# Building a live group on a quarter board where two sides are already black

This exercise is kind of go club folklore: Given a quarter go board where two sides are already occupied by black (and unconditionally alive), white starts playing. White wins when she is able to create a living group in the quarter board.

``````\$\$ | X X X X X X X X X X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ ---------------------
``````

It is also part of go club folklore that with correct play this task is impossible for white and black kills any white group.

For clarification: Here is an example of white trying to live (and fail):

``````\$\$ | X X X X X X X X X X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . . . . . . . . . X
\$\$ | . 1 3 . . . . . . X
\$\$ | . 2 4 W . . . . . X
\$\$ | . . . 6 5 . . . . X
\$\$ | . 7 . . . . . . . X
\$\$ ---------------------
``````

White starts on the (3,4) point but black counters at (4,2). After the enclosure, the corner has only one eye, and Black's outer stones cannot be captured because of the outer walls helping them. Note that in this setup all ladders are favouring Black.

• As far as I'm aware, there's no proof that white can live anywhere on the whole board even if black starts with just one stone and that stone is not automatically unconditionally alive. ​ See this discussion. ​ ​ ​ ​
– user13741
Commented Jun 7, 2017 at 21:01
• @RickyDemer: It is well known that White can live on boards as small as 6×6 and 6×7 (solved, see mathpuzzle.com/go.html ) and it is very probable that white also lives on 7×7. Experience shows that even a weak Go player can create some living white group on 19×19. Commented Jun 9, 2017 at 15:13

This has been discussed a lot in Sensei's Library (http://senseis.xmp.net/?BiggestCorner and http://senseis.xmp.net/?10x10CornerGame1). The consensus seems to be that white dies with 8 free spaces, but can live with 9 free spaces using 3-3 point and some clever tesujis. I copied some variations from Sensei's to EidoGo for easier studying: http://eidogo.com/#1ZUwMVRaH

I'm not familiar with this as folklore, but the setup is similar to the setup a person might use to work on corner problems. I believe that this could be answered by looking a many examples of corner joseki. Assuming white's goal here is simply to live, the border formed by black is too far removed from the corner to have a significant effect of white's play. The space enclosed by black may be intimidating, but most corner joseki is contained in a much smaller space.

See Sensei's Library for more examples, but I'll provide one here. Two note: I'm choosing one that I'm familiar with rather than a "best" example and white goes first in this because that's what you stipulated in your question.

W(3, 4) B(5, 4) W(5, 3) B(6, 3) W(4, 3) B(6, 3) W (3, 6) B(5, 7)

Now, given the black border of stones, black may play move 6 (5, 7) differently than the standard joseki. However, I believe that white's moves before that to provide a sufficiently strong foundation that black would lose the fight, or have to run back allowing white to take up more territory in the corner.

• As far as I'm aware, there's no proof that white can live anywhere on the whole board even if black starts with just one stone and that stone is not automatically unconditionally alive. ​ See this discussion at Sensei's Library. ​ ​ ​ ​
– user13741
Commented Jun 7, 2017 at 21:12
• While a complete joseki may easily fit in the given space, Black can make use of the power of his immortal walls and deviate from joseki from its first move on. I tried it a lot of times, and it is really difficult to make life with white. Commented Jun 8, 2017 at 8:58
• I'm not a strong enough player to rely solely on my own analysis. Can you provide a sequence that you tried that was unsuccessful for white?
– BBS
Commented Jun 8, 2017 at 15:02
• See my edit on the question with a simple example. Commented Jun 9, 2017 at 13:38