I wonder if there are any unsolved problems in Go. Like Life and Death problems where the status is unknown.

Yes. Of course.

See also: senseis.xmp.net/?IgoHatsuyoron

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Occupy Babel!

The game of go is unsolved. That's the first response you'll most likely receive.

After this, I believe many of the classic problem collections didn't originally include answers so were later solved and written down by dedicated players in later editions of these classics. IIRC the most famous one is Igo Hatsuyoron problem #120 :

Click Here To Show Diagram Code

[go]$$B Black to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . X O O . X O . . . . O . |
$$ | . . . . . X . O . . . X . . . . O . . |
$$ | . X O , . . . . . O . X . O O , . . . |
$$ | . . X X . X . . . . O X X . X X O O . |
$$ | . X . O . O . . . . . . X . X O . . . |
$$ | . O O O . . O O . . O O . O X . . . . |
$$ | O . . X . . . . . . . . . . X X X X X |
$$ | . . . X . . . O . . O . X X X X . O O |
$$ | X O O , . X . . . O . X . O O O O . . |
$$ | X . . O X . . . . O . X . . O . . X X |
$$ | X . . O X . . . X O . . . . . X X O O |
$$ | X X . . X . . O . O . . . . . . X X O |
$$ | . O O X O X . . . O . . X . O . . O O |
$$ | . . X . . X . . . . X . . . X . O O O |
$$ | O X X , X . . O . , O O O . O X O . X |
$$ | . . . . O X . . . . . . . . . X X O X |
$$ | O . X . . . . . O . . . O X O X . . . |
$$ | . X . . . . . . . . . . O X X X . . . |
$$ ---------------------------------------[/go]

I think a new western book just came out early this year about the problem, but I don't know if it's considered definitively solved now.

Other than this, you can also ponder over the many problems that editors dropped from later editions of classics because they were 'found not to work.' Maybe there's something to be found in those. The Guanzi Pu usually receives a high amount of editing whenever a new version is published.

Also, you can consider positions where the status changes depending on ruleset. Perhaps these perplexed people in the past (though for slightly difference reasons).

This is what you want.

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Poka King of the south east.

Countless of go theory research questions are unresolved.

I don't know your definition of "is considered definitely solved".

Indeed, there are two challenges that refer to "definitely" and "considered by whom".

We do not know any professional publication that includes the all-decisive Guzumi in the top right corner, leading to a Black win.

The latest professional publication (on Igo Hatsuyoron in total), by Cheng Xiaoliu 6p in 2010, now includes several moves that we found earlier, and used in our solution for problem #120. However, the solution given by Cheng, ending with Jigo, is not correct, because he missed another valuable move for White, a Tsuke in the upper left corner, found by Yamada Shinji 6p, giving White a win by two points. We do not think that Dosetsu created a problem "Black to play and lose by the smallest possible margin."

It is extremely difficult to get professionals involved into the problem, because it is so very complex and difficult.

However, we got very valuable feedback from professor Jeong SooHyun 9p from Myongji University in Seoul, including a statement that there were no grave mistakes in our solution.

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The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

I wonder if there are any unsolvable problems in Go. Would be nice.

What do you mean by "unsolvable"? That the given task is impossible to fulfill?

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Sanity is for the weak.

To find a consistent set of axioms for all mathematics is an unsolvable problem. ( see [url="http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems"]Gödel[/url] ). Likewise there might be unsolvable problems in go. But what should be considered as valid problem in Go? For example "get RJ and MW to agree" I wouldn't consider as a go problem .

One of the unsolvable because undecidable problems you find here:

http://home.snafu.de/jasiek/mistakes.html

Seems to me that this does not qualify, as the distinction between a "no result" and a tie is irrelevant when both are better than losing (and worse than winning).

Such a condition could be overriding indeed. Suitable global conditions are needed for a decision between tie and no result to become relevant.

