Excellent point! And not just at the kyu level. I think that a major reason for the relative weakness of today's bots for semeai is their inability to count as humans do.Cassandra wrote:Knowing the current status of Black's Main Semeai Liberties at every moment of the game is mandatory to identify "natural looking" moves as mistakes.
I thought that this knowledge would be helpful, at least at amateur (Kyu) level.
KataGo @ Igo Hatsuyoron 120
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Bill Spight
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Re: KataGo @ Igo Hatsuyoron 120
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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Cassandra
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Re: KataGo @ Igo Hatsuyoron 120
Now, let' go back some moves, until Black's atari in the lower left.
White remembers that it is not mandatory to connect her two stones with a move at a, but plays her move 124 in the hanezeki, stopping Black's kikashi there.
White will win the Semeai Variation by at least three points (@ komi=1).
This implies that Black has to prevent White's move in the hanezeki by playing B 123 at this point himself in sente (White will not tenuki to cut at a in the centre), before inserting his second kikashi in the lower left.
Again, the final scores will become W+2 / W+2 (@ komi=1).
What is eventually remaining in our "no kikashi" line?
Black still has his kakashi at the top that compensates for White's newly found ko threat in the left centre. However, fighting Dany's ko was hopeless for Black even before.
White remembers that it is not mandatory to connect her two stones with a move at a, but plays her move 124 in the hanezeki, stopping Black's kikashi there.
White will win the Semeai Variation by at least three points (@ komi=1).
This implies that Black has to prevent White's move in the hanezeki by playing B 123 at this point himself in sente (White will not tenuki to cut at a in the centre), before inserting his second kikashi in the lower left.
Again, the final scores will become W+2 / W+2 (@ komi=1).
What is eventually remaining in our "no kikashi" line?
Black still has his kakashi at the top that compensates for White's newly found ko threat in the left centre. However, fighting Dany's ko was hopeless for Black even before.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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Cassandra
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Re: KataGo @ Igo Hatsuyoron 120
Did I already mention that painting diagrams works like fertiliser for the variation tree?Cassandra wrote:Now, let' go back some moves, until Black's atari in the lower left.
White remembers that it is not mandatory to connect her two stones with a move at a, but plays her move 124 in the hanezeki, stopping Black's kikashi there.
White will win the Semeai Variation by at least three points (@ komi=1).
Black will NOT capture at a immediately, but start Dany's Ko, instead.
White's previous move was played outside the Main Semeai, so Black can safely give atari with 125.
Black keeps things simply by capturing in the lower left, instead of the ko with a move at a, in order to dissolve his potential shortage of liberties after a White move at b.
White is forced to defend her upper side, to keept the territorial balance, and connects at 128.
Black plays his remaining kikashi at the top, well knowing that White is unable to connect the ko in the left centre at a.
This connection would by her THIRD move outside the Main Semeai area, and result in TEN Main Semeai Liberties for Black. White would be unable to capture Black's large group in the upper right in the Semeai Variation. And Black is also ahead in the Capture Variation.
This implies that Black will capture this ko, and connect thereafter.
The final scores will become B+4 / W+2 (@ komi=1)
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
White will have to play her move in the hanezeki one move earlier.
Thereafter, she will also keep the atekomi of a in reserve.
Again, White will win the Semeai Variation by three points (@ komi=1).
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
This implies that Black must play his kikashi in the hanezeki much earlier.
White must replay locally, at a.
She is unable to give atari at b, for example.
Black would connect the hanezeki's tail with c, and cut at a after White's following oki.
Black lost one of his potential ko threats in the very beginning, so the final scores of the game will be W+2 / W+2 (@ komi=1) again.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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Cassandra
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Re: KataGo @ Igo Hatsuyoron 120
Our Igo Hatsuyôron 120 website has just become updated with the current results of our "No Kikashi" analysis.
