Largest solved go board?

[iam3o5am]

Hello all,
Just wondering if anyone can point me to any link discussing whatever is currently considered the largest solved go board. I can find articles from a few years ago discussing a solution to 7x7 go, though I am wondering if anyone is aware of current attempts at solving go. Thank you.

[Krama]

Hello all,
Just wondering if anyone can point me to any link discussing whatever is currently considered the largest solved go board. I can find articles from a few years ago discussing a solution to 7x7 go, though I am wondering if anyone is aware of current attempts at solving go. Thank you.

5x6 has been solved I think. As for 7x7 I don't think it has been solved so far.

I think in the near future with the usage of quantumn computers we could expect 9x9 to be solved.

[YeGO]

5x5 seems to be the largest square board that has been rigorously solved (with a mathematical proof for a clearly specified rule set):
[1] http://erikvanderwerf.tengen.nl/5x5/5x5solved.html

5x6 along with several other rectangular boards have also been rigorously solved:
[2] http://erikvanderwerf.tengen.nl/pubdown ... GA2009.pdf

There are some that have claimed solutions on larger boards:
[3] http://www.mathpuzzle.com/go.html
[4] http://senseis.xmp.net/?7x7BestPlay
However, those claims seem dubious given the lack of details in rule set, methodology, and mathematical proofs. In fact, [2] specifically refutes some of the claims made by [3].

[YeGO]

Ok, I did some more googling. Erik van der Werk's thesis, found here:
http://erikvanderwerf.tengen.nl/pubdown ... erwerf.pdf
references personal communication with John Tromp and a 1995 article by James Davies, where human players have claimed to have found optimal solutions on the 6x6 and 7x7 boards (see page 54). However, these solutions have not been verified by computer (since his 2004 thesis, at least).

It is worth noting that Erik van der Werk's computer-verified solution for the 5x6 board proved all other previous human solutions to be incorrect.

Edit: fixed the misspelled name. Sorry!

[luigi]

Apparently, 7x7 Go has been weakly solved, but the article is in Chinese and I can't make heads or tails of it (Google Translate doesn't help).

[Bonobo]

[..] references personal communication with John Trump [..]

It’s TROMP, John Tromp, for heaven’s sake! Is not even this forum a safe place?

https://scholar.google.com/citations?us ... AAAJ&hl=en
https://senseis.xmp.net/?JohnTromp
https://tromp.github.io/ (nice visit counter there)

(and pls forgive the late reply, only now I noticed the typo )

[vier]

[..] references personal communication with John Trump [..]

It’s John Tromp,

Two lines earlier and two lines later another name is misspelled.
We also got some spam.

[billyswong]

Apparently, 7x7 Go has been weakly solved, but the article is in Chinese and I can't make heads or tails of it (Google Translate doesn't help).

Some other points made in the Chinese article (not in order):

• The need of komi stems from existence of tengen, as for a board without tengen, white can play mirror go to get a draw. (true for small boards at least)
• A suggestion in solving small board go: For 8x8 board, let's first make sure black always win for non-komi games, then for small komi games, then inch closer and closer towards optimal solutions by branch cutting etc.
• Four problems in small board go solving:
  (1) what is the standard of strong proof and weak proof
  (2) are there any "exploration space" in method of proof
  (3) Aside from exhaustion, are there any other way to prove a closed territory is not survivable for opponent to invade (endgame judgment)
  (4) for example 7x7 board, why playing first move to 1st/2nd/3rd line won't be optimal
• For Li Zhe's 7x7 optimal solutions, the first three moves are unique; the first seven moves branch into the five core gameplay sequences in illustration, each with irrelevant minor variations later on of course
• The solution is a weak proof, thus we should better call it a "study"
• We should do some alpha-beta game tree search to confirm/disprove Li Zhes' suggested solution

To translate it all is tedious so a lot of points are left out. Especially those that are less relevant after AlaphGo is published and win the world.

[Bill Spight]

Apparently, 7x7 Go has been weakly solved, but the article is in Chinese and I can't make heads or tails of it (Google Translate doesn't help).

