to prescribe as follows: "Two successive passes end the game". But we cannot, as explained above. Since simple exchange ("miai" in Japanese, that means "meet face to face" literally in English) (inevitable exchange) as well as remoulding ("teire" in Japanese) are omitted, the game ends.

The results of the game have already been made clear, so that it is a real end. But as usual, it is too vague to be applied to any rule, so that after dame is cleared ("tsumeru" in Japanese, and that means "checkmate" literally in English) and remoulded, the game shall be ended. The former may be called "temporary end", and therefore, two successive passes shall mean the temporary end of a game, and afterwards, furthermore, two successive passes shall end the game completely.

The last two passes happen when both players agree that their further moves will be disadvantageous to them. Between the temporary end and the real end, the provision for alternate move is unnecessary: therefore, the numbers of stones used during a game need not be always the same until the end of the game. It was extremely important when we consider the rules of Go. This too is one of the characteristics of Japanese calculation which I have long overlooked. In order to avoid confusion, we will not think of seki now. When all the "dead stones" are removed from the board at the end of a game, the board is divided into two parts: Black and White. For convenience, I use the words: "Black spot" (similarly "White spot") to mean where the Black stones are placed, and points are the crosses in the territories enclosed by the Black stones -- the total points shall be A1.

[page 116]

"White spot" shall be defined similarly, and White's total points shall be A2. (the number 1 means Black, and 2 means White hereafter). The number of moves which have been played until the end of the game is B. Then, judging made of the comparison between Al - B2 is always accurate. All problems take place in A1 and A2, but they can also be clarified by moves. These moves are done after the end of the game, so they do not affect B1 and B2. And by the moves of Black, the points where the Black stones are placed will increase and the points enclosed by the Black stones will decrease. And as a result, the total does not change. After the end of the game, if the agreement reaches A1 and A2 between both players, the calculation will be done according to conventional law -- it is the expedient way. If no agreement is reached, the players play stones, and take away the "dead stones" -- they continue moving until "living stones with two eyes" remain. The judging is made, and the calculation of A1 and A2 is no longer doubtful.

Diagram 19

[page 117]

Let us now study the case including seki. Inside of a seki, "'captured territory' ("ji" in Japanese) is enclosed by one side's stones". This is the simplest seki, and the next simplest is "one side dame is 'captured territory' (like "a" and "b" in Diagram 19, either side can "live"). Inside of a seki is not "captured territory". This pattern causes much trouble, but [? only] according to our conventional law. Then the rules can be as follows:

At the end a pattern of two successive passes is called "decisive pattern". The number of wins and losses is judged as follows:

"Living Stones with Two Eyes:"

Let us adopt the statement in section IV (see p. 99)

"seki"

These are the stones which are not "living stones with eyes" in decisive pattern. After the end of a game, the stones increases in seki are "C"

"Black's spot: (Al)":

In a decisive pattern, the points where the Black stones are placed, and the way of Black living stones with two eyes. A2 is defined in the same way.

Black's score

(A1 - Bl - C1). Similarly, White's score is (A2 - B2 - C2)

[page 118]

The difference between the scores shall decide the game. This is a rule. The reason for the subtraction of C2 is caused by the change of A due to the moves after the end of a game.

The definition of "living stone with two eyes". C is necessary because inside of seki is not 'captured territory'. After three times of two passes for each, the decisive pattern comes up. At first I emphasised the agreeable feeling "Here we are at the end". One may call it a luxury. After the temporary end, whenever the players agree with each other on "life" "seki" and "death" of stones, "remoulding at the end", they may calculate the results according to conventional law. The number of points at the end is calculated correctly in either way. It is necessary in this rule to study how to solve "remoulding". This problem is not solved by the present law; it can be settled in any way so long as unusual situation takes place.

Diagram 20

In diagram 20, if the "eternal alternation" is kept in the pattern by Black "a" until the end of the game, White gains one point. This is to say, it is unnecessary to do "remoulding". If I explain it according to the rule, whether White "b" is placed before or after the "end of the game", one point difference is made in A2.

