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 Post subject: Broken ladder games
Post #1 Posted: Fri Jan 15, 2021 4:14 pm 
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Besides Lee Sedol's famous ladder game (https://senseis.xmp.net/?YiSeTolHongChangSikLadderGame) and that one handicap game I remember involving Fine art, anyone know of any other notable historical games where the right action was for the laddering side to play out a ladder the whole way even though it was broken?

Ideally across a reasonable distance of the board, as short broken ladders of course happen all the time in things like driving tesuji.

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Post #2 Posted: Fri Jan 15, 2021 8:00 pm 
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Aloha.



Edit: This game is a candidate for Beat Elf. In its commentary Elf reckons that :b59: in the actual game is 10½% better than Elf's choice, which is the AlphaGo kosumi cum peep at E-04. Elf also reckons that :w60: is a blunder, losing 39½% to the bamboo connection at P-07.

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Last edited by Bill Spight on Sat Jan 16, 2021 6:19 pm, edited 1 time in total.

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 Post subject: Re: Broken ladder games
Post #3 Posted: Fri Jan 15, 2021 8:23 pm 
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I don't know if this fits the bill, but it is a famous ladder game. :)



Edit: I have taken a look at the Elf commentary of this game, and Elf approves of nearly all of the ladder plays by both sides. :o I.e., :b23: - :b43: and :b45: - :w50:. It thinks that :w44: loses only ½%, however. It also thinks that the double ladder favors Black, and it thinks that :b51:, which escapes the ladder, was a blunder, losing 38½%. :shock: It would be interesting to see what KataGo and other bots think. :)

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Last edited by Bill Spight on Sat Jan 16, 2021 8:26 am, edited 2 times in total.
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 Post subject: Re: Broken ladder games
Post #4 Posted: Fri Jan 15, 2021 11:47 pm 
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Aloha.


Mahalo.

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 Post subject: Re: Broken ladder games
Post #5 Posted: Sat Jan 16, 2021 8:13 am 
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Ferran wrote:
Bill Spight wrote:
Aloha.


Mahalo.


I used to think that mahalo meant trash, because it was on the trash cans in shopping centers in Honolulu. :lol:

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 Post subject: Re: Broken ladder games
Post #6 Posted: Sat Jan 16, 2021 1:30 pm 
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The following is an article from the GoGoD Encylopaedia which lists various interesting ladder situations. The formatting is lost in the transfer here, and you will need the GoGoD database for the games, but I don't think you'll find a bigger XXXX of ladders.

We need a collective noun for ladders! Any suggestions?

Quote:

THERE'S BARELY a game that does not feature a ladder somehow. But the threat is stronger than the execution, so that very, very few are played out. This article surveys several games from the GoGoD database where the ladder did materialise. There is a separate article on the origin of the term "ladder" and its Japanese version shichou.

Misreads
One of the alternative renderings mentioned in the above separate article seems apposite here: dead birds. Sick as a parrot may be how a pro feels when he's misread a ladder. It's pretty rare anyway, but even rarer to admit to it.

In 1952-06-04a Yamabe Toshiro misread a ladder (after Black 72) against Kitani Minoru in the Oteai. We know that only because the Fukumenshi (Yomiuri go reporter) Yamada Torakichi bumped into him on the steps of the Nihon Ki-in on his way out. Yamabe just said, "I resigned." Yamada had the wit not simply to offer commiserations and replied, "Bit early isn't it? What on earth..." Yamabe then unburdened himself just enough: "I must be mad. I misread a ladder so there's nothing to talk about."

In 1994-01-06c Rin Kaiho misread his White 80 against Takemiya Masaki in the 33rd Judan. He didn't say so but that was the pro opinion led by Oya Koichi and Nakayama Noriyuki in the press room. Nakayama was a late arrival and not initially aware of who was playing. Apparently he took one look at the scorekeeper's diagram to know that one side was Takemiya. But White 80 merited a double-take.

2000-05-24a was Game 1 of the 55th Honinbo title match between O Meien v Cho Sonjin. It was O who blundered but at least he went on to win the title for the first time.

Most unusual ladder breaker
When ladders do surface in pro play, the action is nearly always to do with ladder breakers rather than the ladder itself. The game 1978-05-11e is our nomination for the most unusual ladder breaker. Kato Masao played Black 29 against Hashimoto Utaro. But White 34 was a most surprising move to leave the ladder working, too.