Please note that this update contains the presentation of the subvariations only, supplemented by a short introduction and legend that can be accessed via
http://igohatsuyoron120.de/2015/0513a.htm
The course of the move sequences might look a bit confusing, but this could not be helped (as already mentioned earlier here).
The presentation of the respective variation tree table is still on the to-do-list.
I am afraid that the elaboration of our main findings for the presentation in Volume II (the theoretical part of the website) will last longer than only a few weeks ...
Please also note that I did not crosscheck each and everything, so please be indulgent in the case you find any mistakes.
The same applies for any potential inconsistencies that remained in the older parts of the website (I am afraid that there are still some todos).
Any information about mistakes in the calculation of subvariations will be processed not earlier than 2021 ...
Please note that this update contains the presentation of the subvariations only, supplemented by a short introduction and legend that can be accessed via
http://igohatsuyoron120.de/2015/0513a.htm
The course of the move sequences might look a bit confusing, but this could not be helped (as already mentioned earlier here).
The presentation of the respective variation tree table is still on the to-do-list.
I am afraid that the elaboration of our main findings for the presentation in Volume II (the theoretical part of the website) will last longer than only a few weeks ...
Please also note that I did not crosscheck each and everything, so please be indulgent in the case you find any mistakes.
The same applies for any potential inconsistencies that remained in the older parts of the website (I am afraid that there are still some todos).
Any information about mistakes in the calculation of subvariations will be processed not earlier than 2021 ...
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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Cassandra
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Re: KataGo @ Igo Hatsuyoron 120
The table of the "No Kikashi" variation tree has been uploaded.
Next, I will successively adapt the 2019 "KataGo" variation tree to our new 2020 findings.
Next, I will successively adapt the 2019 "KataGo" variation tree to our new 2020 findings.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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Bill Spight
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Re: KataGo @ Igo Hatsuyoron 120
Thank you all for your Herculean efforts!Cassandra wrote:The table of the "No Kikashi" variation tree has been uploaded.
Next, I will successively adapt the 2019 "KataGo" variation tree to our new 2020 findings.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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Cassandra
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Igo Hatsuyoron 120 => new specific KataGo network in develop
We – the four amateurs' research team – are very pleased to announce that a new specific KataGo network for Igo Hatsuyoron 120 is in development.
Friday9i, a Go player from France also vividly interested in "our" problem, carried out the training of a new KataGo network from end of August last year. He started from lightvector's best official 40-block network (g170-b40c256x2-s5095420928-d1229425124; lightvector's known specific Igo Hatsuyoron’s network, igoh120-s618909184-d292623510.txt.gz, is a 20-block one), running two graphic cards (RTX 2080 + RTX 2070 until mid-November, an RTX 3080 + RTX 2070 thereafter) almost full time. Lightvector very kindly assisted him with precious help and advice for adjusting the run’s parameters.
Due to KataGo's further development, the new network can now handle several rule sets, such as Japanese Rules, which is quite an important factor for evaluating its results! It is still in training, and will be furthermore in development for at least another three months from now on, according to Friday9i's current schedule.
We received an intermediate result for trying / testing mid of December.
The new network might still have evaluation troubles or blind spots in some places. If we found such major blind spots or evaluation mistakes, the training could be focused for trying to improve those lines decisively.
In addition, we were asked for variations that we had already investigated, but not yet published, as well as for lines those we were interested in to become analysed much deeper. These could also help improving the network during selfplay.
As we know already, it is mandatory for the network to encounter those "not yet sufficiently explored" positions during training, in order to become really stronger. Otherwise, the network would be unable to "learn" about those lines, making it necessary to have a high-end machine at hand during "play" for (some) compensation.
This new network is already much stronger than the older one.
Starting from the problem's starting position, it evaluated Black's win rate for komi = -0.5 / -1 / -1.5 with (about) 5% / 50% / 95 %, which should be sufficient evidence that White will really win the game by two points at a komi of 1 point! And that the problem does not have any flaw!
