I was looking at many of the posts on the threads about
how things scale with humans and computers and I'm
trying to reconcile many of the various opinions and
intuitions. I think there were many legitimate points
brought up that I appeared to be brushing off.
In computations done by computer, there can usually be a
trade-off between time and memory. In the discussions,
we rarely talked about memory and how it figures in to
the picture. A lot was said about just knowing
something (where a strong player looks at a position and
instantly knows a weaker player made a mistake for
instance) and the feeling expresses by many was that
this was a barrier that could not be penetrated by
thinking about the position no matter how much time
was allowed.
Although I consider the evidence pretty strong for
rating curve in both humans and computer, the model of a
fixed strength increase per doubling is actually a
simplification - in the real world it is more
complicated than that.
It's important to realize that the ELO formula is based
on assumptions about human playing strength that are
only approximations. One of those assumptions is that
playing strength is transitive and can be expressed as a
single value - a number that we call a persons "rating."
Nevertheless, intransitivity is a real thing. The way
we sometimes erroneously think about GO is that you have
some fixed strength expressed as a kyu or dan "number"
and that every move is a reflection of this level of
play.
A better model, which is still a simplification, is that
a move is either right or wrong and the stronger you
are, the more likely you will choose the better move.
Some move are easy to find and the weaker players find
them, but on average you are faced with moves of every
level of difficulty and the difference between stronger
and weaker players is how many of these positions they
solve - kind of like a big test with a mixture of easy
and hard problems and the one that gets the most answers
right wins!
>From a purely theoretical point of view, a move really
is either best or not-best but as humans we judge moves
on a sliding scale of "goodness" and refer to some moves
as being horrible and others as being brilliant, good,
second best, etc. On this group we recently discussed
how to define error vs blunder and so on.
The intuition behind judging moves like this is that
indeed, some moves give you better practical chances in
the real world. So if you are slightly losing, a move
my be referred to as "a good try" because it complicates
things, or at least requires the opponent to find a
refutation that in human terms is difficult to find.
Sometimes a good player, or even a computer can
instantly find the right move where a weaker player has
no clue and is not likely to discover the correct
principle even given several hours of meditation. This
has been mentioned a number of times recently. This an
example of a chunk of knowledge having a profound effect
on the quality of a single move. Even with computers it
is possible that a good life and death routine can
discover things (more or less) instantly that might take
a very long time to find with a global brute force
search.
Because knowledge can be imperfectly and unevenly
applied, one player might play some types of positions
much better than others. So even among players of
roughly equal abilities, one player may see at a glance
what another player would have a very difficult time
discerning.
What this causes in my opinion is instransitivity. It
doesn't cause a player to stop improving substantially
with time as many experiments have proved. But it's a
known phenomenon that because of intransitivity and
these knowledge gaps, you might improve much more
against a particular opponent (opponents just like
yourself for instance) and much less against other kinds
of opponents.
But this is also about memory scalability. Better
players have more knowledge about the game. It's very
difficult to measure knowledge quantitatively in humans.
How do you have twice as much knowledge in Go? How do
you test this? But it's clear that stronger players
have much more knowledge, probably much of it in the
form of trained intuition about go positions in the form
of pattern recognition. Some knowledge is expressed as
cute little proverbs of wisdom such as "the opponent's vital
point is my vital point" among others.
Because no two players play alike, and especially computers
and humans, bits of knowledge and processing power have
different scaling characteristics. Even a particular piece
of knowledge could help you more against one opponent that
another.
So let me restate my feelings based on the above
considerations:
1. Game playing skill is a function of time.
2. Memory (or knowledge) can proxy for time - saving
enormous amounts of time in many cases.
3. "Technique" is a function of knowledge and how it's
organized - which translates to a big time savings
indirectly. This is really the ability to apply knowledge.
4. Because these various aspects of game playing ability
can be mixed and matched, you are sure to get very
interesting intransitives.
So although I believe in good scalability characteristics
with time and skill, the improvement may not ramp up as
quickly against certain kinds of opponents. You may need more
"doublings" to make the same improvement against a
particular opponent than you would against another.
A probabilistic way to look at this is on a move by move
basis. Some of you noted that some moves are "beyond them"
such that a player 2 stones stronger sees it at a glance and
you have no chance of seeing it. And yet you still have
about 7% chance of beating a player 3 stones higher. I
suggest that in these types of positions only, you are many
stones weaker, but in other types of position you might
actually be equal or even stronger. You cannot look at one
position in isolation and draw conclusions that you could
never beat such a player.
When I played tournament chess I was exposed to players much
weaker and much stronger than myself. I discovered that I
was better in some positions that even players significantly
stronger. And I was aware of much weaker players that I had
to steer away from certain kinds of positions. Stronger
players often recovered when I outplayed them - but that
doesn't change the fact that it's possible to out-play them
in positions you understand better. If they are not too
strong you will even win once in a while due to the fact
that you did indeed outplay them.
In computer go, the differences between humans and computers
is enormous - and I don't mean just in strength, but in
style.
When I was developing Botnoid, I even saw this in
computer/comptuer. At one point in 9x9 Botnoid development,
Botnoid could score about even with Gnugo 3.6 at the levels
I tested with. This was quite amazing when you consider how
good gnugo was tactically compared with Botnoid. Botnoid
had a bad habit of playing into self-atari - a problem I
patched up a bit but never solved completely. And yet it
could win about half the games. You could look at
individual moves of Botnoid and conclude that it was not in
the same league as gnugo and should never win, but you would
be wrong. That's why I'm not impressed too much with
arguments about isolated positions and how superior 3 ranks
can be in selected positions because it's all about playing
the WHOLE game. Botnoid excelled in some areas that gnugo
didn't and there were games where it seemed like everything
was over for gnugo before it even had a chance to get into
the game.
Anyway, I think this note reflects a more balanced viewpoint
of how things really work. To a certain extent, I think you
could say that in practical terms it's hard to overcome a
serious rank difference - as you would not only have to
overcome the geometric time explosion which by itself is a
practical barrier for anything more than 4 or 5 ranks but
you might also have to overcome the "intransitivity barrier"
where you don't get the same effective strength increase
against a particular opponent. I still believe that many of
us on this group underestimate our abilities at longer time
controls but it's not productive to debate this here.
- Don
_______________________________________________
computer-go mailing list
[email protected]
http://www.computer-go.org/mailman/listinfo/computer-go/