Some other points made in the Chinese article (not in order):

• The need of komi stems from existence of tengen, as for a board without tengen, white can play mirror go to get a draw. (true for small boards at least)

Mirror go does not produce a draw for the 6x6; Black wins. Ted Drange had already proved that in the 1970s.

[luigi]

[*]For Li Zhe's 7x7 optimal solutions, the first three moves are unique; the first seven moves branch into the five core gameplay sequences in illustration, each with irrelevant minor variations later on of course

Is there a link to the actual solutions?

[billyswong]

[*]For Li Zhe's 7x7 optimal solutions, the first three moves are unique; the first seven moves branch into the five core gameplay sequences in illustration, each with irrelevant minor variations later on of course

Is there a link to the actual solutions?

They are posted in the Chinese article, right after the meeting photo

[billyswong]

Apparently, 7x7 Go has been weakly solved, but the article is in Chinese and I can't make heads or tails of it (Google Translate doesn't help).

Some other points made in the Chinese article (not in order):

• The need of komi stems from existence of tengen, as for a board without tengen, white can play mirror go to get a draw. (true for small boards at least)

Mirror go does not produce a draw for the 6x6; Black wins. Ted Drange had already proved that in the 1970s.

They demo'd a 5x5 board with tengen crossed out. They are not using a even line board.

Also I mistranslated a little bit. The exact wording is "Black play first move at tengen and end the game with 9 komi. In reverse, when tengen point is removed, the game is close to no komi." Thanks for spotting out my mistake in over simplification.

[luigi]

[*]For Li Zhe's 7x7 optimal solutions, the first three moves are unique; the first seven moves branch into the five core gameplay sequences in illustration, each with irrelevant minor variations later on of course

Is there a link to the actual solutions?

They are posted in the Chinese article, right after the meeting photo

Oh, my Chrome didn't show those pictures. I just resorted to Internet Explorer to see them.

Here are, for future reference, the first three:

1.png (14.72 KiB) Viewed 19189 times

2.png (14.83 KiB) Viewed 19189 times

3.png (17.59 KiB) Viewed 19189 times

[luigi]

And here are the remaining two:

4.png (12.46 KiB) Viewed 19189 times

5.png (14.95 KiB) Viewed 19189 times

[gamesorry]

I have a question on the third game of Li Zhe's 7x7 optimal solutions above:

When black plays , why can't white resist at a?

$$Bc
$$ -----------------
$$ | . X . 1 O . . |
$$ | . . X O X 2 . |
$$ | . a O O X O . |
$$ | . . X X O O . |
$$ | . . X . X O . |
$$ | . . . X . X . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------
$$

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . X . 1 O . . |
$$ | . . X O X 2 . |
$$ | . a O O X O . |
$$ | . . X X O O . |
$$ | . . X . X O . |
$$ | . . . X . X . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------
$$[/go]

After that, black can't fight back:

$$Bc
$$ -----------------
$$ | . X 7 1 5 3 0 |
$$ | . 6 X O X 4 8 |
$$ | . 2 O O X O . |
$$ | . 9 X X O O . |
$$ | . . X . X O . |
$$ | . . . X . X . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------
$$

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . X 7 1 5 3 0 |
$$ | . 6 X O X 4 8 |
$$ | . 2 O O X O . |
$$ | . 9 X X O O . |
$$ | . . X . X O . |
$$ | . . . X . X . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------
$$[/go]

(edit) Never mind, I missed the following variation:

$$Bc
$$ -----------------
$$ | . X . 1 O . . |
$$ | . . X O X 3 . |
$$ | . 2 O O X O . |
$$ | . . X X O O . |
$$ | . . X . X O . |
$$ | . . . X . X . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------
$$

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . X . 1 O . . |
$$ | . . X O X 3 . |
$$ | . 2 O O X O . |
$$ | . . X X O O . |
$$ | . . X . X O . |
$$ | . . . X . X . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------
$$[/go]