Double ladder breakers
Moves that break two ladders simultaneously have a long history. The famous Pressing the Divine Head position was reputed to be such a move discovered by a top Chinese player in Tang times to defeat a visiting "prince" from Japan. 1996-01-31a - Kobayashi Satoru vs Cho Chikun is a modern example, and another flawed but intersting example is in a game between Masubuchi Tatsuko and Yasunaga Hajime when Muasubuchi was on the verge of becoming pro (1922-07-00b). It is flawed because Black 61 should have been at 73, winning at once, and because White 60 should have been at 77.

Manego ladders
One unusual pro use of a ladder is in breaking a mane-go (mimic go) strategy. 1977-12-07a betweeen Hanawa Yasutoki and Nakayama Noriyuki shows this feature. Of course, no mention of mane-go should omit Fujisawa Hosai and we can see the ladder tactic in game 1961-09-13a against Sugiucho Masao.

There are a couple more examples in 1987-12-11a, Cho Hun-hyeon against Chang Tu-chin (not played out here but still relevant) and 1963-11-04a, Sakata Eio against Fujisawa.

Playing out the ladder unexpectedly
Probably the most interesting and spectacular examples are those where the ladder is played out unexpectedly. A player deliberately plays out the ladder knowing that he will lose it (the chased stones will connect up safely), but he reckons that he can get enough compensation from the surrounding position. Such games are not quite as rare as hen's teeth. In fact, for one example we can go back as far as 1740hcem241, where the great master Shi Dingan gave four stones to Zhang Zhenxi. This repays study: did Shi resign and if so was it too soon? Either way it was a quite brilliant conception.

Old Chinese games turn up lots of marvellous things. 1850JQXG494, the monk Qiuhang against Shen Jiezhi, is another fascinating example. A modern Chinese example is 1982-12-11a.

Instinctively, perhaps, we may feel that such things are not likely to occur among modern pros playing each other. If so, what about 1974-06-10b, Seo Pong-su against Cho Hun-hyeon in the exalted arena of the 6th Myeongin Final? The tactic was reckoned to work here as there was enough compensation for the ladder loser.

1983-10-19f, an all-female affair between Shinkai Hiroko and Tanimiya Ayoko in the Japanese Oteai, is worth noting. We'll come to why in a second. 1999-12-19a was noteworthy in that it was a rare example from international play: Game 3 of 1st Nong Shim Cup between Kudo Norio of Japan and Mok Chin-seok of Korea. But for the purists, Kudo's conception was flawed in that he could simply play a normal breaker to achieve his goal.

In 2002-04-06a, Yi Seong-chae against Weon Seong-chin in the 7th Ch'eonweon, the idea certainly was flawed because the compensation just wasn't big enough.

Now for a case where the idea paid off big time. In 2003-04-23a Yi Se-tol caught Hong Chang-sik by surprise in a KAT Systems Cup semi-final. It was a brilliant plan, and this probably was the first ladder game to become famous on the internet. However, it was precisely the ability of fans worldwide to discuss this game instantly on the internet that made this game so celebrated. Yet the conception seems strongly redolent of the barely known Shinkai-Tanimiya game, so the purists may not want to give it a full 10 out of 10 for artistic merit. Still, it's a real beauty.

There is a nice example of rescuing a dead group by playing out a ladder in 2002-04-25n - Zhong Wenqing was the insightful player this time, against Zhang Weijin in the Chinese National Team Tournament.

A further example of playing out a broken ladder was provided by Bernd Schmidt: 1989-07-06b: Ishida Yoshi vs Takemiya Masaki.

A new form of duelling
Was it James Thurber who came up with the gags about settling disputes: submarines at 30 yards, or dirty words at forty paces? Anyway, how about two ladders fighting each other? 1953-03-05a, Takagawa Kaku against Sakata Eio, makes for an amusing finale.

And, finally, a ladder used for threats in the oldest form of duel, the ko fight. Game 1998-09-27b is between two Korean youngsters who were then still amateurs but were on the verge of turning pro. [Surce: GoGoD Encylopaedia]

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 Post subject: Re: Broken ladder games
Post #7 Posted: Sat Jan 16, 2021 1:57 pm 
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John Fairbairn wrote:
We need a collective noun for ladders! Any suggestions?


Ladderati?

