Re: Fraud Benson's Rule?

["Weimin Xiao" <ranxiao@xxxxxxxxxxxx>]

Region is defined as a maximum connected empty point block in Martin's Play
It Safe. Thus, the partial board should have few regions:
Region 1: A1                    up left corner
Region 2: B2                    diagonal next to the up left corner
Region 3: D1~D4~A4        L shaped region
Region 4: F1                    top line
Region 5: H1                    top line

Am I right?

Weimin

-----Original Message-----
From: Ray Tayek <rtayek@xxxxxxxxxxxxxxxxx>
To: computer go <computer-go@xxxxxxxxxxxxxxxxx>
Date: Sunday, October 04, 1998 6:27 PM
Subject: Re: Fraud Benson's Rule?

...
>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 Safe, 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/