Five Million Dollar Prize Offered to First Computer to Defeat Master at Go

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Gerry Forbes

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May 19, 1997, 3:00:00 AM5/19/97
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In article <5lj7l0$6...@camel1.mindspring.com>,
sl...@ishipress.com (Sam Sloan) wrote:
>Five Million Dollars Offered
>to the First Computer Go Program
>that Can Beat an Expert Player

(SNIP)

>Human intelligence is not brute force! If one wishes to mimic human
>intelligence on a machine, chess is not the game best suited to
>accomplish this. The game that IBM and others in the field of
>artificial intelligence should be concentrating their efforts on is
>the oriental strategy game of GO.
1.The choice of chess instead of go had nothing to do with which
game best reflected human intelligence; it had to do with culture,
propaganda, and business. Chess was familiar to computer pioneers
and their audience (and customers - how many $billions has the
computer chess industry raked in?), and once chess programs became
popular it would be difficult to judge progress if you had to
compare chess programs to go programs.
2.If go is so strategical, then how come long variations are given
in notes and the evaluation is something like "this line is one
point better than that played in the game"? This suggests to me that
the game is very tactical. Also, don't some players feel that the
19x19 game is "played out" and experiment with 21x21 games? In chess
it is the tactical opening variations that are played out, not the
strategic ones.
3.If chess is just tactics, then how do strong human players play
blitz? Not by crunching variations - if you watch masters playing
blitz you will notice that they are primarily guided by strategy.
They have problems with computers at this speed because they do not
have time to calculate all the tactics.

(SNIP)
Determining the best move requires subtle judgment
>which takes into account the various weaknesses and strengths of
>positions in different parts of the board. This is a skill which no
>computer and its program will ever have.

Just like no computer will ever defeat a Grandmaster at chess, eh?
This is exactly the argument that was put forth in that case.

>A foundation in Taiwan, The Ing Chang-ki Goe Educational Foundation,
>is offering US$1,000,000 to the programmer of the first computer
>program that can beat a selected twelve-year-old GO player. At
>present, the best computer programs today play at a level of around
>10-class, which is very weak, a bit stronger than an absolute
>beginner.
>
>Now Professor Elwyn Berlekamp has upped the ante by offering
>US$5,000,000 to the first computer program that can beat a 5-dan
>player, which is equivalent to a strong expert player.

Completely untrue. If you equate a 9-dan with 2700 Elo and give
100 points for each dan, then a 5-dan would be Fide Master
strength, two levels above a strong expert. Since the differentiation
between dans is probably less than 100 points, a 5-dan would
probably be more like a strong International Master/weak GM.

Why do Western go players have such an inferiority complex that
they need to constantly belittle chess? This story is just as
interesting without the exaggerations, which will only mislead the
media and actually hurt your chances of popularizing the game.
Chess promoters have made the same mistake time and again, with the
result that the media considers Kasparov to be the only chess player
in the universe. Keep to this path and go will be perceived as a
game only for Oriental mystics and Westerners too weirded-out for
chess.

Programmers will take Deep Blue's victory (such as it was) as a sign
that there are no great strides left to be made in chess programming
and will look for new challenges, even without the prizes offered. A
go program will be an attractive challenge for programmers who wish
to concentrate more on intelligence than artifice. Deep Blue may
serve as a benchmark for chess programs allowing experimentation with
"intelligent" programming (the computer chess market will become
moribund when GM strength programs are bundled with PCs) and the go
and chess programming fields will cross-fertilize each other. When
the go prize is claimed expect that there will also be chess programs
that rely more on positional awareness than tactic crunching.

And they will still be stupid machines.

Relax,

Gerry

Sam Sloan

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May 20, 1997, 3:00:00 AM5/20/97
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You are mistaken about Dan ratings.

There are more than 30 players in the world rated 9-dan. Thus, 9-dan
is somewhat less than 2700.

At the top levels, it is hard to equate dan rankings with Elo points,
but one dan level is clearly less than 100 points.

However, the five million dollar prize is for defeating a 5-dan
amateur player, not a 5-dan professional player.

A 5-dan professional player is probably at least 2500 in Elo points.

A 5-dan Amateur player is no better than 2200. I believe that there
are more than 5,000 players in Japan alone who have a 5-dan
certificate. There are presumably an equal number of players of that
strength in China and Korea.

So, to win the five million dollar prize, your program will need
merely to defeat one of the top 15,000 players in the world.

Sam Sloan

Zhengyang Wu

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May 21, 1997, 3:00:00 AM5/21/97
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Gerry has right in that chess also has strategies. However, compared to go,
the strategy in chess is much more limited. You have a clear target to attack:
the king; you have only 64 squres to move (but not evevy piece can reach every
square: they are limited by their way to move), and, you have much more cearer
approach (occupy the center, make exchanges there you exchange your less
valuable pieces with your opponent's more valuable ones), etc.

While in go, things are different:

You have a goal: to make as many points as possible, but you have no practical
goal: you can either enclose your own territorium, or destroy your opponent's.
you can try to kill his dragon, or just make peace. So, there is a goal in go,
but still no clear goal to aim your concentration to.

The stones have equal values in the beginning. There is no difference between
them. However, their value vary depending on your strategy and strength, and
the progree of the game. It is far more difficult to master the value of
different stones on different places of the board than to master the value
of Queen or a horse in chess. The value of stones are much more subtle (
in other words, it need human intelligence to evaluate it. I think that the
biggest problem for a computer to play go is that it lacks the human
intelligence to judge the value of the stones).

In go, the battle field is much bigger. Just count how many crosspoints there
are. However, the size is less important because one can always increase the
size (to match the size of go, one can theoretically draw a monster chess with
lets say 5 queens, 10 horses etc). But there is a huge difference which makes
go more difficult for computer to play: there is no clear target in go, like
the king in chess, the direction of the fight is much more flexible and unclear
. It depends much on the personality of the players. In chess, the personality
of the players is less significant.


my humbor opinion.

regards


gfo...@vcn.bc.ca (Gerry Forbes) writes:

>(SNIP)

>>Now Professor Elwyn Berlekamp has upped the ante by offering
>>US$5,000,000 to the first computer program that can beat a 5-dan
>>player, which is equivalent to a strong expert player.

