Re: Fraud Benson's Rule?

[Ray Tayek <rtayek@xxxxxxxxxx>]

At 05:52 PM 10/4/98 -0700, you wrote:
>Hi, there,
>
>I have the following up left part of a board, and the blacks (@; O white, +
>empty) are dead:
>
>+OO+@+@+O +
>O+O+@@@OO+
>OOO+@OOO+
>++++@OO+
>@@@@O+
>OOOOOO+
>+++++++++
>
>Based on Martin Muller's description of Benson's Unconditional Life rule
>(Playing it Sage, M. Muller),
>1. The up left region (spaces) between white and black is color-enclosure,
>small, and healthy for the black.

no, the black enclosed region includes the white stones and the eyes.
it is not a small black-enclosed region because the 2-2 point is empty and
not on the border.
if the 2-2 point were filled by white, then the region would be small
black-enclosed.
but even so, it would not be healthy for black because the 1-1 point is an
empty intersection that is not a liberty of black.

recall that:

1. in order for a region to be small x-enclosed each intersection must be
on the border or contain a ~x stone or both.
2. in order for a small x-enclosed region to be healthy for an x-block,
every empty intersection must be a liberty of the x-block.

>2. the black has another same type region at top.
>3. From 1 and 2, the black has two vital counts, so sure-alive.

even if the region was small black enclosed and healthy for the block with
an eye. the cuttable back block of 4 stones also would also need 2 healthy
regions.

i have a java implementation of benson's algorithm on my home page (under
go) if you are interested.
hth

Ray (will hack java for food) http://home.pacbell.net/rtayek/
hate Spam? http://dorkslayers.com/