[page 119]

This situation is very significant. I remember that one Go expert insisted on lack of necessity for "remoulding" in this pattern. This is not an unusual situation but rather "a large eternal alternation", so that it is "eternal alternation". Therefore, it is not easy to hold out while "dame" is "tsumeru" ["checkmate" in English], the players can enjoy the game because of this situation.

But in this meaning [interpretation], a one point struggle takes place in connection with "half eternal alternation". If the next step to the "half eternal alternation" can be postponed until after the end of the game, the player can get one more point. At the temporary end, if there are three or more than ten dames [!?*^!] -- it is very normal -- there will be five points difference in "kozai", at the temporary end, so this one point is out of the question.

Very seldom there is a small number of dames at the temporary end. Then this one point becomes controversial. If it is permissible, we can think of checkmating "dames" in the way of making "half eternal alternation" on purpose. (See Dia. 19, page 15 - [reproduced below]) -- White starts at "a"; we have a, b; c, d; e, f; a (takes ko), g; h, d (re-takes ko); i, j; a (ko), pass; d (connect) -- White has more ko-threats.

Diagram 19 from page 15

[page 120]

Diagram 21 a

Diagram 21 b

The probability of "half eternal alternation" played at the end of the game is one-half because "half eternal alternation" appears in the odd numbers at this moment, the number of "dames" is very small, and conveniently the probability of "kozais" on one side only is considerably small, too. In my view, the probability of the questionable one point is more or less one-hundredth, and this one point determines the result of the game even less often than this. Some people may like to leave this problem untouched, and some others may insist that, even though it is a slight probability, something must be done about it. I am inclined to agree with the latter.

In order to deal with this problem, it would be best to admit one exception for "half eternal alternation", as follows: The "half eternal alternation" in the pattern at the end of the game (one of them in diagram 21(a)) is the decisive pattern as in Dia 21(b), and one point is subtracted from Black's total score. This is, however, the exception only in the "half eternal alternation".

Diagram 22

For instance, White can hold out one point in Dia. 22. Although this exception is simple, it is extremely difficult to set down accurately. In the next section, I will sum up my point of view on this, and I do not use this exception more than for convenience's sake.

From the viewpoint of the necessity of "teire", we have to add the following byelaw: "Then the game is ended with 'Black(White) take 'eternal alternation' 'White passes' and 'Black passes'. In this case, one point shall be subtracted from the total Black (White) score". Then both eternal alternation and seki, or both eternal alternation and death, are abused [?], and the means to get one point more is contrived. In order to avoid this: "But, except the end with White eternal alternation, and Black eternal alternation, White passes, and Black passes". I am inclined to add this clause. But this is not sufficient. I think we may be satisfied with the exception for "half eternal alternation".

7. The Rules of Go ( One Plan )

Excepting Article 4 and the written rules of primitive Go, I adopt here all rules and exceptions up to article 3. Please see page 19. The following articles are continued from that page.

Definition:

If the right to move is abandoned twice successively, this becomes the temporary end.

Afterwards, if the right is abandoned twice successively again, then this is the end.

Until the end, the number of moves which have been done are as follows: Black Bl and White B2.

Afterwards, if the right is abandoned twice successively, the pattern on the board shall be called the "decisive pattern". In the decisive pattern, the Black stones which cannot be taken away by any number of successive moves by White shall be called "stones with two eyes".

White's stones with two eyes shall be defined similarly.

In the decisive pattern, the crosses where the Black stones are placed and the way-outs [liberties] of the Black stones with two eyes shall be called Black's points ["jiten" in Japanese]. The number of points shall be A1.

[page 122]

White's points, and A2, shall be defined similarly.

In the decisive pattern, the parts of the board which are not "stones with two eyes" and their way-out [liberties], shall be called "seki". After the end, the number of stones increased in the part of seki shall be C1 and C2.

Article 4:

(A1 - B1 - C1) and (A2 - B2 - C2) are compared. Then, if the former is bigger, Black wins. As for White, vice versa. If both are equal, Jigo shall be declared.