> Completely untrue. If you equate a 9-dan with 2700 Elo and give
> 100 points for each dan, then a 5-dan would be Fide Master
> strength, two levels above a strong expert. Since the differentiation
> between dans is probably less than 100 points, a 5-dan would
> probably be more like a strong International Master/weak GM.

> Why do Western go players have such an inferiority complex that


> they need to constantly belittle chess? This story is just as
> interesting without the exaggerations, which will only mislead the
> media and actually hurt your chances of popularizing the game.
> Chess promoters have made the same mistake time and again, with the
> result that the media considers Kasparov to be the only chess player
> in the universe. Keep to this path and go will be perceived as a
> game only for Oriental mystics and Westerners too weirded-out for
> chess.

> Programmers will take Deep Blue's victory (such as it was) as a sign
> that there are no great strides left to be made in chess programming
> and will look for new challenges, even without the prizes offered. A
> go program will be an attractive challenge for programmers who wish
> to concentrate more on intelligence than artifice. Deep Blue may
> serve as a benchmark for chess programs allowing experimentation with
> "intelligent" programming (the computer chess market will become
> moribund when GM strength programs are bundled with PCs) and the go
> and chess programming fields will cross-fertilize each other. When
> the go prize is claimed expect that there will also be chess programs
> that rely more on positional awareness than tactic crunching.

> And they will still be stupid machines.

> Relax,

> Gerry
--
--------------------------------------------------------------------
Zhengyang Wu, e-mail: zyw...@lysator.liu.se
Vastanagatan 20-215, S-582 35, Linkoping, Sweden

Hans-Georg Michna

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May 21, 1997, 3:00:00 AM5/21/97
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gfo...@vcn.bc.ca (Gerry Forbes) wrote:

> 2.If go is so strategical, then how come long variations are given
> in notes and the evaluation is something like "this line is one
> point better than that played in the game"? This suggests to me that
> the game is very tactical.

Gerry,

I know both chess and Go and can assure you that Go has a
stronger strategic factor in the opening. Of course, Go is also
a tactical game, but strategic superiority is worth a lot in Go,
certainly more than in chess.

What does this mean? Nothing much, perhaps only that players who
like strategic thinking should tend to play Go, while players
who are excellent tacticians may get more from chess.

Hans-Georg

Zoltan Mark

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May 21, 1997, 3:00:00 AM5/21/97
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Gerry Forbes wrote:

> >Now Professor Elwyn Berlekamp has upped the ante by offering
> >US$5,000,000 to the first computer program that can beat a 5-dan
> >player, which is equivalent to a strong expert player.
>
> Completely untrue. If you equate a 9-dan with 2700 Elo and give
> 100 points for each dan, then a 5-dan would be Fide Master
> strength, two levels above a strong expert. Since the differentiation
> between dans is probably less than 100 points, a 5-dan would
> probably be more like a strong International Master/weak GM.

Just as a remark on comparing the upper ranks of these games. I remember reading a book
some years ago that claimed that in a given sense Go is 'deeper' than chess, and offered
the following measurement for 'depth'.

You can set up a chain of players in either game using three rules:
1. the first player is a complete beginner, with an understanding of basic rules only;
2. two consecutive players relate to each other in strength in such a way that each
player wins against the previous one 3/4 of the time - 3 games out of 4;
3. the last player in the chain is the best you can have, in other words, you stretch
the chain to be as long as it possibly can.

Depth of a given game is then simply the length of the chain one can make for that game.
Unfortunately, I do not remember the exact numbers from the book, but the claim was that
in Go you can set up a much longer such chain than in chess. Which, if true, must mean
that the equation 2700 Elo points = 9 Dan does not hold - it is almost as if you would
be able to progress further in Go than in chess because there is more room left by the
intrinsic complexity of the game. This also would mean there is no equivalent to 9 Dan
in chess - the chess ladder would end earlier.

(Interestingly enough, the book also claimed that by a similar comparison applied to
teams, soccer has a depth of 11 - good one, I remember this but not the one for Go! -,
while basketball has something like 20+ and the author commented that apparently the
soccer allowed a much better chance for the world's worst team against the best that
basketball would do, exactly because the difference in depth.)

Sorry for not being able to give exact numbers. The book was written by a Hungarian guy
named Laszlo Mero, and I read it in Hungarian. The title is something like 'Ways of the
mind' or 'Walking styles of the mind' ('Eszjarasok' - the original title is better :) )
I do not know whether it was translated to English or not, but the claims referring to
relative depth are said to be based on somebody else's research which should be
available from other sources. (He even gives the bibliography, just I do not have access
to the book and will not have it for a couple of months.)

The problem furthermore is that this is how I remember something I have read many years
ago in a book addressed to the popularization of AI and brain research - imagine the
distortion factors. It would be interesting to read the original research papers
instead.


Zoltan

klgt...@spam.cornell.edu

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May 21, 1997, 3:00:00 AM5/21/97
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Zhengyang Wu (zyw...@lysator.liu.se) wrote:
: Gerry has right in that chess also has strategies. However, compared to go,

: the strategy in chess is much more limited. You have a clear target to attack:
: the king; you have only 64 squres to move (but not evevy piece can reach every
: square: they are limited by their way to move), and, you have much more cearer
: approach (occupy the center, make exchanges there you exchange your less
: valuable pieces with your opponent's more valuable ones), etc.

: While in go, things are different:


Please please please. I'm begging. Stop the thread now--especially in the
politics group (removed from follow-ups). This debate gets tiresome real
quickly and has been done to death. Use deja news if you want to be
entertained by the exchanges.

K


Paul Clarke

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May 22, 1997, 3:00:00 AM5/22/97
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In article <3383C03D.4618@remove_this_segment.erols.com>,
mzoltan@remove_this_segment.erols.com says...

