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Profit and Loss Connected with Ladders

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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]

シチョウの損得 [Shicho no Sontoku] Ladders: Loss/Profit

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, March 1977

Pursuing a Ladder

I was wondering what kind of subject matter to use for this column this month, flipping through the pages of the issue of this magazine last month when I came across the "Flash" column. There, the highlight from a game between Rin Kaiho and Kuroda Yukio (White) was shown.

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Diagram 1

Kuroda 7 dan, playing White, daringly pursued a ladder, starting with White 1, that did not work. White ended up playing 23 through 27, then the move at 29 to kill Black’s group of stones in the lower right. The notes given in the "Flash" column were as follow:

"Although the Black stones were captured, the losses that White incurred in the pursuit was too large. Black won by resignation."

"When moving out under the compulsion of a ladder, it is crudely said that with every move a loss of 5 points is incurred. …In the case of pursuing stones in a ladder where they cannot be captured, what would be the loss for each move?"

In running out in a ladder that is effective for the capture, how many points is the loss per move? At the same time, pursuing a ladder that is not effective for the capture incurs how many points of loss per move? That is the theme of this column this month.

Running Out is a 10 Point Loss

Running away in a ladder when the stones will be captured, or pursuing a ladder where the stones cannot be captured… these are miscalculations that are rarely seen in the games of professional players.

Reading out whether a ladder is effective or not is a relatively simple thing to do. At the end of the Meiji Era [1868-1911] or during the Taisho Era [1912-1925] I have heard that there was a plan for something called a "Ladder Measurement Instrument." If this kind of thing was manufactured it would never have sold. That is because there was no need to deliberately go to the effort to make an instrument to measure ladders. The eye is much faster in determining the path of ladders.

Regardless of that, for effective ladders where the stones can be captured, in regards to how many points the loss is that is incurred by running out, it cannot absolutely be said clearly. That is because it is connected with the question of thickness, and the size of the loss subtly changes. However, let’s consider the matter in terms of the general theory.

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Diagram 2

Black’s two stones can be captured in a ladder. Setting aside any other consideration, White captures with 1.

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Diagram 3

Black moves out with the marked stone, in exchange for White’s marked stone. Putting aside everything else, White captures with 1. The exchange of the marked Black stone for the marked White stone, what in the world is the size of the loss here? That is the question. It seems that it will differ according to the board position, but, well, the first impression is that it is certain that the loss is considerably large.

Compare:

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Diagram 4

and

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Diagram 5

In evaluating the profit in Diagram 5, there are three essential elements to keep in mind.

First, over and above everything, there is one extra prisoner in Diagram 5, a profit of 2 points. This much is surely clear to anyone’s eye. After three stones are removed from the board, the thought that in regards to the three points of territory, there is the possibility that one point may be reduced to a false eye, thus reducing the territory by 1 point, can be dismissed out of hand.

Second, there is next the profit in terms of thickness. When the shape in Diagram 4 is expanded by the addition of a White stone at A, the White marked stone is shifted to B, and the result is Diagram 5.

Third, the unconditional addition of the stone at A is clearly a big profit. In addition, the shifting of the marked White stone to B results in thickness that casts its influence on the surrounding area, which is considerably big. In evaluating these two sources of profit, the structure of the board position naturally cannot be ignored. And also in regards to general theory, those who make the judgment base it on their own style of play, which is quite an important point.

The way that I see it, the difference in profit between 2 and 3 is approximately 7 or 8 points, is it not? Added to that is the hard cash of 2 points, so in the final analysis Black’s loss is approximately 10 points, is it not? So hypothetically, running out in an effective ladder may be seen to incur a loss of 10 points. [Note: presumably this is in addition to the original loss. A go proverb states that a ponnuki is worth 30 points. A ponnuki is a single, one stone capture. The two stone capture in Diagram 2 is called a "tortoise shell" = kame no ko or kame no kora, and another go proverb states that a kame no ko is worth 60 points.]

Players Who Resign, Players Who Do Not Resign

In speaking of a 10 point loss, this will have a significant bearing on the outcome of a game. Even professional players will occasionally commit an oversight, running out once or twice, and at that time they will usually quickly resign. That is because it is virtually impossible to recover from an unconditional 10 point or a 20 point loss. In the past, Kogishi Soji defeated 32 players in a tournament sponsored by the Jiji Shinpo Newspaper, but against his 33rd opponent he committed an oversight regarding a ladder and resigned. I do not know the circumstances of that game, but I imagine that Kogishi Soji probably quickly resigned.