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 Post subject: Re: Broken ladder games
Post #8 Posted: Sat Jan 16, 2021 3:02 pm 
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John Fairbairn wrote:
The following is an article from the GoGoD Encylopaedia which lists various interesting ladder situations. The formatting is lost in the transfer here, and you will need the GoGoD database for the games, but I don't think you'll find a bigger XXXX of ladders.

We need a collective noun for ladders! Any suggestions?


I'd be partial to a tangle of ladders

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 Post subject: Re: Broken ladder games
Post #9 Posted: Sat Jan 16, 2021 4:19 pm 
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An escalation of ladders?


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 Post subject: Re: Broken ladder games
Post #10 Posted: Sat Jan 16, 2021 5:03 pm 
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John Fairbairn wrote:
We need a collective noun...


"Mahalo" :)

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 Post subject: Re: Broken ladder games
Post #11 Posted: Sat Jan 16, 2021 5:18 pm 
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I really like the Lee Sedol ladder game but it seems to me that the common description is a bit off? (maybe I'm just a pedant)

Click Here To Show Diagram Code
[go]$$B Valid ladder capture?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O . O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


It seems to me that the ladder is working for black on the basis that black has forcing moves against the bottom right situation that he would rather not play out but can be played out at (almost) any time.
If black plays out the moves ahead of time they are loss making so Lee would rather get away without making the exchanges. Black shouldn't need to make these exchanges to capture in the ladder.

Click Here To Show Diagram Code
[go]$$B Ladder maker?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . 3 . X . X O . |
$$ | . . . . . . . . . . 5 4 2 X . X . O O |
$$ | . . . . . . . . . . O 1 O X X O O O . |
$$ | . . . . . . . . . . . a O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


(I think 4 may also be at a and 5 would still work. After this I see no way to keep the lower right corner white but still avoid ladder capture?)

White misreads and thinks that the ladder is not working and so tries to pull out the stone. Black is happy to keep it captured in the ladder.
As white compounds the mistake by playing out the ladder and making this obligation heavier and heavier, at some point it becomes better to save the ladder stones than to save all of white's corner stones - At this point I would say that the ladder is no longer working as the ladder making moves wouldn't be sente. I'm not sure what point this is but I'm guessing Katago could probably help answer that by testing out some variations where each player takes the trade at different points?

I'm calling it a white mistake but of course it's a level of mistake that a high level pro can make and we can only spot with heavy benefit of hindsight.
Perhaps I'm missing something? The technique and execution is still stunning.

A 'headache of ladders' in this case?


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 Post subject: Re: Broken ladder games
Post #12 Posted: Sat Jan 16, 2021 8:08 pm 
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MikeKyle wrote:
I really like the Lee Sedol ladder game but it seems to me that the common description is a bit off? (maybe I'm just a pedant)

Click Here To Show Diagram Code
[go]$$B Valid ladder capture?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O . O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


It seems to me that the ladder is working for black on the basis that black has forcing moves against the bottom right situation that he would rather not play out but can be played out at (almost) any time.
If black plays out the moves ahead of time they are loss making so Lee would rather get away without making the exchanges. Black shouldn't need to make these exchanges to capture in the ladder.

{snip}

White misreads and thinks that the ladder is not working and so tries to pull out the stone. Black is happy to keep it captured in the ladder.
As white compounds the mistake by playing out the ladder and making this obligation heavier and heavier, at some point it becomes better to save the ladder stones than to save all of white's corner stones - At this point I would say that the ladder is no longer working as the ladder making moves wouldn't be sente. I'm not sure what point this is but I'm guessing Katago could probably help answer that by testing out some variations where each player takes the trade at different points?


Well, Elf agrees with you in its commentary. :)

Click Here To Show Diagram Code
[go]$$Wcm66 Blunder after blunder
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . d X . . . |
$$ | . . 1 O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O 3 4 . . . . . . . . . . . . . |
$$ | . . a 2 5 7 . . . . . . . . . . . . . |
$$ | . . . . 6 . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , b X . |
$$ | . . . . . . . . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O . O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . c . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]

Elf thinks that the rot starts with :w66:, which it reckons loses 21½% to the atari at a. Then :w68: is even worse, losing 37% to the cut at b. Next, :w70: loses 8½% to the shoulder blow at c. Then, :w72: loses 4½% to the side attachment at d. At this point, it's all over.

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 Post subject: Re: Broken ladder games
Post #13 Posted: Sun Jan 17, 2021 9:35 am 
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It used to be the case that KataGo had trouble reading out broken ladders fully due to knowing ahead of time that they wouldn't work.