>
>Gerry Forbes wrote:
>
>> >Now Professor Elwyn Berlekamp has upped the ante by offering
>> >US$5,000,000 to the first computer program that can beat a 5-dan
>> >player, which is equivalent to a strong expert player.
>>
>> Completely untrue. If you equate a 9-dan with 2700 Elo and give
>> 100 points for each dan, then a 5-dan would be Fide Master
>> strength, two levels above a strong expert. Since the differentiation
>> between dans is probably less than 100 points, a 5-dan would
>> probably be more like a strong International Master/weak GM.
>

I think there's confusion here between 5-dan amateur and 5-dan professional.
5-dan amateur as equivalent to strong expert (2000-2200 Elo) doesn't sound
unreasonable, nor does 5-dan pro as strong IM/weak GM. I think the right
way to compare the grades between the games would be to look at the percentage
of players that achieve a given level. Does anyone have figures on this?

>Just as a remark on comparing the upper ranks of these games. I remember
reading a book
>some years ago that claimed that in a given sense Go is 'deeper' than chess,
and offered
>the following measurement for 'depth'.
>
>You can set up a chain of players in either game using three rules:
>1. the first player is a complete beginner, with an understanding of basic
rules only;
>2. two consecutive players relate to each other in strength in such a way
that each
>player wins against the previous one 3/4 of the time - 3 games out of 4;
>3. the last player in the chain is the best you can have, in other words, you
stretch
>the chain to be as long as it possibly can.
>
>Depth of a given game is then simply the length of the chain one can make for
that game.
>Unfortunately, I do not remember the exact numbers from the book, but the
claim was that
>in Go you can set up a much longer such chain than in chess.

The numbers I've seen quoted are about 45 for go and 14 for chess. The figure
amounts to about 1 level per kyu (assuming a beginner at 35 kyu). The figure
for chess seems to be derived from 75% winning chance = 200 Elo points (I
think
this is about right) and assuming that 0 is the lowest Elo (which is dubious).

> Which, if true, must mean
>that the equation 2700 Elo points = 9 Dan does not hold - it is almost as if
you would
>be able to progress further in Go than in chess because there is more room
left by the
>intrinsic complexity of the game. This also would mean there is no equivalent
to 9 Dan
>in chess - the chess ladder would end earlier.

I think the number of levels is at least as much to do with the probability of
superior skill translating into victory than the game's complexity. Consider a
game that I've just invented: 'Gotac'. Gotac = 'Go, Toss a Coin': you play a
game of go, following which the loser tosses a coin. If the coin comes down
tails, he still loses, if it comes down heads the game is a draw. The best
player
in the world will score about 75% against the worst, so the game has only 1
level.
However, anything you know about go strategy and tactics can be applied to the
game and will improve your chances of winning, so it's at least as complex as
go.

Comparing chess and go: if you play slightly better than your opponent in go,
you will win by a small margin; in chess, you may well draw. In go, if you
make a mistake against a weaker opponent, you will usually get chances to
catch up; in chess, it may instantly lose you the game. Thus, there's a better
chance of superior skill winning a game of go than a game of chess. This, I
suspect, explains much or all of the difference in the number of levels.

>
>(Interestingly enough, the book also claimed that by a similar comparison
applied to
>teams, soccer has a depth of 11 - good one, I remember this but not the one
for Go! -,
>while basketball has something like 20+

Again, I think this is explained by the smaller role for chance (and the
unlikeliness of draws) in basketball. A weaker team in soccer might sneak
a lucky goal and hang on for a 1-0 win. I doubt if the weaker basketball
team can get a lucky basket and hang on for a 2-0 win :-). Of course, there
may also be a difference in the possible levels of skill in the two games,
but as I'm about 35 kyu/ 0 Elo at both, I'm not really qualified to judge :-).

> and the author commented that apparently the
>soccer allowed a much better chance for the world's worst team against the
best that
>basketball would do, exactly because the difference in depth.)
>

Saying that basketball has more levels is the _same_ as saying that the
world's worst team has a better chance against the best, it's not an
explanation for it.

[snip]

Paul C. (34th level Go player, 8th level chess player)


Mats Lofkvist

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May 22, 1997, 3:00:00 AM5/22/97
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Zoltan Mark <mzoltan@remove_this_segment.erols.com> writes:

>
> Gerry Forbes wrote:
>
> > >Now Professor Elwyn Berlekamp has upped the ante by offering
> > >US$5,000,000 to the first computer program that can beat a 5-dan
> > >player, which is equivalent to a strong expert player.
> >
> > Completely untrue. If you equate a 9-dan with 2700 Elo and give
> > 100 points for each dan, then a 5-dan would be Fide Master
> > strength, two levels above a strong expert. Since the differentiation
> > between dans is probably less than 100 points, a 5-dan would
> > probably be more like a strong International Master/weak GM.
>

> Just as a remark on comparing the upper ranks of these games. I remember reading a book
> some years ago that claimed that in a given sense Go is 'deeper' than chess, and offered
> the following measurement for 'depth'.
>
> You can set up a chain of players in either game using three rules:
> 1. the first player is a complete beginner, with an understanding of basic rules only;
> 2. two consecutive players relate to each other in strength in such a way that each
> player wins against the previous one 3/4 of the time - 3 games out of 4;
> 3. the last player in the chain is the best you can have, in other words, you stretch
> the chain to be as long as it possibly can.

One interpretation of this is simply that chance affects the outcome of a
Go game less than it affects the outcome of a chess game. (E.g. backgammon
and poker probably have short chains.)

Since there is no element of chance in Go or chess, this leads to the
interresting conclusion that Go is better understood by its top players
than chess is (*). This is a bit unexpected since Go is (?) quite a lot
more complicated in a mathematical sense (with a much larger state space).

