Re: computer-go: Evaluating positions

[Don Dailey <drd@xxxxxxxxxxxxxxxxxxxxx>]

Yes, you are correct.   A few days ago  I worked out all the  possible
states  a given  intersection can  have,  from  the perspective  of  a
perfect player.  There  is only one state  (in my definitions) that do
not change as the  game progresses even to a  perfect player and  it's
what   I  call  "absolute     ownership."  Absolute  ownership   of an
intersection means that a player is  guaranteed, with best play on his
part (but not  necessarily the opponents part) to  keep ownership of a
square without suffering any disadvantage.

Another kind of intersection may have implicit ownership, but it could
be in your best  interest to give up  this ownership (for bigger gains
elsewhere.)  My base  definition of  "ownership" is any   intersection
which the opponent cannot stop you from owning by the time the game is
over  if you really  want to keep  it.  It's  not  always in your best
interest however to keep some of these "owned" intersections.

A  third  type of ownership  I  call  "proper  ownership" because with
proper  (best)  play  on  both sides  you  are guaranteed  to own that
intersection when  the  game is complete.  Without  best  play  on the
opponents part, it may be more  advantageous to seek profit elsewhere,
so this kind  of intersection is not  absolute, however it's  equal in
value to absolute ownership.

A lot of intersections, especially early  in the game have uncontested
ownership.   At the very start of  the game who  owns which particular
corners may be decided by alternating choices,  like choosing up teams
in informal sporting contests.

At the beginning of the game, a perfect  player can correctly say that
he  owns n squares  (n  depends on what  komi should  be to a  perfect
player) but he cannot  say which squares  they are.  But already, some
of these squares can be  assigned ownership status.  For instance  the
first player may  even be able to  claim  base ownership of  the whole
board (which  just means he can pick  any intersection he wants to and
have it in his control  at the end of  the game if he is  determined.)
Most of this ownership goes away as soon as he places the first stone.

Does any of this  have a practical use?  I  don't know for sure, but I
have always  found it useful to  think about stuff   like this from as
many different viewpoints as possible.   It cannot hurt to have  extra
perspective   on things.   Cognitively, it's very    easy to imagine a
perfect player thinking about intersections like  this because it maps
in a very directly way to the goal  of the game.   "Hot on the attack"
does not map very well to anything useful to the perfect player.

 
Don




   From: Christian Nentwich <c.nentwich@xxxxxxxxxxxxxxxxx>

   > A perfect player doesn't see a board the way we see it.  His vision of
   > a board is  not what it is now,  but what it  will be.   For instance,
   > what to us looks like a completely uncontested corner of the board may
   > appear to be clearly colored to a perfect player.

   I'm not sure this thread should be continued, but anyway.. this perfect 
   player of yours seems to be assuming that there is only one line of perfect 
   play, which is a tough nut to prove.  There may be 100 perfect replies to 
   each move.

   The perfect player sees the next perfect move. If he sees further, he's 
   reading the opponent's mind.

   If the perfect player goes for a pint after hearing the komi announced, it's 
   because of experience in playing him/herself.

   Christian