Biggest Corner

    Keywords: Life & Death, Tactics, Problem, Variant

Table of contents Table of diagrams
White to move and try to invade the corner.
Simple start
Winning line on 9x9 fails on 8x8.
The key difference
Wall is too close.
White to move and try to invade the corner.

[Diagram]
White to move and try to invade the corner.  

Expected Result

White cannot live[1].

Teaching Value

This shows the power of walls even when they are far away. Also beginners are constantly asking if a 3-3 invasion under a 4-4 stone can live. The real answer is that it depends on the surroundings. So much so that in this case there isn't even a 4-4 stone, yet white still cannot live in the corner!

Simple start

[Diagram]
Simple start  

The key is that black takes away white's eye space by playing on the 2nd line. Usually black cannot do this because it allows white to escape to the center easily. However here due to black's rock-solid wall, running to the center is of no use.

Also notice that the shape in the corner is a basic LGroup with no legs. This shape locally only has 1 eye.


Winning line on 9x9 fails on 8x8.

The line given at 10x10CornerGame1 fails on 8x8. On 9x9 white could use this line to live.

[Diagram]
Winning line on 9x9 fails on 8x8.  
[Diagram]
The key difference  

Here black can play B4 instead of at A since the wall is close. If the wall was line further this would fail.

[Diagram]
Wall is too close.  

See Also


Challenge

[Diagram]
White to move and try to invade the corner.  

Tapir: Are you sure? I would like a demonstration...

yoyoma: I added a typical example. If you like we can play it here. I hope I do it right because I don't actually know all the variations. :)

Tapir: I was essentially asking for the variations which are given now... so we don't need to continue here.


Discussion

ThorAvaTahr: The behavior of this corner seems to hold up to even a larger area. Maybe even 10x10, see 10x10CornerGame1.

yoyoma: Ah thanks for the 10x10CornerGame1 link. That page also talks about the pro article on the subject, and shows how white can live in the larger area. I think it should be changed to 9x9CornerGame? because I think the article mentioned on that page deals with that size, and white can still live. That's why I made this one 8x8, because it's my understanding that some of his variations don't work on that size.

Bill: Since the 10x10 is larger, maybe this page should be renamed to Smaller Corner. ;)

yoyoma: This page is supposed to be the largest corner that cannot be invaded.


Biggest Corner last edited by Unkx80 on July 26, 2008 - 19:43
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