Normally, since KataGo takes the shortcut of having a ladder input, it handles the 99.9%-frequency "ordinary ladder" case better than pure zero bots. For example you can find a few of the sgf games in https://lifein19x19.com/viewtopic.php?p=262982#p262982 where even the latest/near-latest LZ285 network still has trouble due to poor handling of ladder threats, including at least one game where the ladder actually is partly played out, followed soon by resignation.

Also from playing with KataGo in some test ladder positions, KataGo tends to do okay in analyzing maker/breaker tactics - whereas for example when I've tried for example LZ and ELF, this has not been the case even with large numbers of playouts (large enough to initially solve the ladder) and using it interactively in Lizzie. If there are multiple possible choices for the maker/breaker and multiple possible ways for the opponent to resist - ending up in a maker/breaker fight on the other side of the board where the ladder status flips every move - getting correct analysis is quite hard. KataGo also has trouble too sometimes, but also partially does a lot well on its own, which helps greatly. This means that using it interactively, even if occasionally it misses the correct breaker tactic initially (which sometimes it does), it gets enough right automatically that with the interactivity of being able to ask about moves it seems to be undersearching to verify them, analysis is quite doable.

But the issue for full broken ladders is that KataGo therefore also has trouble playing a ladder that it "knows" won't work, so generally wouldn't find those cases where it was right to play a full broken ladder. Similarly, it had trouble with ladder magnification, since that involves amplifying a ladder that doesn't work, which goes against the initial prior, and thereby requires makers/breakers to be solved with very low playouts in that branch of the search, which although decent at this point, isn't quite reliable enough at low playouts. But again it is at least easy enough in interactive analysis to manually play the "magnify ladder" move and see the opinion.

Both seem to be improving noticeably though with some more training though! :) At the start of kata1, I added a few examples of correct broken ladders and ladder magnification examples to the training, including the Lee Sedol game position, as an experiment to see if the neural net was capable of learning these things - i.e is it really fundamentally the neural net's difficulty to learn, or is it more that the AlphaZero process just fails to generate the right data?

In-sample on these positions, the latest kata1 network is doing *much* better, although some of them are not fully learned yet. The exciting thing is that out-of-sample, on some fresh broken ladder positions, it also seems to be doing better too. So the motivation for starting this thread was hoping to obtain some more examples for training, to expand that learning further and see if we can really have it working in almost all cases.

Thanks @Bill for that example, and also to 'kira' who in the LZ discord linked a fantastic video from Alexandre Dinerchtein 3p with a bunch more examples, which I will be adding. :)
https://www.youtube.com/watch?v=HPfSpSvqorg


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Post #14 Posted: Sun Jan 17, 2021 10:33 am 
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Coming back to the Lee Sedol position, @MikeKyle - as far as I can tell, it really is a broken ladder situation assuming white tries to resist. Indeed white should give up the ladder right away instead of running. But if white does run, then the correct path for black is to play the full broken ladder, and *not* attempt to simply get a ladder maker the normal way, because White does appear to have a way to fight to keep the lower right corner *and* escape from the upper left ladder, although global judgment also comes into play. Analysis below.

Firstly, black should *not* attempt to establish the ladder maker beforehand:

Click Here To Show Diagram Code
[go]$$B Too early, white is winning by a lot now
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . . 7 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . 8 . . , . X . |
$$ | . . . . . . . . . . . 6 3 . X . X O . |
$$ | . . . . . . . . . . 5 4 2 X . X . O O |
$$ | . . . . . . . . . . O 1 O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


If black goes for the maker right away, white is happy to let black have it, and take a large advantage in the center.

Black should magnify the ladder at least once. Of course, knowing what's to come, white shouldn't try to escape at all, but that's true of any sufficiently severe ladder tactic, regardless of whether it's a full-broken-ladder tactic or an ordinary maker tactic. So we suppose white resists.

Click Here To Show Diagram Code
[go]$$B Make ladder bigger
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O 2 . . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O . O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


Now if black tries this again, white's actually still happy to let black have it, the gain in the center is enough to compensate white to make it still a reasonable game for white:

Click Here To Show Diagram Code
[go]$$B white still takes the center influence
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O O 7 . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . 8 . . , . X . |
$$ | . . . . . . . . . . . 6 3 . X . X O . |
$$ | . . . . . . . . . . 5 4 2 X . X . O O |
$$ | . . . . . . . . . . O 1 O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


So black should make the ladder even bigger first.