My guess is that the human mind simply is much more suited for Go. The
movements of the chess pieces is a complication that makes the game hard
for humans but (relatively) easy for e.g. computers. Go skill on the other
hand seems to depend more on abilities natural for humans, e.g. pattern
recognition, gain vs. loss tradeoffs etc. (Of course this is not black
or white, chess also need "human" skills and Go have its "unnatural"
complications, but I still believe there is a difference between the games.)

_
Mats Lofkvist
m...@algonet.se


(*) Or is it the Go beginners that are much worse than chess beginners ?-)
Well, I think not since I suspect the Go chain would be longer even
if you replaced the beginners with players that have spent say 100 hours
on the game.


Wei-Hwa Huang

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May 22, 1997, 3:00:00 AM5/22/97
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no_mail_please-H...@cis.compuserve.com (Hans-Georg Michna) writes:
>I know both chess and Go and can assure you that Go has a
>stronger strategic factor in the opening. Of course, Go is also
>a tactical game, but strategic superiority is worth a lot in Go,
>certainly more than in chess.

>What does this mean? Nothing much, perhaps only that players who
>like strategic thinking should tend to play Go, while players
>who are excellent tacticians may get more from chess.

I agree perfectly. It explains why I get creamed in Go, even though
I seem to be winning a lot of localized skirmishes.

And also why I can sometimes give chess players of higher ranking than
me a run for their money.

(Once I managed to stalemate an 1820. That made me happy -- I was
a 1320 at the time.)

--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
-------------------------------------------------------------------------------
The cynical poet -- is worst of the worst.
What others are thinking -- he says out loud first.

Hans-Georg Michna

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May 22, 1997, 3:00:00 AM5/22/97
to

Zoltan,

sounds a bit nonsensical to me. Let us not forget that most
board games are not exhausted, neither chess nor Go nor even
checkers. The number of possible situations on the board is
much, much higher than the number of situations one human, or
even all humans, or all computers, for that matter, can
experience.

Go is more sensitive to players' strength than chess. In other
words, chess has a higher random factor. That may be the grain
of truth in the idea you cited. Go also rewards strategic
thinking more highly than chess. But otherwise both games are
similarly beyond total understanding.

Hans-Georg

Zoltan Mark

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May 23, 1997, 3:00:00 AM5/23/97
to

Hans-Georg Michna wrote:

> Go is more sensitive to players' strength than chess. In other
> words, chess has a higher random factor. That may be the grain
> of truth in the idea you cited. Go also rewards strategic
> thinking more highly than chess. But otherwise both games are
> similarly beyond total understanding.

Sure they are way beyond my understanding :( I am not sure whether a professional 9 dan
has or has not an almost complete understanding of Go. I have read somewhere that among
professional players the rank differences become really small strength differences as
you approach 9 dan and the komi is often deciding the outcome of a game. This is
characteristic to a system approaching a perfection limit - there are less and less
opportunities to improve, although I guess the 'small' improvement from 8 dan to 9 dan
is the result of a not so small effort. If this is not just a bad analogy, then it would
mean that 9 dan is really the top of Go - either because our limits as humans or because
of Go's limits as a game, a 9 dan (*) could be interpreted as practically understanding
the game of Go as a whole.

(Interestingly enough, a former colleague of mine claims that the limit appearing at 9
dan - us two did not seem to have doubts about the existence of this limit, as if we
were anywhere close to it - can be attributed to the traditional ways of play taught to
Go students, such as basic josekis and typical shapes, and that an exhaustive search of
the Go game tree would not necessarily lead to the well known josekis and techniques. As
an example, he put it: the best opening move well may be in the center of the table, but
our limited knowledge does not allow to exploit it in the course of the game; those
learning Go are too busy learning the traditional ways which will hopelessly shape their
way of thought thus they will not be able to see this out-of-box opportunity again. I
bring this up only as an alternate idea, as I believe the orthodox ways of playing Go
are perfect for humans, that classic joseki are unlikely to be dismissed in the near
future and that the first move placed on the middle of the table is an offense for
white.)

I think moreover that it is unfortunate to use the word 'random factor' related to chess
- just to be politically correct, and not to attact flame warriors who happen to like
chess over Go. I would propose the term 'chaotic' instead of 'random', meaning that
decisions regarding individual moves seem to carry a greater weight in chess than in Go,
and non-perfect players - i.e. probably the whole mankind - will accidentally make
decisions in chess that make a big difference, even if they themselves do not foresee
the outcome perfectly. In this sense, Go on 9X9 table seems to be more chaotic than on
19X19 - on 19X19 you have more opportunities to correct/compensate for mistakes. For the
ultimate chaotic game, see Reversi (a.k.a. Domination - what a name!).

I have got a lot of answers to my original post stating that the difference in the
length of chains could also be attributed to Go allowing a finer, more continuous
ranking in strength and not necessarily to a richer set of achievable understanding.
(Formulations may vary.) Let me check with you all if I understood it correctly: If you
were to draw an axis on which to point out the quality of players as demonstrated in
individual games, then people would collect over a time period a lot of different marks
on this axis, one for each game, and they would not stick to one single point. This
would be attributable to the fact that their performance varies with each game, as the
opponent may involuntarily make a move that forces the game to evoluate towards one's
strengths or weaknesses (in knowledge, not in Go sense position). The claim is that in
chess this cloud of marks you put on the axis for a given player is wider than in Go.
This seems to be as probable as the book's interpretation, but which did not occur to me
before I wrote the original posting. I am now busily figuring the implications...

Zoltan


(*) By the way, are the dan ranks the measures of mere present strength? In other
martial arts, dan ranks are kind of watermarks, showing the achievements of the
individual during his active life. Dan ranks are not revoked from somebody who is unable
to denonstrate or fight due to his old age. If this applies to Go, just substitute 'n
dan' with 'player who is able to play at the level expected to obtain n dan' or
something similar, and tell me as well.

