Re: computer-go: perfect play

[Don Dailey <drd@xxxxxxxxxxxxxxxxxxxxx>]

Hi Roland,

That's a  lot  to thing about!   I have  heard the stability reasoning
before, that advantages or disantvantage accumulate and are not likely
to be wrecked by a single move.

However, and I'm just guessing at this, I don't think that has much to
do with complexity.

Whether we are trying to just WIN or maximize score makes a little bit
of a difference.  If we are trying to WIN, then small errors that lose
a little territory but still permit a win are ok.  If we are trying to
maximize our territory, then we  have several classes of errors,  some
hurting us more  than others,  but  all them wrong (except  just those
that    happen to maximize  the final   territory.)   In this case, it
probably becomes more  like chess.  But I  will argue shortly that the
minor errors are extremely important.

Now before we continue, I want to construct a NEW game, that will make
Chess  fit more into your  description of Go.   The new game is played
exactly like Chess, but really consists of a series  of games.  One of
these series (really  a match) will  be condensed into a single result
which we  will redefine   as  a one "game".   To   be fair,  you  will
alternate color, count  a win as 1,  a draw  as 1/2  and a loss  as 0.
After  the 10 game   chess match is over,   the one with highest score
wins (or draws if 5-5.)

One instance of this    10 game match   is called  a single game    of
Chess-10, ok?   We can even try  to be cute and  call each sub-game, a
"move."   Now  we  have a new    game that has  much different  rating
properties, and also  is more  forgiving  of errors.   If you  lose  a
sub-game foolishly, it need not be fatal.  Also, if  you win the first
6 sub-games, then, like  go, you can be quite  sloppy with the rest of
your "moves" or sub-games.

Now  in normal chess, a  100 rating point  superiority has about a 70%
win probability.  But this new game will be won much more often by the
superior  player.  In Chess-10, this increases to over 95%!  

Several people on this site have posted, and I agree, that Go has many
more "levels" of  skill than Chess has.  But  I can create more levels
of  skill in a  chess-like  game by  arbitrarily choosing n  in a game
called  Chess-n.  n of   course is the   length  of the matches  to be
played.   If Chess-10 were  played  instead  of  Chess, and rated   in
exactly the same way,  you  would find   that Chess-10 had  many  more
levels of expertise than regular Chess.

One  thing we should also note  about Go, is  that there are many more
moves played in a typical game.   In my opinion,  that means there are
many more opportunities  to  make errors,  whether you   consider only
game-theoretic ones or minor territorial ones.  

Probably, a reasonable ChessDevil strategy is to simply delay the loss
or draw as   long as possible  to  give the  opponent more chances  to
error.  Of course there are  probably more effective strategies if you
know  something about  your  opponent (like knowing   he  is human for
instance!)   In Go, this probably doesn't apply too much.
 
In a nutshell Roland, I am guessing  that in Go, the occasional "minor
error" is actually  quite  critical, it's  probably represents a  huge
difference in outcome  because  these errors accumulate.   If  you are
making two tiny errors for each 1 of your  opponent, he will beat you.
I'm guessing that even  the very top Go  players make little territory
errors frequently (errors which  make the final score  vary by a stone
or more given  perfect play.)  If they don't,  then there shouldn't be
anything distinguishing  the top players  from each other.


Don 




   Date: Fri, 22 Sep 2000 17:24:51 -0300
   From: Roland <goprog@xxxxxxxxxxxxxxxxx>
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   Hello Matt,

   Thursday, September 28, 2000, 11:03:57 AM, you wrote:
   <snip>
   MG> picture looks very different.  For humans, it may be that Go is little more difficult
   MG> than chess to master, but it doesn't seem greatly so and it is actually easier for a
   MG> child to learn and easier to become novice-proficient.  Based on all the discussion
   <snip>

   It's certainly an interesting question which of the two games is more
   complex. I honestly think that chess is the more complex game meaning
   that it is harder to achieve perfect play with it.
   The advantage that Go has, which makes it simpler is a kind of
   stability. For example once you have a living group, this group will
   live till the end of the game, and so will all connected groups do.
   You don't have to read any moves ahead to know it. To
   say it more generally, in Go it's unlikely that you will lose the game
   due to an amazing tactical combination from your opponent, except if a
   huge group will be killed. You build up strategic advantage that will
   be maintained because of the stability of the game. And a good player
   can know what groups of him are alive and how much of the board he
   owns without having to read many moves ahead. So even against a
   perfect player he will play reasonably, being able to maintain a large
   area of the board for him.

      In chess we have a different situation. Now matter how great the
   strategic advantage seems to be, a great tactical combination may
   destroy it. A slight mistake on your side may be enough. And in
   chess there is no stability, a weakness in a position "propagates"
   making the global position weak also. And here comes the problem,
   because of this instability in chess, you can never be sure if there
   isn't an amazing tactical combination of say 40 or more moves that
   will destroy your position...So a human player will always be in great
   disadvantage against a perfect player who knows the complete game
   tree.

   Or saying it in another way: In Go mistakes will cost you some amount
   of territory, which a good player could keep small by playing safe. In
   chess a mistake will cause you to lose the game.

   Is this complete nonsense what I'm saying?


   -- 
   Best regards,
    Roland                            mailto:goprog@xxxxxxxxxxxxxxxxx