Igo Hatsuyōron 120 shows a position that could almost be taken from a real game. Although it it Black's turn, however, there are 71 Black stones on the board, but only 70 stones in White.

One of the conventions chosen for tsume-go problems of high calibre like those in Igo Hatsuyōron is that all the stones of the initial setting must be useful.

We assumed for a very long time that White must have captured a Black stone before the problem was set, since consequently not a single Black stone may be taken from the board to resolve the supposed imbalance.

When we investigated a suspicion that the opposite might be the case, we came across a significant difference in the perceptual abilities of AI and human players, which makes it necessary to consider KataGo's analysis results very cautiously in certain cases.

At the end of all our efforts it turned out that the classical convention applied after all and that it must have been White who had started the game.

Let's go back in time and enter the world of amateurs ...

( 2022MainLine)
Joachim Meinhardt once counted the stones on the board and realised that White has one more stone than Black ().
Cheng's 1988 introduction into the problem also has a comment that White has one more stone on the board.

Explanation option #1:

White captured a Black stone at . And connected there later.
The logical consequence is a komi of 1.

We followed this option for the vast majority of our engagement with the problem.
In his 2010 book, Cheng explicitly states that White has captured one of Black's stones on the first line on the right edge. He also mentions that it is important to consider this stone to get the correct outcome under Japanese rules.

Explanation option #2:

White started the game. Perhaps a kind of homage to the origin of the game of Go, ancient China, in which it was White who made the first move.
The logical consequence is a komi of 0, as usual in the Edo period in Japan.

This second option will turn out to be Inoue Dōsetsu Inseki's true intention, as we shall see further below.

Let's make a short detour into KataGo's world ...

Karl Desfontaines mentioned that – according to his trials with KataGo – Black's trapped stone in the upper right corner might be superfluous.
However, we have known for a very long time that this stone was placed on purpose!
KataGo's assessment (based on Karl's configuration) must consequently suffer from a hitherto unknown weakness.

To check this, I analysed three different scenarios for the upper right corner.

You may wonder what this topic is doing here in this section. Well, the results of the analysis unintentionally shed new light on the question of Black's (seemingly) missing 71st stone, as we will see much further on.

Scenario A: ( 2023)

Black's stone at was taken off the board.
This scenario cannot exist in KataGo's world.

Scenario B: ( 2023)

One Black stone was added at .
Purely theoretical, this scenario would be conceivable in KataGo's world (although not very realistic).

Scenario C: ( 2023)

Black's stone at was taken off the board, while a White stone was added at . The resulting shape is the same as after capturing the original Black stone.
Purely theoretical, this scenario would be also conceivable in KataGo's world (although not very realistic again).

But first, let's highlight a key difference in the perceptual abilities of humans and AI.

In the world of amateurs ...

The sequence of moves to create the hanezeki is - seen in itself - a self-contained, single element of the solution.

The sequence of moves of the wandering of the hanezeki's tail through the centre of the board is - seen in itself - another self-contained, single element of the solution.

The sequence of moves of the Crosscut Sequence is - seen in itself - another self-contained, single element of the solution.

The same is true for the two throw-in in the hanezeki, ...

... as well as all the ensuing forcing-moves in the hanezeki.

The total view of a clustered one-way street in human understanding, massively reducing the complexity of the problem.

This implies the following ...

From the starting position of Igo Hatsuyōron 120, ...

... in a way, human players only need two moves – independent (in principle) of a large part of the board, especially of the upper right corner (humans are capable of concentrating on the part of the board relevant to this sequence and blocking out everything else) – ...

... to reach the position before both sides' engagement on the left side of the board and in the upper right corner.

VAR

Conversely, this means that human players can analyse minimal changes, e.g. in the upper right corner, locally, completely disregarding the rest of the board.

But in the world of KataGo, ...

From the starting position of Igo Hatsuyōron 120, ...

... KataGo still needs 76 single moves – always considering the whole board – ...

... to reach the position before both sides' engagement on the left side of the board and in the upper right corner.

VAR

For KataGo, the minimal change in the upper right corner has created a new whole-board position that it has never ever seen before.

KataGo is still a player of superhuman strength, and also still has the specific knowledge about the problem. Therefore, it will not fail entirely with solving the "new" problem.

However, the impact of the "small" change may realise too far in the future (i.e. hidden behind KataGo's event hoziron), so it is not unlikely that KataGo will just follow its "first instinct", which would mean "playing as usual".

Let's now find out what KataGo thinks about the three scenarios described above, starting with the first one ...

Scenario A: ( 2023)
Black's stone at has been removed, so we would first suspect that White would win the game by only one point, due to the one prisoner now missing.

:
KataGo starts with Black's connection in the lower right corner.