Remark 1:

During the optional time from the temporary end to the end, when agreement is reached between the players as to the "life", "seki" and "death" of all stones, calculation according to conventional law can be made. The results will be the same.

Remark 2:

Okigo ("oki" means "to place" in English -- hence "okigo" = "Handicap Go"): In okigo, the definition of B1 shall be made as follows:

"The number of stones [played] up to the end" plus "the number of the [handicap] stones placed".

Remark 3:

If C1 and C2 are not counted, dame on one side in seki can be regarded as "captured territory".

As for "teire" at the end, the following exception can be recognisable as a rule.

"After 'hanko' ["half eternal alternation" in English] and 'toru' ["take" in English], pass, and pass, then the game ends. The results are one point better than the sequence 'hanko' and 'toru', pass, 'hanko' and 'tsugi' ["tsugu" means "to succeed" in English], and pass, pass. Then this one point is subtracted".

[Apparently, some original text not rtranslated here] Comments:

I rationalise Igo with the rules in the next page.

[page 123]

1:

1. No-judging game is avoided by the prohibition of the repetition of the same pattern.
2. Suicide move is permissible in order broaden the freedom of moving.
3. The definition of "life and death" of stones by "possibility" is avoided.

Please see Chapter II about (1); page 14 about (2), and page 104 about (3).

2:

In case the first move is not advantageous, pass is permissible. This is the temporary end.

3:

After the temporary end, the players can continue their moves, that it to say they checkmate "dames". If the number of remaining "dames" (including "teire") is even, then pass is permissible. But if the opponent passes, and the number of remaining dames is odd, then one of the dames should be checkmated. If the player passes at this moment, the game ends, and he loses one point. Anyway, it would be safest if dames are checkmated, without a pass. After dame is checkmated and "teire" is over, then the player can pass; otherwise, he loses.

4:

At latest, up to the end, both players reach an agreement, and calculation according to conventional law is made -- see section 6. This is the most common case, but otherwise, moving continues. Playing must continue until there is no place for more stones. If one of the players passes on the way he may lose.

[page 124]

5:

During this time, all dead stones are taken away from the board. The "four stones in a corner" and "three points without capture" are settled in a proper way. And all stones on the board are stones with two eyes, or are in a seki. Untouched dead stones shall be regarded as seki".

6:

In the decisive pattern, A1 : Black's points in the end are foreseen in most cases. After the pattern of the end, the number of the stones in "seki" is P1. Living stones in other places are Q1. Unplaced crosses in the space of Black (the crosses on White's dead stones) are R1. Then:
A1 = P1 + Q1 + R1
As for White points:
A2 = P2 + Q2 + R2

By moving, if Q is increased, then R is decreased [by the same amount]. In the decisive pattern, Q is increased, and R consists of the stones with two eyes only. The total does not change. Calculation according to conventional law is made as follows:

Instead of the decisive pattern, P, Q, R are used at the end:

A1 - B1 = P1 + Q1 + R1 - B1
A2 - B2 = P2 + Q2 + R2 - B2

These two formulas are compared. By how many moves (B) how many points (A) are captured is the main question. and this is the difference (A-B). We can understand Igo thus.

[page 125]

7:

As for the question of teire; "Teire is not done for unnecessary places": this matter-of-course attitude is taken up for it. But, on account of this attitude, contrary to the expectation of some people, there are some cases where one point error is made in calculation. The problem on "half eternal alternation" is as discussed before.

8:

Seki is regarded as a neutral zone in conventional Go, and "captured territory" is not recognised in this area. This statement is adopted as it is to these rules. The crosses placed by the stones of seki are points, but these are not advantages because the number of moves is subtracted from the points. The crosses enclosed in seki are not counted as points, and therefore the only stones included in calculation are the stones which have been taken away - as our common sense on Igo.

[Apparently some original material here was not translated].

If the number of the stones are increased in seki because of moving after the end, this increased number is not regarded as points. This is the byelaw for C in article 4. This seki is in the decisive pattern.

