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Regarding Thickness

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秀格棋話 [Shukaku Kiwa = Honorary name of Takagawa Kaku, based on the House of Honinbo head name of Shu with the suffix of Kaku; Kiwa = Game Talk]

厚みについて [Atsumi ni Tsuite] Regarding Thickness

名誉本因坊高川秀格 [Meiyo Honinbo Takagawa Shukaku] Honorary Honinbo Takagawa Shukaku; by tradition, when a player wins the Honinbo title, that player chooses a name starting with Shu- and appends something personal to the end; most players use part of their own name, but Sakata chose to honor Honinbo Shusai with his adopted name and others have done different things.

From Kido, September 1977

The Process of Exchanging Profit for Thickness

The topic is thickness, meaning that the contrast between thickness and profit is the focus

The most fundamental and important clash in go regarding contrasting opposition is between profit and thickness. These two elements are always in contention on the go board. If one wonders about this, it is because thickness can be converted to profit in an instant, a change of essence that is wondrous.

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Diagram 1

Here is a 5-4 point joseki that everyone knows. Supposing that this division is taken as equal, White’s profit is 10 points. Black’s thickness can be seen as a solid 20 points.

If the question is why White has 10 points, the territory indicated by the "x" symbols is 8 points (including the points due to two prisoners). If White cuts at A and captures a stone, it is equal to 3 points, if Black connects there it is zero, so that means that White’s territory there is 1 1/2 points. Besides that, there is something of a possibility that the point at B will become 1 point of territory for White. Therefore, the point at B is perhaps equivalent to 1/2 point. In that case, White’s territory is 8 points + 1 1/2 points + 1/2 points for a total of 10 points.

If the question is why Black’s thickness is equal to a solid 20 points, the reason is that in this joseki Black has used one extra stone. Looking into this…

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Diagram 2

…if the single marked White stone is added to the position, the number of stones is equal. If the joseki in Diagram 1 is considered to be equal for both sides (with the difference in the number of stones also taken into consideration), Black’s thickness is worth White’s 10 point portion plus the portion of one move. The point being that in the opening the value of one move (White’s marked stone in Diagram 2) is approximately 10 points. Therefore, the upshot is that in the end Black’s thickness is in general worth 20 points.

If Black has 20 points (thickness) and White has 10 points (profit), isn’t Black 10 points better off?! In that case, how could this joseki be equal! I ask that this kind of thing not be said. That is because repeating what I have just explained would wear me out.

What is more, the theme here is the conversion of a stable formation of thickness into profit, and how many points are involved. No one in particular made any of those remarks. I decided to write that on my own.

To Convert into Profit

Regarding Black’s thickness in Diagram 1 as being worth 20 points, the numerical value has been derived simply. That is so that for a general theory of the opening, the narrative is advanced. In speaking of a general theory, to establish a suitable factoring element, devising a conversion formula for profit and thickness is possible. (However, even though devising one is possible, in terms of go, mathematics has no meaning. The reason is that in go a general theory does not work since the reality on the board changes constantly.)

If there is such and such an amount of muscular strength, it is possible to calculate how much work can be performed. Mr. Antonio Inoki [Japanese wrestler] has a degree of physical power in his pinky, but if that pinky is taken to be material profit, roughly calculating how much that is worth in yearly earnings is close to impossible. This is a stupid metaphor, but it is absolutely not an overstatement. Go is difficult.

However, let’s think about this. At some point, this thing that is called thickness can be converted into profit. That will inevitably happen in the endgame, but sometime or another it will happen. (Do you say, "That is not what happens in my games,”? I do not know about that.) Concerning that, it is sufficient for evaluating the conversion of thickness into profit.

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Diagram 3
Those interested in replaying the game move by move can click here to do so.

This is a game played long ago, Sakata–Takagawa (Black). In this board position, White has just played 68 to make life on the upper side.

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Diagram 4

Analysis of the Outlook in the Game

<White Territory>

Lower Right Corner = 5 points

Upper Side = 8 points

Right Side = 7 points, approximately (indicated by the "x" symbols; this absolutely cannot be evaluated as being as much as 10 points)

Upper Left = 12 points (taking into consideration the circumstance where Black invades at A

and the circumstance where White plays first)

Lower Side = 3 points (with the [endgame] sequence White B, Black C, White D and Black E used for the evaluation)

White Territory Total = 35~36 points

<Black Territory>

Lower Right = 10 points

Lower Left = 12~13 points (splitting Black F and White G)

Lower Side = 2 points (around the point of H)

Upper Right Corner = 5 points, approximately (splitting Black I and White I)

Lower Side = 3 points (with the [endgame] sequence White B, Black C, White D and Black E used for the evaluation)

Black Territory Total = 30 points, approximately

Concerning profit, White is 5 points better off, but it is Black’s turn to move here. Seeing the value of that as typically 5 points, it seems that the territory is balanced. In this game, there was no komi.