:
White answers with the small knight's jump in to the right centre.

KataGo run in Analysis Mode with a komi of -1 here.

:
Black pushes into White's upper right corner "extreme early".

:
White plays her forcing move in the lower right corner first, ...

:
... before defending in the upper right.

However, White's "usual" block with is a mistake here, losing one point overall.

It would be correct to occupy a liberty of Black's large group at , instead, as we discovered a long time ago.

:
KataGo inserts the Guzumi Exchange , "early", ...

:
... followed by Harry's Hasami-Tsuke .

The solution sequence will continue with a Black move at in the centre.

White will win the game by one point.

In my experience, it is a good idea to vary the komi for the self-play games in order to find out to what extent there are "hidden traps" for KataGo in a previously "unknown" position.

The final scores were as follows:

• Komi = 0 => final score = Jigo
• Komi = -0.5 => final score = Black + 1.5


• Komi = -1 => final score = White + 1


• Komi = -1.5 => final score = White + 0.5
• Komi = -2 => final score = Jigo
• Komi = -2.5 => final score = Black + 0.5

Starting from komi = -1, the final scores appear to match the increase in reverse-komi.

However, decreaing the reverse-komi in White's favour produced final results that were inexplicably better for Black.
This jump in development is a clear indication that "something is wrong". For example, there may be a "hidden" effect that is still far beyond KataGo's reach so early in the game.

VAR

Referenced by ( 2024)

We lend KataGo a helping hand by saving it the trouble of thinking about the first 76 moves of the game and only start the self-play game after White's move on the left side.

:
Black pushes into White's upper right corner.

:
KataGo blocks to the left with , as we did, so choosing the correct reply to Black's previous push.

It seems that the consequences of this move are now within reach of KataGo's computational skills.

We will explain the continuation in thematically connected units (using changes in the order of moves), while KataGo loves to bounce back and forth on the board in its self-play games.

; :
Twice Black pushes further into White's corner.

:
Black initiates the Guzumi Exchange.

Further reducing White's territory at the top with , instead, would be futile, as White's reply with would take Black's large group a decisive liberty.

Due to the missing Black stone at , the sequence from to would not work here, as White would be able to connect her stones in atari with .
If were on the board, Black could capture White's connected stones with thereafter.

Please also note that Black does not have the time to play the descent to here (which would not lose a Main Semeai Liberty), as this move is gote. White would defend her left-hand group through immobilising Black's nakade stones, winning the game with ease.

:
The game continues with the Nakade Sequence on the left side of the board, as usual.

:
Black ends in gote there.

:
White pre-empts a Black descent at the same point.

Black could give atari at (White will connect with ), but to no effect, as he would remain unable to connect this stone with a move at .

:
Black closes one of the holes in the lower encirclement of his upper left corner, also occupying one of White's Main Semeai Liberties there.

Alternatively, Black might give atari at White's two stones in the lower left with .

:
White must play Yamada Shinji's Tsuke just now, because ...

:
... KataGo's Immediate Crosscut will not work any longer, once Black has solidified the lower border of his upper left corner with another move at .

; ; :
Any continuation on the left side, either , or to , would be gote for White, in principle. This would allow Black to reduce her territory in the upper right corner.

Therefore, she has to defend there first. She can do so in sente, as Black is par with the Punishment Semeai Liberty Level.

:
Now, as there are only one-point holes into her territory remaining, White continues with the usual course of the endgame at the left.

:
Black is par with the Punishment Semeai Liberty Level, so it is best for White to continue with the Main Semeai, forcing Black to follow her.

; ...; :
White must close all one-point holes into her territory in the upper right, before ...

:
... she connects her single stone at the upper edge, so terminating the endgame on the left side of the board.

:
White lost one tempo in the Main Semeai by her connection, so Black is able to play the push at the top in sente.

Connecting his stone in the lower right with a move at , instead, is out of the question, as this would lose two Main Semeai Liberties, one too many.

Black will continue with the atari of in the nakade.

Capture Variation:

Compared to Our Solution (2021), ...

• White's cumulated gain at the upper edge is four points.
• White's cumulated gain in the upper right corner is two points.
• Black destroyed one point of White's territory at the top.
• Black got an additional point of territory in the left centre.
• White got an additional point of territory in the right centre.
• Black captured White's two stones in the lower left, so gaining four points.

In total, White gained one point.

White + 2 => White + 3

A final score of White + 1 was to be expected, so the missing Black stone in the upper right corner gives White a net advantage of two points.

Semeai Variation:

Compared to Our Solution (2021), ...

• White's cumulated gain at the upper edge is four points.
• Black's cumulated gain in the upper right corner is two points.
• Black destroyed one point of White's territory at the top.
• Black captured two White stones less at the left, so losing three points.
• White captured one Black stone less in the right centre, so losing one point.