Tord Kallqvist Romstad

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May 23, 1997, 3:00:00 AM5/23/97
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Zoltan Mark <mzoltan@remove_this_segment.erols.com> writes:

Interesting thoughts.
What do you think the result would be in games between a perfect player and
a 9-dan professional? I am almost certain that the perfect player would
always win non-handicap games, but how many handicap stones would she be able
to give and still win? My guess is about three stones, but I am a very weak
player. I would like to hear some stronger players' opinions about this.

Tord


Nick Wedd

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May 23, 1997, 3:00:00 AM5/23/97
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In article <wab3ere9l...@refil.ifi.uio.no>, Tord Kallqvist Romstad
<tor...@refil.ifi.uio.no> writes

>Interesting thoughts.
>What do you think the result would be in games between a perfect player and
>a 9-dan professional? I am almost certain that the perfect player would
>always win non-handicap games, but how many handicap stones would she be able
>to give and still win? My guess is about three stones, but I am a very weak
>player. I would like to hear some stronger players' opinions about this.

I am a weak player. But I have heard that there should be a difference
between the correct handicap for a 9p playing against God, and a 9p
playing against the devil. God, of course, always plays the best move
on the board in any position. But the devil is aware of any delusions
and misconceptions in his opponent's mind, and plays to take advantage
of these. This must be worth at least one more handicap stone, IMHO.

Nick
--
Nick Wedd ni...@maproom.demon.co.uk

Minghao Liao

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May 23, 1997, 3:00:00 AM5/23/97
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Nick Wedd (Ni...@maproom.demon.co.uk) wrote:
: In article <wab3ere9l...@refil.ifi.uio.no>, Tord Kallqvist Romstad
: <tor...@refil.ifi.uio.no> writes

I also remember someone here mentioned a long time ago that Goseign said he
didn't know who would win if he were to play God in a handicap 2 game, while
he was confident to beat god in a handicap 4 game.

Ming

: Nick
: --
: Nick Wedd ni...@maproom.demon.co.uk

Hans-Georg Michna

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May 23, 1997, 3:00:00 AM5/23/97
to

Zoltan,

somehow I don't believe that all possible Go games are known.
You assume that that yourself, when you say that perhaps we
don't know the best opening move.

With the Go board having so many more positions than chess, we
should first exhaust chess, but even that, I believe, will not
happen.

With the higher "random factor" of chess I meant that two
players that are slightly different in strength, will have more
predictable results in Go than in chess.

Hans-Georg

Gerry Forbes

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May 24, 1997, 3:00:00 AM5/24/97
to

In article <5luqn0$dro$1...@newsy.ifm.liu.se>,

zyw...@lysator.liu.se (Zhengyang Wu) wrote:
>Gerry has right in that chess also has strategies. However, compared to go,
>the strategy in chess is much more limited. You have a clear target to attack:
>the king; you have only 64 squres to move (but not evevy piece can reach every
>square: they are limited by their way to move), and, you have much more cearer
>approach (occupy the center, make exchanges there you exchange your less
>valuable pieces with your opponent's more valuable ones), etc.
>
>While in go, things are different:
>
>You have a goal: to make as many points as possible, but you have no practical
>goal: you can either enclose your own territorium, or destroy your opponent's.
>you can try to kill his dragon, or just make peace. So, there is a goal in go,
>but still no clear goal to aim your concentration to.

Unfortunately, you are saying the same things about go as you are
saying about chess while claiming that there is a difference! You
are overrating the importance of checkmate and underrating the im-
portance of capturing territory. In chess, it is true, checkmate
does end the game absolutely and it can come as early as Black's
second move, but in most games checkmate is only implied: players
resign more often because they cannot prevent their opponent from
queening a pawn than because they cannot prevent checkmate. Even
when they lose a piece it is more likely, if the game were played
to the end, that the opponent would seek to queen a pawn before
pursuing checkmate.

And how come occupying the centre or seeking favourable exchanges
are clear goals in chess, while securing space or attacking the
opponent's groups are not clear goals in go? Of course they are!
As in chess, these are local skirmishes in a larger strategic plan.

>
>The stones have equal values in the beginning. There is no difference between
>them. However, their value vary depending on your strategy and strength, and
>the progree of the game. It is far more difficult to master the value of
>different stones on different places of the board than to master the value
>of Queen or a horse in chess. The value of stones are much more subtle (
>in other words, it need human intelligence to evaluate it. I think that the
>biggest problem for a computer to play go is that it lacks the human
>intelligence to judge the value of the stones).

What is the value of a queen or knight? So you have read a beginner
book on chess that tells you a queen is 9 and a knight 3? Maybe I
should hide my queen in the corner and save my 9 points? Then all
go stones have a value of 1; this is what you are saying about chess.
The value of the pieces in chess is very flexible, depending on the
position and the material balance. A knight is very close to the
same value as a bishop but there is a general preference for the
side with two bishops vs. two knights or knight and bishop IF the
position is open and IF the knight doesn't have a secure square in
the centre. And when is a rook and pawn (5+1) equal to knight and
bishop (3+3)? Hardly ever! It depends on the position and what other
pieces are on the board (the side with rook and pawn is usually
worse off if he has no knight or bishop, unless the bishop is locked
behind its pawns or the rooks can double on the seventh rank or...).
What is the most important thing in chess? Pawn structure. If that
isn't strategic, then I don't know what is. Computers are given a
few rules of thumb about pawn weaknesses as far as evaluation of
position is concerned but it takes "human intelligence", as you say,
to understand how the pawn structure affects the position and what
plan to follow as a result.

Do you really think it is so difficult for a computer to judge the
value of a go stone because of its position on the board and the
population in the neighbourhood? There is a whole field of computer
science dealing with problems of this kind --Artificial Life. Find
out about Conway's Game of Life (you can "play" it on your go board!)
It is possible that good go programs won't be written, they will
"evolve".

>
>In go, the battle field is much bigger. Just count how many crosspoints there
>are. However, the size is less important because one can always increase the
>size (to match the size of go, one can theoretically draw a monster chess with
>lets say 5 queens, 10 horses etc). But there is a huge difference which makes
>go more difficult for computer to play: there is no clear target in go, like
>the king in chess, the direction of the fight is much more flexible and unclear
>. It depends much on the personality of the players. In chess, the personality
>of the players is less significant.