Diagram 23

Diagram 23: questions concerning "teire" often become controversial. According to conventional law, teire is not necessary. Neither is it on the basis of this law. It is left out, and regarded as seki as a whole. However the move to capture two stones by Black at "a" increases four points and decreases two in Black's territory as an inevitable order, at the same time it increases four points and decreases two in White's, it does not make any difference in calculation.

After the end, Black "b" does not increase Black's points. (article 4)

[page 126]

9:

[Apparently some original material here was not translated].

The byelaw for C in article 4 is delicate. Some may say it is one of the difficulties in Japanese Igo as long as it is necessary. On the contrary, I am inclined to think of the better rule.

When the byelaw for C in this article looks strange, the almost unimaginable case comes up as to seki. It has seemed seki about time of the end, and before disordered, and then again it becomes seki in the decisive pattern. This can only be imaginable in connection with "four stones in the corner" or "mannen ko" ("mannen" in "mannenko" means "ten thousand years") -- generally it is the pattern "kozukushi" ("kozukushi", "zukushi" means "continuance")

In this case there are some changes in the order after the end. We feel as if a new game has started after the end of the game. As a matter of fact, the game may turn.

I will give two diagrams as examples. The possibility of their appearing in an actual game is small so that they are unusually arbitrary. They are drawn on a miniature, 11x11, board.

[page 127]

Diagram 24 a

Diagram 24 b

[page 127]

Dia 24(a): let us assume that we are at the end of the game with forty moves each already played. The bottom-left corner is "seki", and Black loses by four stones. After the end therefore, Black tries to capture the White stones. They then play the sequence: Black A2 (atari), White D1(captures 4 stones), Black B1, White A1(atari), Black A2(captures single stone -- atari), White J11(atari), Black L11 (captures 2 stones), White A1 (recaptures ko), Black A8(atari), White A10 (captures 2 stones), Black A2(retakes ko), White B11(takes 2 single stones), Black C1 (takes White group), White K11(captures single stone), Black C6, White D11, Black C2, White L11. We now have Dia 24(b). (To complete "living stones with two eyes" after Black 19, it is necessary to move several times more).

In this decisive pattern, there is only one seki -- in the upper right. It was seki at the end, and turned to disorder, and finally became seki again. By White 18, one point increased after the end, but it is not counted.

Black and White have 59 points each. Each player has played 40 moves. The difference is 19 each, and the game is Jigo.

[page 128]

Diagram 25 a

Diagram 25 b

Dia.25: After each player has played 50 moves, the next move was Black "a", Then the game ended. White 2, Black 3, White 4 are passes. If Black 5 is a pass, it becomes decisive pattern. Then White wins by 1 point. And therefore, Black wants to get the White stones on the upper left. We will go on playing thus: Black D11 (atari), White B11 (takes ko), Black J11 (atari), White L8 (captures), Black A11 (ko), White D1(captures -- threatens to make life), Black B1(steals eye), White B11 (ko), Black K10 (threatens to be able to start ko next), White K11(atari), Black A11 (ko), White E1(atari), Black G1 (takes 3 stones), White B11 (ko), Black L10, White D10 (takes 4 stones -- ends ko), Black A1 (takes), White J11, Black C1 (atari), White B10, Black E2, Black B2.

If Black 7 at L8 is kodate ("ko" means "eternal alternation", "-date" means "stand" or "rise"), two "kozai" ("zai" in "kozai" means "materiel") remain, but White has 5 kozai, so Black will be at a disadvantage. The position has now become Dia 25(b). This is the perfect decisive pattern, and a seki remains in the upper right. In this area Black does not have many stones, and it does not concern article 5. White's points have increased by three points, but they are not recognised as White points. We feel very strange about this. The original purpose of the rules is that the rule does not admit one stone -- J11 -- [as] a one sided dame.

Black score: 60 - 51 = 9
White score: 58 - 50 - 3 = 5

Black wins by 4 points.

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