The new network met us at a time when we were intensively working on the topic of an "extra late" guzumi, showing that this move must not be delayed as long as the old network "thought" to be possible. Now, the new network "wants" to play the guzumi – confirming our assumption that we already had for long – latest just before the Crosscut Sequence in the left centre starts, whereby the guzumi is often chosen earlier.
Friday9i himself was also interested in a "very early" guzumi (after the creation of the hanezeki in the lower right), with which he had already dealt intensively with the old network.
With the new network, he found that a "very early" guzumi is also feasible, provided that it is played at the right moment and White chooses the correct reply, also ending with a two-point win for White (komi = 1). The ensuing game will be completely different from what we know so far, and look much more like a "real" game than the known solution to the problem.
We are looking forward for the final result of Friday9i's work.
For the meantime, you will find some details about our findings so far in the following postings, just for your interest.
Friday9i, a Go player from France also vividly interested in "our" problem, carried out the training of a new KataGo network from end of August last year. He started from lightvector's best official 40-block network (g170-b40c256x2-s5095420928-d1229425124; lightvector's known specific Igo Hatsuyoron’s network, igoh120-s618909184-d292623510.txt.gz, is a 20-block one), running two graphic cards (RTX 2080 + RTX 2070 until mid-November, an RTX 3080 + RTX 2070 thereafter) almost full time. Lightvector very kindly assisted him with precious help and advice for adjusting the run’s parameters.
Due to KataGo's further development, the new network can now handle several rule sets, such as Japanese Rules, which is quite an important factor for evaluating its results! It is still in training, and will be furthermore in development for at least another three months from now on, according to Friday9i's current schedule.
We received an intermediate result for trying / testing mid of December.
The new network might still have evaluation troubles or blind spots in some places. If we found such major blind spots or evaluation mistakes, the training could be focused for trying to improve those lines decisively.
In addition, we were asked for variations that we had already investigated, but not yet published, as well as for lines those we were interested in to become analysed much deeper. These could also help improving the network during selfplay.
As we know already, it is mandatory for the network to encounter those "not yet sufficiently explored" positions during training, in order to become really stronger. Otherwise, the network would be unable to "learn" about those lines, making it necessary to have a high-end machine at hand during "play" for (some) compensation.
This new network is already much stronger than the older one.
Starting from the problem's starting position, it evaluated Black's win rate for komi = -0.5 / -1 / -1.5 with (about) 5% / 50% / 95 %, which should be sufficient evidence that White will really win the game by two points at a komi of 1 point! And that the problem does not have any flaw!
The new network met us at a time when we were intensively working on the topic of an "extra late" guzumi, showing that this move must not be delayed as long as the old network "thought" to be possible. Now, the new network "wants" to play the guzumi – confirming our assumption that we already had for long – latest just before the Crosscut Sequence in the left centre starts, whereby the guzumi is often chosen earlier.
Friday9i himself was also interested in a "very early" guzumi (after the creation of the hanezeki in the lower right), with which he had already dealt intensively with the old network.
With the new network, he found that a "very early" guzumi is also feasible, provided that it is played at the right moment and White chooses the correct reply, also ending with a two-point win for White (komi = 1). The ensuing game will be completely different from what we know so far, and look much more like a "real" game than the known solution to the problem.
We are looking forward for the final result of Friday9i's work.
For the meantime, you will find some details about our findings so far in the following postings, just for your interest.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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Cassandra
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KataGo @ Igo Hatsuyoron 120 => "very early" guzumi
Black can play the guzumi earliest with move 31, just because the length of the hanezeki's tail 
has to be at least two stones to enable a tenuki from the bottom.
As a matter of course, White could answer locally at a as usual, reverting to the known solution.
However, according to the new KataGo network, she might also consider blocking the hanezeki's tail with
at the bottom. After this block the game will also end with two points for White (komi = 1).
Jumping to b, instead, threatens Black's lower left corner, and secures life for White's bottom group. The further path of the hanezeki's tail will be stopped with White c latest. However, according to our trials, this alternative line will be one point worse for White.
