Unsolved Problems in Go

[RobertJasiek]

the choice is no longer undecidable.

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.

[TheBigH]

the choice is no longer undecidable.

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.

[Cassandra]

Any unsolved problem is only because ... the problem is too open ended (IE that igohatsu book having a 100+ move variation, cant be sure of answer).

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.

[RobertJasiek]

I disagree.

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

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.

Yes.

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

you seem to be saying that the problem is undecidable because you're missing information that would help you decide what to do.

Yes.

This would include the situation on the rest of the board,

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.

how the tournament rules handle jigo v no result,

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.

your current standing at the tournament,

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.

I don't consider that "undecidable". I would call that "under-determined" instead, if that information is not provided.

It is undecidable because it is under-determined.

An undecidable problem would be one that cannot be solved even when all the relevant information is known.

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

[HermanHiddema]

the choice is no longer undecidable.

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.

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.

[RobertJasiek]

is tournament dependent

And this means that some tournaments do not specify the handling.

The handling of no-result should not be part of the game rules.

Anything under-determined such as 'no-result' without further specification should not be part of the rules of play.

[HermanHiddema]

is tournament dependent

And this means that some tournaments do not specify the handling.

Still, that does not make it an unsolvable problem. One can simply ask the organizers how a no-result will be handled.

[RobertJasiek]

One can simply ask the organizers how a no-result will be handled.

And the organiser can answer: "I do not tell you because the referee / tournament committee may make an arbitrary decision!" When I posed similar questions to relevant organisers, then usually they tried the hardest to avoid having to clarify.

Besides not every game is played in a tournament. It is also possible that game positions are studied without being played.

[HermanHiddema]

One can simply ask the organizers how a no-result will be handled.

And the organiser can answer: "I do not tell you because the referee / tournament committee may make an arbitrary decision!" When I posed similar questions to relevant organisers, then usually they tried the hardest to avoid having to clarify.

Besides not every game is played in a tournament. It is also possible that game positions are studied without being played.

Similarly, an organizer might tell you: We have not yet decided whether winning or losing is better. That decision will be made later, and points will be awarded accordingly. Such a problem is artificial, IMO, and has nothing to do with go theory. Perhaps we can consider it an unsolvable problem of go politics

For study of positions by themselves, I would no consider the result of the game a consideration. For partial board positions, it is similar to e.g. the result of the position depending on who is ko-master. For full-board, it is similar to depending on komi. To me, those are external considerations.

[RobertJasiek]

For study of positions by themselves, I would no consider the result of the game a consideration.

It is the major consideration.

[HermanHiddema]

For study of positions by themselves, I would no consider the result of the game a consideration.

It is the major consideration.

To me, the major consideration would be the score of the position, both for partial board and full board positions. Whether that score translates into win, draw, or loss is not, in a mathematical sense, as relevant. Two lines of play that both "win" can still be distinguished by score.

[hyperpape]

Herman is right. Questions about go concern the results achieved in various positions. The question about how no result vs. tie affect the result of a tournament is no more a theoretical question concerning go than the question of which tesuji will best impress the woman of your dreams--it involves go, but isn't about go.

[RobertJasiek]

The question about how no result vs. tie affect the result of a tournament is no more a theoretical question concerning go

The question is relevant also independent of tournaments.

[TheBigH]

So the only question is which of the following applies:

Loss < Jigo < No Result < Win
Loss < No Result < Jigo < Win

and you've constructed a go problem that illustrates that question. In my opinion, the problem is solved if you can provide correct play for both those alternatives. A good analogy is differential equations; if I find the general solution I don't call the problem undecidable just because I don't know the boundary conditions. I call it solved. It's the same sort of thing here- we've identified the set of all possible solutions.

[RobertJasiek]

we've identified the set of all possible solutions.

We have identified all possible resulting sequences (not: solutions) but we have not identified which of them is better (that would provide solutions).