Amateur players when they commit an oversight in the beginning of a game do not resign. Running out twice or three times, they stop and look at the situation, then say, "Ah, now I see that the stones will be captured, without a doubt." making out the truth on the board. But while saying that, they do not resign. They play on, thinking that at some point there will definitely be a chance to stage an upset. The fact that amateurs do not resign, but tenaciously persevere may be considered typically amateurish. Among these players, there are some who will using running out in the ladder as threats in a ko fight. A ko threat that loses 10 points! [son ko — it makes no sense to lose 10 points in playing a move as a ko threat… unless it is in a huge ko fight for the game, which is called tenka-ko, or a "ko for heaven and earth."]

There are even more terrible players. Some run out in a ladder, move after move, to a certain extent and then start a ko fight. They create a tremendously big ko threat beforehand, which shows just how much they want to win the ko fight. When it comes to this, there is no other way to characterize it but as heroic. Like a kamikaze pilot with a suicide bomber mentality.

An Empty Corner Competes in Value

Here is another way of thinking about the 10 point loss incurred by running out in a ladder.

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Diagram 6

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Diagram 7

Considering that in Diagram 6 and Diagram 7 there are no Black stones at the points marked with X, in Diagram 6 the marked White stone has been played. The number of stones is the same. If asked which White would choose, a materialistic appraisal of the marked White stone played in the empty corner in Diagram 6 would probably cause that way to be chosen. However, White’s thickness in Diagram 7 is considerably attractive, and not much inferior to Diagram 6. Furthermore, the move of the marked White stone has a value of 10 points. Whether White plays the marked stone, or Black plays at the point of the marked stone, totals 20 points, but the true and pure value of the profit gained by a move on the point of the marked White stone is 10 points. The marked White stone produces an advantage of 10 points in the board position. Diagram 7 is hardly inferior to Diagram 6, with the shape of the three stone capture compared to the shape of the two stone capture producing an advantage of close to 10 points. Added to that is the 2 point increase due to the extra captured prisoner, so in the end White has made a profit of approximately 10 points. Speaking from the reverse perspective, Blacks running out once in the ladder produces a loss equivalent to 10 points.

Pursuing, a 5 Point Loss

On the other hand, how many points are lost in pursuing a ladder that does not work? This is also difficult.

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Diagram 8

It is possible for Black to run out with 1 here. Since Black’s stone cannot be captured in a ladder, White’s choice of this 5-4 point joseki is already no good, but this has been done to simplify the situation. Now White pursues Black move by move starting with 2, and play proceeds to Black 43. Of course, White is very badly off. As the result of this, let’s examine the situation and determine to what extent White will lose. Following Black 43, both sides play in the usual manner, so supposing that White loses by 100 points, at the point of Black 43 the outlook is 100 points worse off. The reason for being 100 points badly off is pursuing the ladder from White 2 through 42. Dividing that 100 points by the number of times pursuing, the average one move loss in pursuing emerges. The number of times pursuing is 21 times.

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Diagram 9

However, in so saying, how the play will proceed from here on is again an inexplicable question. What must be focused on is the immense number of White stones stuck up against Black’s stones. From the start, all of them must be considered throw-away stones. The area around the points of "X" must be seen as "Black’s thickness."

By Black’s just biding time, White loses by approximately 80 points. Speaking in a simple and easy way, in the upper right quadrant White plays at 1, and then the sequence from 2 through 7 is standard. In the lower left quadrant Black 1 through White 6 is played. After this, Black plays at A, and White lives with B. Following this, when play proceeds as usual, in the upper right Black will outstrip White by 50 points, while in the lower left Black will win by 30 points. With a total of 80 points, Black’s win is the result. When the 80 point pursuit is divided by 21 times, it becomes clear that each move of the pursuit represents an average loss of 4 points. Seeing things in a little more expansive manner, it is my hypothesis that pursuing the ladder incurs a loss of 5 points each move. However, this way of looking at the situation is a very rough estimate. For instance, in Diagram 9, depending on the disposition of the upper right corner and the lower left corner, White could lose by 60 points, or end up losing by 100 points. The only thing that can be said is that everything depends upon the board position. Whether it is something like running out in a ladder or the board position where thickness is completely ineffective after stones are taken, each move is just a 2 point loss.

My theory of 10 points and 5 points is probably mistaken. I would be gratified if some bright person works out a formula for this.

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Diagram 10

Here is a television game contested between the late Miyashita Shuyo 9 dan and myself (Black). Miyashita san committed an oversight in regards to Black 9 (ladder), leading to the capture of Black 11. Having White’s two key stones captured was terrible. Usually at this point White would have resigned, but since this was a television game that could not be done. He continued playing, and I started making some odd moves and I ended up losing the game.

I ask that the amateur players who refuse to resign do not laugh.

And yet, when I come to think about it, taking up this kind of thing seriously means that I have too much time on my hands. When fighting a complicated battle on the front line, this kind of thing would never come to mind. So before I start thinking of even more stupid things and embarrass myself, I will stop here.

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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