For your interest, I add an example of the ensuing play on the board.
(Disclaimer: my laptop is quite weak, so please take the SGF with a grain of salt.)
EDIT: The "Date" shown in the SGF is not correct, had not been updated...
has to be at least two stones to enable a tenuki from the bottom.As a matter of course, White could answer locally at a as usual, reverting to the known solution.
However, according to the new KataGo network, she might also consider blocking the hanezeki's tail with
at the bottom. After this block the game will also end with two points for White (komi = 1).Jumping to b, instead, threatens Black's lower left corner, and secures life for White's bottom group. The further path of the hanezeki's tail will be stopped with White c latest. However, according to our trials, this alternative line will be one point worse for White.
For your interest, I add an example of the ensuing play on the board.
(Disclaimer: my laptop is quite weak, so please take the SGF with a grain of salt.)
EDIT: The "Date" shown in the SGF is not correct, had not been updated...
- Attachments
-
- KataGoNew_GuzumiMove31.sgf
- (4.84 KiB) Downloaded 1365 times
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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johnsmith
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Re: Igo Hatsuyoron 120 => new specific KataGo network in dev
I assume the original komi of 1 in the starting position is due to white taking a black stone at t6. Thus the komi of 1 to accommodate that one stone, making the starting count of black and white stones of both 71. Though I like your idea hereCassandra wrote:Starting from the problem's starting position, it evaluated Black's win rate for komi = -0.5 / -1 / -1.5 with (about) 5% / 50% / 95 %, which should be sufficient evidence that White will really win the game by two points at a komi of 1 point! And that the problem does not have any flaw!
How did that go under radar for so many yearsigohatsuyoron120.de wrote:The original of Igo Hatsuyoron does not give any aims to achieve, but has either "Black to play" or "White to play" only. There is another possible explanation for the fact that there are 71 White, but only 70 Black stones on the board – leaving aside the capture of one Black stone before the problem's setup: It was White – and not Black– who initiated the game.
So, in that case:
black to play, starting stones: black 71, white 71. komi=1 => w+2 (komi of 1 because of the captured black stone)
black to play, starting stones: black 70, white 71. komi=0 => w+1
Did I get this right? How did you get jigo?
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Cassandra
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Re: Igo Hatsuyoron 120 => new specific KataGo network in dev
Yes, you are right.johnsmith wrote:So, in that case:
black to play, starting stones: black 71, white 71. komi=1 => w+2 (komi of 1 because of the captured black stone)
black to play, starting stones: black 70, white 71. komi=0 => w+1
Did I get this right?
Neural networks in Go work best, in the case they encounter a game as close as possible.How did you get jigo?
Therefore, even if we assume a White win by one point with komi = 0, the game ends not as close as possible.
To achieve this aim, we have to set komi = -1, which will turn the outcome of the game to jigo. This corresponds with Black's assumed win rate of 50% in the very beginning of the solution sequence.
Let's assume that komi is set to -0.5, what will happen?
It is clear that Black will be unable to win the game (remember the assumed 5% win rate for Black in this case), but the AI player who has the Black stones will tend to choose somewhat "risky" moves, intending to create some complications that might enable him to turn the tables.
As a result, it is not unlikely that White will win such game by more than only 0.5 points (due to "objective" mistakes that Black made).
Another example:
If you wanted the AI to provide you with the best counter for White after a Black mistake (this will also be true for a "real" game), you should reduce the komi (seen from White's point of view) according to the (probable) value of Black's mistake.
After this adjustment of the komi, the game is "close" again, and White will do as best as she can.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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Friday9i
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Re: KataGo @ Igo Hatsuyoron 120
Just a precision regarding the game from Cassandra above:
After the "very early guzumi" at move 31, White can simply answer with W S14, which reverts to the standard solution.
As shown by the game provided by Cassandra, a (riskier) possible continuation for W is L3.