This is slander! In chess playing style is VERY significant. I bet
even your Swedish go playing friends are saying that their countryman,
Ulf Andersson, would do better against Deep Blue than Kasparov did
because he is a better STRATEGIC player. How about this: in the 50s
and 60s the scientific Botvinnik had to defend his title against the
fluid Smyslov, the gaseous Tal and the solid Petrosian (after tying
a match against the eclectic Bronstein). In the Soviet Union, which
tried to dominate sports by producing robotic athletes, trainers
insisted on players developing their OWN style, because there is no
single way of understanding chess.

I suspect that your understanding of chess came to an abrupt halt
because one must acquire much tactical knowledge before being able
to play at a rudimentary level. Dropping pieces before move ten is
very frustrating. Go is much kinder to beginners! But if you had
persisted you would have discovered that every aspect of go has its
analog in chess: sente=initiative, miai=opposition, damezumare=
zugzwang, etc. Well, almost every aspect; each has unique points.
But one thing is the same: it is inconceivable that a computer could
defeat the best human player. OOPS! After Deep Blue's victory over
Kasparov computer programmers will seek another challenge and when
as much time and money is directed to "solving" go as it was to
chess, you will be saying OOPS too! With the publicity of these
millions available for the first decent program there will be more
incentive. I would predict that these prizes would be claimed by
2005 (they will be claimed, but everyone will say "Fix! Fix! That
amateur threw the match for his percentage of the prize!"). And
you will go over the game with your friend and shake your head and
Tsktsk.

And then you will say,"Let's have a game. Two stones, wasn't it..?"

Regards,

Gerry

Geoffrey E. Caveney

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May 25, 1997, 3:00:00 AM5/25/97
to

Zoltan Mark (mzoltan@remove_this_segment.erols.com) wrote:
: Hans-Georg Michna wrote:

驗覻阗_溫腚涬槣赯u薩q踖xploit it in the course of the game; those :


learning Go are too busy
learning the traditional ways which will hopelessly shape their : way of
thought thus they will not be able to see this out-of-box opportunity
again. I : bring this up only as an alternate idea, as I believe the
orthodox ways of playing Go : are perfect for humans, that classic joseki
are unlikely to be dismissed in the near : future and that the first move
placed on the middle of the table is an offense for : white.)

: I think moreover that it is unfortunate to use the word 'random factor'


related to chess : - just to be politically correct, and not to attact
flame warriors who happen to like : chess over Go. I would propose the
term 'chaotic' instead of 'random', meaning that : decisions regarding
individual moves seem to carry a greater weight in chess than in Go, : and
non-perfect players - i.e. probably the whole mankind - will accidentally
make : decisions in chess that make a big difference, even if they
themselves do not foresee : the outcome perfectly. In this sense, Go on

跶Q t2藷逈谒刿戕\圪麥厮欇橯Q9X9 table seems to be more chaotic than on :
覷蜣}19X19 - on 19X19 you have
mo邫瀅[汶勖Z薠骩筠re opportunities to correct/compensate for mistakes. For


the : ultimate
chaotic game, see Reversi (a.k.a. Domination - what a name!).

: I have got a lot of answers to my original post stating that the difference in the
: length of chains could also be attributed to Go allowing a finer, more continuous
: ranking in strength and not necessarily to a richer set of achievable understanding.
: (Formulations may vary.) Let me check with you all if I understood it correctly: If you
: were to draw an axis on which to point out the quality of players as demonstrated in
: individual games, then people would collect over a time period a lot of different marks
: on this axis, one for each game, and they would not stick to one single point. This
: would be attributable to the fact that their performance varies with each game, as the
: opponent may involuntarily make a move that forces the game to evoluate towards one's
: strengths or weaknesses (in knowledge, not in Go sense position). The claim is that in
: chess this cloud of marks you put on the axis for a given player is wider than in Go.
: This seems to be as probable as the book's interpretation, but which did not occur to me
: before I wrote the original posting. I am now busily figuring the implications...

: Zoltan


: (*) By the way, are the dan ranks the measures of mere present strength? In other
: martial arts, dan ranks are kind of watermarks, showing the achievements of the
: individual during his active life. Dan ranks are not revoked from somebody who is unable
: to denonstrate or fight due to his old age. If this applies to Go, just substitute 'n

: dan' with 'player who is able to play at the level expected to obtain n dan' or

Troy Anderson

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May 25, 1997, 3:00:00 AM5/25/97
to

I remember reading some years back that Takemiya (who else!!!) said that
God could only give him 10 pts komi... of course, this was right before he
lost the possibility of becoming honorary honinbo that year.


Geoffrey E. Caveney

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May 25, 1997, 3:00:00 AM5/25/97
to

1) apologies for the gobbledygook I accidentally posted in this thread
yesterday. If everyone would watch their margins so that I wouldn't have
to go to edit/post mode just to *read* posts, fewer of these annoying
accidental posts would occur!

2) now for what I want to say:

Paul Clarke (Paul....@isltd.insignia.com) wrote:
: In article <3383C03D.4618@remove_this_segment.erols.com>,
: mzoltan@remove_this_segment.erols.com says...
:
: >You can set up a chain of players in either game using three rules:

: >1. the first player is a complete beginner, with an understanding of
: >basic rules only; 2. two consecutive players relate to each
: >other in strength in such a way that each player wins against the
: >previous one 3/4 of the time - 3 games out of 4; 3. the last player in
: >the chain is the best you can have, in other words, you stretch the
: >chain to be as long as it possibly can.

: >
: >Depth of a given game is then simply the length of the chain one can


: >make for that game. Unfortunately, I do not remember the exact
: >numbers from the book, but the claim was that in Go you can set up a
: >much longer such chain than in chess.
:
: The numbers I've seen quoted are about 45 for go and 14 for chess. The
: figure amounts to about 1 level per kyu (assuming a beginner at 35 kyu).
: The figure for chess seems to be derived from 75% winning chance = 200
: Elo points (I think this is about right) and assuming that 0 is the
: lowest Elo (which is dubious).