Click Here To Show Diagram Code
[go]$$B Make ladder bigger
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O O 1 . . . . . . . . . . . . . |
$$ | . . . X 2 . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O . O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


Now, we finally see white make a difference choice, since the ladder is big enough! And we get to see how white breaks the ladder *and* saves the lower right.

Click Here To Show Diagram Code
[go]$$B White's tesuji
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . 3 . X . X O . |
$$ | . . . . . . . . . 6 5 4 2 X . X . O O |
$$ | . . . . . . . . . . O 1 O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


This atari above at :w6: is the tesuji. Continued:

Click Here To Show Diagram Code
[go]$$B White manages sente to fix the ladder
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X 4 . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . 1 . X . X . X O . |
$$ | . . . . . . . . . O X O O X . X . O O |
$$ | . . . . . . . . . 3 O C O X X O O O . |
$$ | . . . . . . . . . . . 2 O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


After black :b1: escapes, the ladder is still broken, so white can capture at :w2: and black now cannot get either the ladder or the lower right due to being out of sente moves. Still, black can get a good position by cutting. Continued further:

Click Here To Show Diagram Code
[go]$$B Black gets center influence
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X O . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . X 3 X . X . X O . |
$$ | . . . . . . . . . O X O O X . X . O O |
$$ | . . . . . . . . . X O a O X X O O O . |
$$ | . . . . . . . . . b 1 O O O O . . . O |
$$ | . . O . . . . . . . . X X X X O O . O |
$$ | . . . , . . . . . , . . O . . O O . 4 |
$$ | . . . O . . . . X . . . . X X X O . . |
$$ | . . . . . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . . . O 2 |
$$ ---------------------------------------[/go]


Black still manages a good position (and better than magnifying the ladder only once would have achieved), but still only a lead of about 2.5 points according to KataGo. Big by bot standards, but not quite as assuring on the human side with so much play left in the game.

Note that the ko capture of "a" is NOT sente for black - white will happily ignore it and play on the top side. This means that black will have the ko aji of white cutting at b hanging over his head. In fact, if you look at KataGo's prediction, the ownership prediction is curiously thinking that black will kill all of white's stones in the center. What's going on is that KataGo anticipates that as black tries to make good on a big moyo on the top and upper right, white can invade seemingly recklessly, including even moves that don't work locally. White expects to escalate the value of those fights until there are big ko threats in those fights, then start the ko at b, and get two moves in a row destroying black's top area, while black captures the center. So while black is leading, it will be a hard fight ahead.

Black of course can do better. By the time white has made the mistake of escaping from the ladder twice, black's best option is to just keep laddering for a while, with the plan to play the full broken ladder. White should not be running at all, but if white does, black's best option by far is not to attempt a ladder maker (because of the way white can resist as above), and just go with Lee Sedol's original play in the game.

Click Here To Show Diagram Code
[go]$$B Best plan is the broken ladder
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . . . X O 2 3 . . . . . . . . . . . . |
$$ | . . . . 1 . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . X . |
$$ | . . . . . . . . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O . O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


But with one modification. Tentatively, if I've done my analysis with KataGo right, then if black really is trying to maximize points, the timing of the forcing move ideally should be a little different from when Lee Sedol played it, which was with 4 stones in the ladder. Below is the approximate point in the ladder where the forcing move should be played if white keeps running that puts white in the greatest bind in terms of sheer points.

Click Here To Show Diagram Code
[go]$$W Around 8 stones in the ladder, plus or minus one, is the time to force
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . X . . . . . |
$$ | . . . O . X . . . , . . . . . X . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X X . . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . . . X O O X . . . . . . . . . . . . |
$$ | . . . . X 1 3 4 . . . . . . . . . . . |
$$ | . . . , . 2 5 7 . , . . . . . , . X . |
$$ | . . . . . . 6 . . . . . . . X . X O . |
$$ | . . . . . . . . . . . . . X . X . O O |
$$ | . . . . . . . . . . O 8 O X X O O O . |
$$ | . . . . . . . . . . . . O O O X X X O |
$$ | . . O . . . . . . . . X X X X O O X O |
$$ | . . . , . . . . . , . . O . . O O X . |
$$ | . . . O . . . . X . . . . X X X O X X |
$$ | . . . . . . . . . . . . . . . . O O X |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ ---------------------------------------[/go]


This post by lightvector was liked by 2 people: Bill Spight, MikeKyle
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