Re: [Go Study] Stone Position & Importance

["P.J.Leonard" <P.J.Leonard@xxxxxxxxxx>]

Mousheng Xu wrote:
> 
> Hi, smart guys,
>         You all know the most important position at the very beginning is around
> position (4,4). I am thinking about relating the position of a stone with
> its importance (or its value).
>         1. Suppose (4,4) is the best (some people may disagree) position on board
> at start, we can easily propose some thing like
> f(x,y)=1/(1+(x-4)^2+(y-4)^2), but how do we know it is a good one based on
> logic or statistics?
>         2. Suppose the value of the first stone on board is determined by two
> factors: how close it is to the corner (territory) and how far it is to the
> center point (influence). There are a couple of theses which discuss the
> influence function. Are there any thing, or could you propose something
> about the affect of the border or corner? Even the influence functions
> discussed in Zobrist's and Ryder's theses are quite arbitury, how do you
> think?

 Something I tried for estimating the potential territory capturing of a
stone
that uses the the properties of the edges/corners walls.

 o Assume that the territory capturing abality of a stone is related to
the possibility of an opponent stone making a path of a certain distance
from it's placement. (e.g. 4 5 6 ? )

 o Note that corner and edge points have less paths to connect out.

 o For each point construct a graph representing the possible
connections
to say the 5'th level.

 o Each point on the 3'rd and 4'th level get awarded a weight that
depends
on the width of the level, the smaller the width the more likely a stone
on this
point will capture the seed point.

 o This proceedure can be refined by looking at the paths from the seed
point to the target level.
A point which belongs to more paths has more weight.

 This procedure will also work for walls.

 
 cheers Paul.