But there are alternative moves: White F2 or White G2 (at move 32) are possible, with comparable winrates (~30% wr like with L3, vs ~50% wr for the standard S14 answer) and apparently identical results, if we believe the net and the thousands of selfplay games played from these starting points.
But these lines are still not 100% clear, opinion of the nets may well evolve in the coming weeks, we'll see.
After the "very early guzumi" at move 31, White can simply answer with W S14, which reverts to the standard solution.
As shown by the game provided by Cassandra, a (riskier) possible continuation for W is L3.
But there are alternative moves: White F2 or White G2 (at move 32) are possible, with comparable winrates (~30% wr like with L3, vs ~50% wr for the standard S14 answer) and apparently identical results, if we believe the net and the thousands of selfplay games played from these starting points
.But these lines are still not 100% clear, opinion of the nets may well evolve in the coming weeks, we'll see.
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johnsmith
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Re: KataGo @ Igo Hatsuyoron 120
Thanks for the explanation. So you intentionally set the komi to -1 to find the best possible moves there are. That makes sense.
I wonder if Inoue Dōsetsu Inseki had deliberately set the stones for the big sacrifice to trick us into a variation without a solution (by 1 point heh), but he inteded the early gozumi all along.
I wonder if Inoue Dōsetsu Inseki had deliberately set the stones for the big sacrifice to trick us into a variation without a solution (by 1 point heh), but he inteded the early gozumi all along.
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Cassandra
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Re: KataGo @ Igo Hatsuyoron 120
If ever, I would like to assume that it is just the other way round.johnsmith wrote:I wonder if Inoue Dōsetsu Inseki had deliberately set the stones for the big sacrifice to trick us into a variation without a solution (by 1 point heh), but he inteded the early gozumi all along.
With the very early guzumi, there are too many roads to Rome for a human player, whilst the known solution is a one-way-street (changes in the order of moves not considered).
No two games after the very early guzumi were the same on my laptop. It seems that there are always several miai options, at every stage of the game. The handling of the area around the nakade, of the entire centre, and to top left corner can be completely different from game to game.
EDIT: If W 32 at G2 was feasible to produce a White win by two points (komi = 1), then this would be the also true with a length of three, and four, stones of the tail (for the moment of Black's guzumi).
Probably, this alternative line found by Friday9i was unavoidable, a kind of side effect due to the middle-game starting position of the problem.
Apparently, our very early evaluation of this very early guzumi (can be found in the section "Timing of the Guzumi" on our website) was mistaken (it favoured White too much), mainly because our weakness in the endgame (and our missing knowledge of some of KataGo's strategies for Black). But let us meet about halfway and assume that we had calculated a White win with 6 points after Black's guzumi with move 31. The growing tail of the hanezeki destroys potential White territory in the centre; the larger it becomes, the more destructive it is (until a certain point). Even in that case, there would be a(nother) moment in the game, when an early guzumi with White tenuki would have had the same outcome as the currently known solution.
It might be due to the genius of Inoue Dôsetsu Inseki that this moment is the earliest possible one, as it seems now.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)
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johnsmith
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Re: KataGo @ Igo Hatsuyoron 120
Agreed, it's just more beautiful that way. Can't wait for the new discoveries.Cassandra wrote:If ever, I would like to assume that it is just the other way round.johnsmith wrote:I wonder if Inoue Dōsetsu Inseki had deliberately set the stones for the big sacrifice to trick us into a variation without a solution (by 1 point heh), but he inteded the early gozumi all along.
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Cassandra
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Igo Hatsuyoron 120 and KataGo new
Guzumi delayed too long => White's surprising wedge in the left centre
The old KataGo net was fine with delaying the guzumi even until after the Nakade Sequence at the left.
However, our investigation showed that -- after Black's final move
in the lower left -- White will occupy the guzumi point herself with 
.
As usual with the "classical" line of play (i.e. without Black's guzumi), it is best for Black to play Michael Redmond's kikashi
in the bamboo joint just now.
White is forced to answer with the solid connection.
