Re: computer-go: Go Devil

[Don Dailey <drd@xxxxxxxxxxxxxxxxxxxxx>]

Part 2 of Go-Devil.

In my last  post, I talked about  rating curves in  Chess and tried to
make a case that the very best human  players actually don't play very
well compared to what would be possible by omniscient entities.

I have some further thoughts on this taking it from a different angle.

In the previous post I made reference to Kasparov's play and held this
up  as an example of  the best human play.   However  there is kind of
chess that is generally  acknowledged to be of  a much  higher quality
than this,  and it's called   correspondence chess.  I have  talked to
several master on this subject as well as one former world champion in
correspondence chess  and the consensus is  that the level of  play of
top  players   FAR  exceeds    that  of over    the  board   play.  In
correspondence play,  each  player has  many hours  or  even  days  to
respond to a single move, and uses this time to do serious analysis.

As a thought experiment, if you could give a top correspondence player
the   ability to  make  the same  high   quality moves  but  in normal
tournament time controls, you  would  have a  player far  superior  to
Kasparov in over  the board play.  I  have  never heard a  good player
deny this conjecture and I have talked to several about it.

When games of the top players are analyzed later, it is common to find
flaws in the  play.  It is so common  in fact that  it is clear we are
playing far from perfectly.  There is a still a very large gap between
the current level of play of top humans and perfect play.

Because of our limited perception, it is  difficult for us to see much
farther than from our own vantage point.  To us, brilliant and perfect
play is simply whatever the best of us  can achieve.  We are impressed
with   our own   accomplishments.  But to   a  God,  what  we consider
brilliant and perfect might very well be simple minded and naive.

I would like to also point  out that player perfect  moves most of the
time does  not  mean you  play good  Chess  (or Go)   in general.  The
difference between a  great player and  an  excellent player might  be
that the excellent  player plays  perfetly  90% of  the moves and  the
Great player gets it  right 93% of  the time.   Over a long  series of
games the great player will  amass a huge lead, especially considering
that the bad moves of the weaker player will get punished more often.

In a real sense, there is no such thing as a good or excellent move in
2 player games  of perfect information like  Chess and Go.  There  are
only bad moves.  A good move is a human label  applied to a move which
is difficult to find or is  "pretty", a Go Devil  kind of move!  A bad
move is  a  move that doesn't   maintain  the game  theoretic outcome.
There is a maxim in chess that says the winner is the next to the last
person to make a mistake!   

Finally, I don't know how to apply this to Go.   I feel that we are at
least a few hundred elo rating points from perfect chess, even as many
as 1000 (which means a hypothtical player exists who would rarely ever
lose to Kasparov, and yet there still exists a player who would rarely
lose to this player!)

Christoph gave the rough  rule of thumb  that  1 stone equals 100  ELO
rating points.  If this is  approximately right, then  the idea of the
best players  being  close to perfect  (within 1   or 2  stones) seems
fairly ludicrous.  200 rating points (or two stones?) means that among
equal players, the handicapped player would still win about 15% of the
time although losing about 85% of the games.

I think Go  is MUCH more profound and  difficult to master than Chess,
and this by a really wide margin.  I have heard similar numbers quoted
for  chess, where it's been  hypothesized that we  are only 200 or 300
points away from perfection.  I even admit that it's hard to imagine a
player  who could achieve  a score of  over 80% against  the great and
wonderful Kasparov, but I think that kind of  thinking is what ties us
in knots, we really shouldn't make our guesses by comparing to players
we worship because they are too close to God in our minds!


Just for reference here is a simple table of expectancies that the ELO
rating system predicts.  For instance the last entry indicates that if
you are 400 points higher rated, you will win 97% of the games against
your weaker opponent.  Most of  the experiments I mentioned earlier in
computer chess, for those not familiar, were based on playing hundreds
of  games against programs   of  various depths,  and calculating  ELO
ratings   based on winning   percentages.  In the  experiments, it was
shown  that  by searching 1  ply deeper  you  could  obtain a stronger
program, one that could  expect to win about 80% or more of the time.


    ELO diff    wins %
    --------    ------
        0        0.50
       20        0.53
       40        0.58
       60        0.62
       80        0.66
      100        0.69
      120        0.73
      140        0.76
      160        0.79
      180        0.82
      200        0.84
      300        0.93
      400        0.97