Igo Hatsuyoron 120: Recent AI Analysis Applied to the Hardest Problem Ever

Here is the famous go problem Igo Hatsuyoron 120

Black to play and win

Source and Context

This problem originates from the Igo Hatsuyoron, a legendary classical collection of tsumego composed by Inoue Dosetsu Inseki in 1713. Sensei’s Library states the following about this collection:

Designed for the training of the highest caliber students at the school. It was kept secret from all but a few of them, who studied the book under the direct supervision of the Inoue.

The problem above is number 120 from the collection, which has gained a reputation as the “Most Difficult Problem Ever”*. Despite several decades of research by many professionals, amateurs, and, most recently, AI-assisted analysis, this problem appears to still be unsolved, with “many classical solutions seemingly refuted and modern lines still not entirely certain” (ref: Jane Street Tech Blog, linked below).

Prior to the rise of strong AI, the state of the art (as of 2011) human research appears to be documented on this multi-lingual website: http://www.dgob.de/dgoz/trmdpe/

A Stunning Hanezeki

I cannot say that I even begin to understand this problem. However, I can say that one of the most profound features of this problem, which screams out at anyone that even casually scrolls through its main line, is this incredible hanezeki position:

image032

Despite a huge 20-stone black chain being in atari, surprisingly neither black nor white should try to save or capture it, since making any move to do so would actually put them at a decisive disadvantage.

For more about hanezeki, see the Sensei’s library page or another forum thread where we discuss and analyze a related hanezeki that was composed by Harry Fearnley, as inspired by his study of Igo Hatsuyoron 120.

Recent AI Analysis

A difficulty with applying modern AI to the problem is that it was composed for Japanese rules with no komi (since komi was not widely adopted until centuries later). However, the problem’s requirement for very deep reading and understanding of large-scale, long-distance fights plays a larger role in leading all previous attempts of using AI to fail.

I recently found out from this reddit post and a LifeIn19x19 discussion thread that a custom trained version of KataGo has been applied to this problem, seeming to yield some promising and possibly novel results. The main announcement is on this site:

*yes, yes, one could say that an empty board would be an even harder problem
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yebellz… thank you :heart:. You introduce me some of the finest Go porn :nerd::thinking::face_with_monocle:

Definition of "Porn"

television shows, articles, photographs, etc., thought to cater to an excessive, irresistible desire for or interest in something (source)

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Curiously, the commenters in the linked Senseis definition conclude that this is not “hanezeki”!

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To be fair, it seems undecided. The conversation reflects that there is no appropriate language to describe this. Suggestions are made, opinions are shared, but it seems undecided and up in the air. I wish they had continued their discussion. I would love to have seen what they came up with and their reasoning behind it.

In a very fun way this is a moment in Go history where new language might actually be birthed. All Go language originates from somewhere. Many situations, just like this one, end up birthing terminology that future generations will use for hundreds of years or more. The word nerd inside me is giggling like a little school girl at the thought :smiling_face_with_three_hearts:

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To be clear, this is purely a linguistic debate, which arises since the term “hanezeki” has clear etymology from combining “hane” and “seki” (with the “s” sound becoming a “z” sound due to Japanese linguistic conventions). This combination appears to come from the prototypical hanezeki pattern (the one shown first on the SL page) in which a hane stone on the first line is in atari.

However, despite the narrow definition suggested by this etymology, it does seem that some authors have taken to using this term to refer to the broader class of seki that the Igo Hatsuyoron 120 problem falls under. Namely, this class could be defined as seki positions that include some stones that are in atari (but surprisingly should not be captured or saved). However, there is no widely established term to refer to that, and the combination “atari” and “seki” may also be problematic (as discussed on SL).

I think to be careful, one could call it a (temporary) “seki analogous to hanezeki”. After all, to understand it, one must understand hanezeki positions.

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I wish I could marry your words. Please, never stop :smiling_face_with_three_hearts:

In my previous post in this thread, I discussed how the term “hanezeki” is sometimes more broadly applied than its etymology would suggest, and I proposed a broader definition to capture of a larger class of seki positions analogous to hanezeki:

However, I realized that there are other positions that are also analogous to the prototypical hanezeki (in the sense that it is a seki where any further play will cause one to lose a capturing race), but these positions do not require any stones to be in atari.

Juha Nieminen discovered and analyzed such a position:
http://warp.povusers.org/go/UndeadBentFours/

So, maybe an alternative generalization of the hanezeki concept would be to define it as a seki position where any further play will cause one to lose a capturing race. Perhaps, the terms “semeai” and “seki” could be combined to yield a new phrase “semeaizeki”, if I’m not butchering the Japanese rendaku conventions.

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