And as soon as the global conditions are known, the choice is no longer undecidable. If we take as a given that the global conditions for any game are known, then the problem is never undecidable. (And if we don't, then every position becomes undecidable, I guess).

It seems to me that this is just an issue of insufficient information. I mean, there are two easily identifiable potential solutions. The preferred one depends on information that hasn't been given (ie. whether a jigo is better than a no result), but that doesn't mean the problem is undecidable. That would be like saying the equation x²=1 is undecidable because both x = 1 and x = -1 are solutions, which is of course ridiculous.

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Poka King of the south east.

Any unsolved problem is only because it is impossible to solve (IE black to kill white when white has two eyes) or the problem is too open ended (IE that igohatsu book having a 100+ move variation, cant be sure of answer).

Any problem that has been looked at by 9p and not solved is not worth solving, and probably has no right answer.

Wrong. If the global decision (close game on the rest of the board) remains the local decision between creating either a tie or a no result, then it is undecidable because one does not know which of the two is better because they are uncomparable.

I disagree. If you're behind on the rest of the board, you should go for the "no result" option. If you're ahead on the rest of the board, you should go for the local seki. Perfect play exists so there is, in principle, a way of judging who's ahead on the rest of the board. Therefore there exists an algorithm to tell you what you should do in this situation and the problem is solvable.

Please correct me if I have misunderstood you, but you seem to be saying that the problem is undecidable because you're missing information that would help you decide what to do. This would include the situation on the rest of the board, how the tournament rules handle jigo v no result, your current standing at the tournament, maybe other things. I don't consider that "undecidable". I would call that "under-determined" instead, if that information is not provided. An undecidable problem would be one that cannot be solved even when all the relevant information is known.

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Poka King of the south east.

Igo Hatsuyoron 120 is not "too open ended" at all.

The solution consist of three phases.

Phase 1 (approximately 70 moves long) is preparing the ground. This is the creation of the Hanezeki, including the building of the Hanezeki's tail. If we let aside really wrong moves for variations, it is possible to make some smaller, but not really decisive mistakes (i.e. non-optimal moves), which effect will be shown in phase 3.

Phase 2 if about finding the Guzumi or not (in this case Black will lose). And about White's best answer to the Guzumi (neither of which will lead to a White win). This phase is only two moves long, but extremely complex, because of the large amount of possible variations. And so far, nobody, even no professional, has found a refutation of the Guzumi.

Phase 3 (a further 100 moves until the end; endgame only) is harvesting the fruits. Nothing really decisive can happen here that would affect the outcome of the game (if we let aside really wrong moves again). And again, there is the chance of making some non-optimal, but non-decisive moves.

So the real problem of the problem is the situation before the Guzumi in the top right corner. We have been told by professionals that the Guzumi were a typical endgame move, which "usually" comes into mind automatically.

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The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

You don't disagree, but you discuss other cases.



Yes.

The interesting case is "tie on the rest of the board".



Yes.



The rest of the board can often circumvent the problem of missing information, but cannot do so in the interesting case and cannot do so if the rest of the board's dynamics let the interesting case be somehow relevant.



Rules or tournament rules can provide sufficient information or can not provide it. E.g., the rule "for the sake of making strategic decisions, 'no result' equals 'the score 0' and tournament rules do not alter this" would suffice.



This is meta-gaming. Ok, it exists, and once I was in a position of necessary meta-gaming and strategy depending on setting personal preferences whether I considered a tournament place or a seeding points amount more important; accordingly I had to achieve or avoid a jigo. However, IMO, rules of play should be about what happens on the board only and avoid meta-gaming to have any impact.



It is undecidable because it is under-determined.



All relevant information is known because the rules makers have not had the intention to provide the missing information.

Within the context of the question, there is no such thing as a "close game". Games are a win, loss, or draw. The handling of the no-result case is meta-information, and is tournament dependent, in the same way that e.g. komi is. The handling of no-result should not be part of the game rules.