Life In 19x19

billywoods wrote:It's a real eye for black if and only if black controls all or all but one of the corners"

I have been using another definition of a real eye, that I think is logically very sound, but not that easy to apply in practice. Something along the lines of it being a real eye if none of the stones that surround it can be put in atari. I might be better of using something simpler, even if it only works 99% of the time. (Not saying this is the case here; I don't know.)

PeterPeter wrote:

billywoods wrote:It's a real eye for black if and only if black controls all or all but one of the corners"

I have been using another definition of a real eye, that I think is logically very sound, but not that easy to apply in practice. Something along the lines of it being a real eye if none of the stones that surround it can be put in atari. I might be better of using something simpler, even if it only works 99% of the time. (Not saying this is the case here; I don't know.)

Defining an eye is not easy. The topic has generated much discussion on Sensei's Library.

Here is a cute example from http://senseis.xmp.net/?TwoEyeFormation .

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[go]$$B Two-eye-formation with four black strings
$$ . . . . . . . . . . . . . . . . .
$$ . . . O O . . . . . . . O O . . .
$$ . . . O . O O O O O O O . O . . .
$$ . . . O O O X X X X X O O O . . .
$$ . . . . O X X O O O X X O . . . .
$$ . . . . O X O . O . O X O . . . .
$$ . . O O O X O O O O O X O O O . .
$$ . . O X X . X X X X X . X X O . .
$$ . . O X O X O O O O O X O X O . .
$$ . O O X O X O . O . O X O X O O .
$$ . O X X O X X O O O X X O X X O .
$$ . O X O O O X X X X X O O O X O .
$$ . O X O . O O O O O O O . O X O .
$$ . O X O O X X X X X X X O O X O .
$$ . O X X X X O O O O O X X X X O .
$$ . O O O O O O . . . O O O O O O .
$$ . . . . . . . . . . . . . . . . .[/go]

OC, such formations are rare.

There are eyes that count for independent life and those that do not. As a practical rule of thumb, these are the types of eyes that count for independent life.

Click Here To Show Diagram Code

[go]$$B Single point eyes
$$ . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . |
$$ . . B X B . . . . . . . B X |
$$ . . X C X . . . . . . . X C |
$$ . . . X B . . . . . . . B X |
$$ . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . B X |
$$ . . . . . . . . . . . . X C |
$$ ----------------------------[/go]

(From http://senseis.xmp.net/?Eye )

The points indicated by are occupied or controlled by Black. Note that Black controls one diagonal of the corner eye, two diagonals of the side eye, and three diagonals of the center eye.

You might also be interested in this page. http://senseis.xmp.net/?TopologicalLife

I'd like to continue this thread, because I am interested in how we look at and understand the points in a shape that may or may not become eyes. Here is a random and relatively simple sample problem taken from Logan's Go Problem & Pro Game Journal:

Click Here To Show Diagram Code

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

My first thought is that the triangled points can never become eyes, which leaves me to look for them within the 7 shaded points.

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[go]$$B shaded
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | T X X X O O . . . . .
$$ | ? ? ? X X O . O . . .
$$ | ? ? ? ? T . . . . . .
$$ ----------------------[/go]

Click Here To Show Diagram Code

[go]$$B alphabetical
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | . X X X O O . . . . .
$$ | a b c X X O . O . . .
$$ | d e f g . . . . . . .
$$ ----------------------[/go]

What I'm curious about is what happens next in your minds. Do you imagine the space being divided for example at b or e? Do you see certain points as being easier to protect, for example at d or c? Do you visualize a black stone for example at b or e and find the shape pleasing? Do you visualize the damage a white stone might do for example at e destroying the potential for the adjacent points of d, b and f to become separate eyes?

I'm guessing that any stronger player will respond: none of the above - my pattern recognition instantly saw that either b or e would create a living shape, both serving to protect eyes at d and c. Perhaps a more difficult problem could illustrate your thought process better?

In any case, my original thought was that it would be great if I could start my search for the correct sequence by seeing the best possible eyes just pop out at me, and select moves that keep these particular eyes viable. Is this a useful or useless approach?

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[go]$$B particularly good eye potential?
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | . X X X O O . . . . .
$$ | . . C X X O . O . . .
$$ | C . . . . . . . . . .
$$ ----------------------[/go]

What about "seeing" some shapes you might want to prevent ?

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[go]$$B bulky five I
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | . X X X O O . . . . .
$$ | ? T ? X X O . O . . .
$$ | ? ? . . . . . . . . .
$$ ----------------------[/go]

Click Here To Show Diagram Code

[go]$$B bulky five II
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | . X X X O O . . . . .
$$ | . ? ? X X O . O . . .
$$ | ? T ? . . . . . . . .
$$ ----------------------[/go]

On this subject, I stumbled upon this page on Sensei's which is very helpful:

http://senseis.xmp.net/?PlacementPrinciples

Click Here To Show Diagram Code

[go]$$B Wrong way
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | 3 X X X O O . . . . .
$$ | 2 4 5 X X O . O . . .
$$ | . 1 . . 6 . . . . . . .
$$ ----------------------[/go]

Bill Spight wrote:

$$B Wrong way
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | 3 X X X O O . . . . .
$$ | 2 4 5 X X O . O . . .
$$ | . 1 . . 6 . . . . . . .
$$ ----------------------

Click Here To Show Diagram Code

[go]$$B Wrong way
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | 3 X X X O O . . . . .
$$ | 2 4 5 X X O . O . . .
$$ | . 1 . . 6 . . . . . . .
$$ ----------------------[/go]

5 at 6 lives.

Shaddy wrote:

Bill Spight wrote:

$$B Wrong way
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | 3 X X X O O . . . . .
$$ | 2 4 5 X X O . O . . .
$$ | . 1 . . 6 . . . . . . .
$$ ----------------------

Click Here To Show Diagram Code

[go]$$B Wrong way
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | O O . . . . . . . . .
$$ | O X O O . . . . . , .
$$ | 3 X X X O O . . . . .
$$ | 2 4 5 X X O . O . . .
$$ | . 1 . . 6 . . . . . . .
$$ ----------------------[/go]

5 at 6 lives.

Oops!

Well, the caption is correct.