5 Points? 10 Points?

On the other hand, the Analysis of the Outlook in the Game above is an extremely simplified breakdown that omits two important factors. First, White’s group in the lower right corner (5 points of territory) is still not clearly alive. The other factor is that Black’s thickness on the upper side is not included in the assessment. In particular, the second factor is critical. If this is entered into consideration, it may be said that at the point of Diagram 4 Black holds the lead.

In other words, White’s territory is 35~36 points. Black’s territory is 30 points + the upper side thickness + the move to play.

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Diagram 5

Well then, concerning the thickness on the upper side (around (A) in Diagram 5), approximately what value does it have? That is the problem. The first impression is that seeing it as 10 points is completely unreasonable. Seeing it as approximately 5 points is the second impression. However, as the true impression, is approximately 5 points correct?

Smaller than 10 Points and Larger than 5 Points

Before getting into that, let’s consider the progress of the game following Diagram 4. In Diagram 5, Black invades at 1, leading to the sequence through White 8. Instead of White 4…

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Diagram 6

…according to Sakata san’s thoughts after the game, White should have played as shown here. I think that is correct. In Diagram 5, Black next invaded at 9. The play through White 24 follows an unbranched path. Since Black is thick and strong on the upper side, during this sequence of moves, White has no leeway to put up resistance. Using White 10 to block at 19 is unreasonable and putting the shape in order to defend with White 24 cannot be helped, either. An unbranched path. With that in mind, is the reader aware of the conclusions to be drawn?

First, Black’s thickness around (A) has disappeared.

Second, it seems that Black has taken profit on the right side.

That is precisely right. Black’s thickness has disappeared in mutual destruction with the thickness White made in the sequence through 24. And then, Black has taken profit on the right side. In other words, the thickness around (A) has been converted into profit on the right side. The vague aspect has come into focus. Once that aspect has shown itself, it can be approached, and it would be good to study that in detail.

Through Black 23, the Black territory here has increased to 15~16 points. The 10 points in the lower right corner previously has grown by 5~6 points. In contrast, White’s territory has shrunk to the 3 points indicated by the "x" symbols. Previously it was 7 points, and so 4 points have been lost. In other words, Black’s 5~6 points combined with 4 points equals 10 points of profit on the right side.

In that case, the thickness on the upper side was equivalent to 10 points. A surprising outcome. However, let’s stop right here and check that we have not overlooked anything. I’ve got it!

With the thickness created by White 22 and 24 in Diagram 5, even if Black makes the turning move at A, White’s group here has become stronger [so that it is less threatened]. In addition, the Black stones that are jumping into the center from the lower side have become a little weaker. And then, there is a stronger possibility that White’s single marked stone will not be captured. When all these scraps are added together, the 10 points cannot be said to be unconditional. A number less than 10 points emerges.

In this way, the conclusion is reached that the value of Black’s thickness on the upper side is less than 10 points and greater than 5 points. When asked why it cannot be stated clearly that the value is 7 points or 8 points, it is because confidence and data are lacking to make a clear declaration.

That is just how go is. When Black turns to play at 25 in Diagram 5, Black clearly secures the advantage. Perhaps it is superfluous, but…

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Diagram 7

…and…

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Diagram 8

… show the progress of the game after that. Using the thickness as backing, Black presses White steadily. When Black slams against White’s stone with 19 in Diagram 8, Black’s advantage is clear.

Monkey and Crab

The thickness in Iwamoto Sensei’s games turned into territory bit by bit in the endgame, the hallmark of his artistic style. In his book covering the 10 Dan Tournament, Osaka’s Saito Kenmei san has written about the "Monkey Faction" and the "Crab Faction." The Monkey Faction chooses the profit right before the eyes, while the Crab Faction looks far ahead, taking seed that will become fruit. In this way, for the Crab Faction the go board is wide open and so at some time fruit will ripen. As for the Monkey Faction, the go board is narrow, and in an easygoing way, rushes ahead.

In the old days, Go [Seigen] san, Hashimoto Utaro san and Sakata san were monkeys, and Fujisawa Shuko san and I were crabs.

Today, of the players in the spotlight, Otake [Hideo] san and Takemiya [Masaki] san are significant crabs, while Ishida [Yoshio] san is quite the monkey. Recently, Kato [Masao] san is unexpectedly a monkey with aspect close to the crab.

It is interesting that all players will lean one way or the other. There is no human being sitting smack dab in the center. Even [Honinbo] Shusaku, if one had to characterize him, was a crab.

Which, dear reader, are you?

Those who wish to comment on the opinions expressed here may send their thoughts to info@GoWizardry.com. The most interesting responses will be addressed in future postings.

Robert J. Terry

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