In total, White gained three points.

Black + 4 => Black + 1

2023

Let's discuss the second scenario ...

Scenario B: ( 2023)
Another Black stone has been added at , so we would first suspect that White would win the game by three points now, due to the additional prisoner.

:
The sequence starts in the lower right corner, as usual.

:
Black pushes into White's upper right corner "extreme early".

:
As typical for KataGo, White inserts an exchange in the hanezeki, ...

:
... before answering Black's push with the "usual" block at .

:
The game continues with the resumption of the interrupted creation of the hanezeki.

White will win the game by three points.

VAR

We lend KataGo a helping hand by saving it the trouble of thinking about the first 76 moves of the game and only start the self-play game after White's move on the left side.

: (A 2023)
Here, KataGo starts with initiating the Guzumi Exchange.

As a matter of course, choosing the push to first is also feasible.

:
Thereafter, Black pushes into White's upper right corner.

:
KataGo favours the immediate block with .

Runner-up is the jump back to .

:
Black plays Harry's Hasami-Tsuke Sequence.

The game will continue with Black's move at in the Nakade Area.

Capture Variation:

Compared to Our Solution (2021), ...

• White got an additional prisoner in the upper right corner.

White gained one point.

White + 2 => White + 3

As was to be expected.

( 2023)
VAR

: ( 2023)
Black pushes into White's upper right corner first.

:
KataGo favours jumping back to for defense.

:
Black pushes once again into White's corner at the right.

:
Another push is played from the left, as Fujisawa Hideyuki had also done in his classical solution.

:
White blocks again.

:
Black gives atari at the upper edge.

:
White connects.

It does not make any sense to start a ko-fight with a move at here.

The game will continue as usual with Black's move at at the left edge.

Capture Variation:

Compared to Our Solution (2021), ...

• White got an additional prisoner in the upper right corner.

White gained one point.

White + 2 => White + 3

As was to be expected.

2023

Let's discuss the third and final scenario ...

Scenario C: ( 2023)
Black's stone at has been removed, and an additional White stone has been added at , so we would first suspect that the game would end in a draw now, due to the missing prisoner and the occupied point of White territory in the corner.

:
KataGo starts in the lower right corner, as usual.

:
Black pushes into White's upper right corner "early".

:
White defends with the "usual" block at , but which is a mistake here, losing one point overall.

It would be correct to occupy a liberty of Black's large group at , instead, as we discovered a long time ago.

:
Black initiates the Guzumi Exchange.

Thereafter, Black will continue with in the centre.

The game will end in a draw.

VAR

We lend KataGo a helping hand by saving it the trouble of thinking about the first 76 moves of the game and only start the self-play game after White's move on the left side.

:
KataGo likes to insert this kikashi at the left edge, ...

:
... before initiating the Guzumi Exchange in the upper right.

:
Black pushes into White's upper right corner.

:
KataGo blocks to the left with , as we did, so choosing the correct reply to Black's previous push.

It seems that the consequences of this move are now within reach of KataGo's computational skills.

; :
Twice Black pushes further into White's corner.

The game will continue similar to Scenario A above with Black's atari at the left edge.

White will win the game by two points.

A final score of Jigo was to be expected, so the missing Black stone in the upper right corner gives White a net advantage of two points.

2023)

Let's return to the amateur world for some final conclusions ...

If Inoue Dōsetsu Inseki had ever wanted to equalise the number of Black and White stones in the initial position of the Igo Hatsuyōron 120, he could obviously have done so without any problem, e.g. with in the top right corner according to scenario B above.

But he had not made use of this option at all.

Thus, in the end, we have to admit that our long-standing assumption that White had captured Black's 71st stone at the right edge with , and later connected there with , is on extremely weak footing.

KataGo has shown us that this assumption was wrong.

Thanks to KataGo it is now clear that White (and not Black) started the game.

This implies that komi has to be reset to zero, as usual in the Edo period in Japan.

The correct solution of Igo Hatsuyōron 120 ends with a White victory by one point.

Let's now take a closing look over the shoulder of John Fairbairn for some supplementary information about the time before the Big Bang ...

" … game records with White playing first in Japan exist around this time, and one of them is Inoue Dosetsu Inseki (GoGoD 16687-03-07a). This was against Lord Makino and may have some sort of deferential or ceremonial significance, but there are other examples where neither of the two players is an aristocrat. These may still have an element of deference, in that they were played in the presence of someone august, but it may also have been the case that playing with White first was then either normal or common, or players just didn't care. At any rate, there seem to be reason to assume a Chinese connection.

There is also the possibility that colours were swapped in the printing process, which we know has happened with other old books."

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