If she chose the atari at a, instead, she would have lost a tempo in the Main Semeai, enabling Black to take the large endgame point of b in the upper left corner, so winning the game.
Black will give atari at White's two stones in the lower left, in order to strenghten his position in the left centre.
White avoids some complications in the upper right (to be explained in some later posting) by defending there with
first.
Black
captures White's two stones.
Blocking at a in the left centre, instead, will result in the same final score, as White will be able to connect her two stones later, or to gain alternatively in the forthcoming endgame on the left side of the board.
Black is still par with the Punishment Semeai Liberty Level, so White starts the endgame on the left side "early".
Black plays tenuki with
, in order to occupy the large endgame point at the top.
After
, we continued with the Main Semeai with White's peep at a at the upper edge, finally scoring a White win by THREE points (komi = 1), which is one point better for her than the known solution to the problem.
KataGo's new net, howewer, found that Black's earlier mistake with not playing the guzumi should be punished even harder.
White will play the wedge at
in the left centre.
Playing KataGo's bad-shape move of b just now would be a mistake.
Black already captured White's two stones in the lower left, so he is able to immediately block at c without endangering his position in the left centre.
Black must give atari from the outside.
is sente.
After Black connected at
, the time is ripe for KataGo's bad-shape move with 
.
Black has to defend his cutting point at
-- sooner or later.
Please note that White's bad-shape move did not lose any tempo in the Main Semeai, but Black got only TWO points of territory in the left centre (one prisoner included), instead of the "usual" three.
If Black does without this defensive move, White would gain by the sequence of W 123, B a, W b, B c, W d in the left centre, once Black had occupied the x liberties of her left-hand group in the Main Semeai.
As a result of White's newly found tesuji in the left centre, she will win the game by FOUR points now (komi = 1).
The old KataGo net was fine with delaying the guzumi even until after the Nakade Sequence at the left.
However, our investigation showed that -- after Black's final move
in the lower left -- White will occupy the guzumi point herself with .As usual with the "classical" line of play (i.e. without Black's guzumi), it is best for Black to play Michael Redmond's kikashi
in the bamboo joint just now.White is forced to answer with the solid connection.
If she chose the atari at a, instead, she would have lost a tempo in the Main Semeai, enabling Black to take the large endgame point of b in the upper left corner, so winning the game.
Black will give atari at White's two stones in the lower left, in order to strenghten his position in the left centre.
White avoids some complications in the upper right (to be explained in some later posting) by defending there with
first.Black
captures White's two stones.Blocking at a in the left centre, instead, will result in the same final score, as White will be able to connect her two stones later, or to gain alternatively in the forthcoming endgame on the left side of the board.
Black is still par with the Punishment Semeai Liberty Level, so White starts the endgame on the left side "early".
Black plays tenuki with
, in order to occupy the large endgame point at the top.After
, we continued with the Main Semeai with White's peep at a at the upper edge, finally scoring a White win by THREE points (komi = 1), which is one point better for her than the known solution to the problem.KataGo's new net, howewer, found that Black's earlier mistake with not playing the guzumi should be punished even harder.
White will play the wedge at
in the left centre.Playing KataGo's bad-shape move of b just now would be a mistake.
Black already captured White's two stones in the lower left, so he is able to immediately block at c without endangering his position in the left centre.
Black must give atari from the outside.
is sente.After Black connected at
, the time is ripe for KataGo's bad-shape move with .Black has to defend his cutting point at
-- sooner or later.Please note that White's bad-shape move did not lose any tempo in the Main Semeai, but Black got only TWO points of territory in the left centre (one prisoner included), instead of the "usual" three.
If Black does without this defensive move, White would gain by the sequence of W 123, B a, W b, B c, W d in the left centre, once Black had occupied the x liberties of her left-hand group in the Main Semeai.
As a result of White's newly found tesuji in the left centre, she will win the game by FOUR points now (komi = 1).
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
Igo Hatsuyōron #120 (really solved by KataGo)