Whatever the significance of these "chain" statistics, I think the
figure of 14 for chess is ridiculously low. At the highest level, it
hardly takes 200 Elo points to have a 75% winning chance. 50-75 points is
more like it. I estimate from Kasparov to a USCF 2400 the length of the
chain is about 7. Even assuming the 200 points=1 "link" equation holds on
average from 2400-800, that's 7+8=15 links already. And it has been
estimated that the average strength of all people in the world who know
how to play chess is 800 -- so 15 only covers half the spectrum!

Enrico SMARGIASSI

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May 26, 1997, 3:00:00 AM5/26/97
to

Geoffrey E. Caveney (cav...@wwa.com) wrote:

: At the highest level, it


: hardly takes 200 Elo points to have a 75% winning chance. 50-75 points is
: more like it.

Sorry, but the ELO scale is *by construction* such that a rating
difference of 200 points - 193 to be precise - corresponds to an
expected 75% score (not winning percentage!) for the stronger
player. So, for instance, if you play a bunch of 1700 players and you
make 6/8 you get an ELO of 1893. And this is not just theory; the ELO
ratings prove to be, in practice, quite accurate in predicting the
outcome of matches and tournaments.

--

Enrico Smargiassi
Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
Ecole Normale Superieure de Lyon - 46, Allee d'Italie - Aile LR5
69364 Lyon CEDEX 07, France
phone: +33 4 72 72 86 32 fax : +33 4 72 72 86 36
URL : http://www.cecam.fr/~esmargia

J. Kroll

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May 27, 1997, 3:00:00 AM5/27/97
to

> Why do Western go players have such an inferiority complex that
> they need to constantly belittle chess?

This is one reason why Go is doomed in the West.

We (in the West) are sick of arrogant Go players saying that Go is better
that Chess when we all know what they really mean.

T Mark Hall

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May 27, 1997, 3:00:00 AM5/27/97
to

In article <Pine.OSF.3.95.970527...@saul4.u.washington.
edu>, "J. Kroll" <hy...@u.washington.edu> writes
I do not belittle Chess (or Bridge, Draughts or any other exercise of
the intellect). They are all exercises in the use of the human mind and
in this are to be applauded. I last played Chess in a club where
everyone else treated the game, and it is only a game, as a semi-
religious activity. I then quit since it had ceased to be a social
occasion. Go is an alternative and, to many, including me, a better one
for spending our time. As someone committed to spreading the knowledge
of Go wider in the West and constantly faced with the response that it
is such a minority interest that it does not deserve publicity, I cannot
condemn those who say that it is "better" than Chess in order to attract
attention to it. Later, when the publicity is gained, then you can say
that the two are different, one having complex rules in a small area and
the other simple rules on a more extensive area. In the end, however,
both games must appeal to people with a commonality of interest. It
would perhaps be better, considering the number of newsgroups that this
was originally sent to, to ask why you wish to belittle Go so much.
Fear, perhaps?

--
T Mark Hall

Geenius at Wrok

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May 27, 1997, 3:00:00 AM5/27/97
to

On Tue, 27 May 1997, J. Kroll wrote:

> > Why do Western go players have such an inferiority complex that
> > they need to constantly belittle chess?
>
> This is one reason why Go is doomed in the West.
>
> We (in the West) are sick of arrogant Go players saying that Go is better
> that Chess when we all know what they really mean.

I can understand being arrogance-averse, but what exactly are you
suggesting that go players "really mean"?


--
"I wish EVERY day could be a shearing festival!" -- The 10 Commandments
=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=
Keith Ammann is gee...@albany.net * "This must be what evil tastes like!"
www.albany.net/~geenius * Live with honor, endure with grace * Analects 2:24


Zoltan Mark

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May 27, 1997, 3:00:00 AM5/27/97
to

Hans-Georg,

first of all, let's rename this subthread, as the original title apparently refers to a
hoax (which, unfortunately, I have believed for several days)

You wrote:

> somehow I don't believe that all possible Go games are known.
> You assume that that yourself, when you say that perhaps we
> don't know the best opening move.

Right. I do not believe, though, that we ought to know all the possible Go games to have
a perfect playing algorithm (somebody called it God on this thread - I like that). There
are sure winner algorithms of games which do not directly imply enumerating the possible
games either in construction or in execution phase. In other words, you do not have to
enumerate the possible games when you write the program and the program does not have to
enumerate them when running. There are such games. Whether Go is similar, I do not know
but would bet it is. Also would bet chess is not exhaustible by any other means than
total enumeration.

> With the Go board having so many more positions than chess, we
> should first exhaust chess, but even that, I believe, will not
> happen.

I assume that we use the word 'exhaust' in similar meanings. I at least would consider a
game exhausted if an algorithm would exist that always plays the mathematically best
line, assuming that the opponent does the same. ('God' algorithm.) In this sense, I am
more optimistic about Go than chess, but, like you, I am not sure whether we will
exhaust either one.

A stronger interpretation would be demanding an algorithm that is easy to execute
mentally by a human, thereby taking away most of the fun of the game. This is also
somewhat more restrictive than 'knowing the game', in the sense I have used it with
respect to a Go 9 dan.

I did not assume a Go 9 dan has such an algorithm in his/her head. In this sense, when
talking about the hypothesis that a 9 dan might 'know the whole game', I did not talk
about 'exhausting' the game by said 9 dan, at least not in the sense you appear to use
that word. Would you agree?

> With the higher "random factor" of chess I meant that two
> players that are slightly different in strength, will have more
> predictable results in Go than in chess.

Agreement here, too. This is the same as I stated in my post, albeit it might have been
a little bit clumsy. I knew all the time that my writing style could stand some
enhancement. Watch me from now on trying to make more intelligible and concise postings
:)

Zoltan

Harry Fearnley

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May 27, 1997, 3:00:00 AM5/27/97
to

Sam Sloan wrote:
>
> Five Million Dollars Offered
> to the First Computer Go Program
> that Can Beat an Expert Player
> :
> :

> :
> Now Professor Elwyn Berlekamp has upped the ante by offering
> US$5,000,000 to the first computer program that can beat a 5-dan
> player, which is equivalent to a strong expert player.
>
> Professor Berlekamp is a wealthy venture capitalist who is attached to
> the Mathematical Sciences Institute at the University of California at
> Berkeley. Professor Berlekamp and his team are developing a
> mathematical theory of GO. So far their accomplishments have been
> modest: they have only succeeded in formulating a theory for the very
> end of the game, where the moves are only worth two points. They are
> presently working to extend this theory to cover endgames where the
> value of moves are worth up to four points. His book, ``Mathematical
> Go Endgames'', is available from Ishi Press.
>

As with everything that Sam Sloan says -- take this with a (big) pinch
of salt. Sam Sloan has made several outrageous attacks on Elwyn
Berlekamp in several newsgroups, as well as on his web pages, and has
claimed that he is taking Elwyn Berlekamp to court.

I have not seen Berlekamp himself make this offer -- has anyone else
(apart from Sam Sloan!)? Let us remember that Berlekamp is perfectly
capable of expressing his own views for himself, and has hitherto not
needed the `help' of Sam `If-It-Moves-Sue-It' Sloan.

Since Sam Sloan is no friend of Prof Berlekamp, perhaps Sam Sloan, in
advertising this alleged offer, is not simply trying to help Professor
Berlekamp.

> More information can be obtained by writing to:
> :
> :
> :
> Professor Elwyn Berlekamp,
> <<< Prof Berlekamp's address removed by me -- HF >>>

Again -- I ask why is Sam Sloan giving us all this information? Could
it be that he is worried that Berlekamp is not receiving enough letters
initiated by loony-tunes?

Harry

--

Alberto Rezza

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May 27, 1997, 3:00:00 AM5/27/97
to

On Tue, 27 May 1997 11:19:36 +0100, T Mark Hall
<tm...@gogod.demon.co.uk> wrote:

>In article <Pine.OSF.3.95.970527...@saul4.u.washington.
>edu>, "J. Kroll" <hy...@u.washington.edu> writes

>>> Why do Western go players have such an inferiority complex that
>>> they need to constantly belittle chess?
>>
>>This is one reason why Go is doomed in the West.
>>
>>We (in the West) are sick of arrogant Go players saying that Go is better
>>that Chess when we all know what they really mean.
>>
>>

>I do not belittle Chess (or Bridge, Draughts or any other exercise of
>the intellect). They are all exercises in the use of the human mind and
>in this are to be applauded. I last played Chess in a club where
>everyone else treated the game, and it is only a game, as a semi-
>religious activity. I then quit since it had ceased to be a social
>occasion. Go is an alternative and, to many, including me, a better one
>for spending our time. As someone committed to spreading the knowledge
>of Go wider in the West and constantly faced with the response that it
>is such a minority interest that it does not deserve publicity, I cannot
>condemn those who say that it is "better" than Chess in order to attract
>attention to it. Later, when the publicity is gained, then you can say
>that the two are different, one having complex rules in a small area and
>the other simple rules on a more extensive area. In the end, however,
>both games must appeal to people with a commonality of interest. It
>would perhaps be better, considering the number of newsgroups that this
>was originally sent to, to ask why you wish to belittle Go so much.
>Fear, perhaps?
>
>--
>T Mark Hall

Very well put, but not enough. You should also have reminded mr. Kroll
that when this this thread started, it was about the difficulty of go
programming.

No poster in the thread ever said anything about go being "better"
or "more difficult" than chess. I have become much stronger in go than
in chess, perhaps go was easier for me!

Chess may well be more difficult than go - for humans.
Fact is, go is much more difficult than chess - for computers.

Kroll seems to know something about programming, yet he refuses
to understand this.

Perhaps, after DB-Kasparov, he is the one with an inferiority
complex...

Alberto

Greycat Sharpclaw

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May 27, 1997, 3:00:00 AM5/27/97
to

Meow, all...

There is an allegation that "J. Kroll" <hy...@u.washington.edu> wrote:

>> Why do Western go players have such an inferiority complex that
>> they need to constantly belittle chess?

>This is one reason why Go is doomed in the West.

>We (in the West) are sick of arrogant Go players saying that Go is better
>that Chess when we all know what they really mean.

I (a chess and go player in the US) have *not* noted either
"arrogance" by go players or any "inferiority complex" by chess
players. I have not noted hostility at all, generally.

Yes, people prefer one game or the other, true. This is a matter of
taste, and is accepted as such, in my experience. In fact, the best
go players and the best chess players I know are generally interested
(and frequently accomplished) in the other game.

Please, we gamers do *not* need this sort of factionalism being
falsely stirred up by the few who seem to feel it.


Greycat

Gre...@idt.net
Does anyone have any spare tunafish??

Remove "spamguard" from return address to reply


Hans-Georg Michna

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May 27, 1997, 3:00:00 AM5/27/97
to

Zoltan,

how can you know the perfect first move, or any perfect move,
without knowing all possible games?

Hans-Georg

Hans-Georg Michna

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May 27, 1997, 3:00:00 AM5/27/97
to

"J. Kroll" <hy...@u.washington.edu> wrote:

>We (in the West) are sick of arrogant Go players saying that Go is better
>that Chess when we all know what they really mean.

What do they really mean? I'm surprised there are any ill
feelings between Go and chess players at all. Wasn't aware of
this.

I prefer Go for the simple reason that my mind is more suited to
that game. I can play Go much better than chess, although I
started out with chess in the beginning, when I didn't even know
Go existed.

But I know very well that there are many people whose brains are
better suited to chess than to Go, and I'm far from having any
negative feelings about this.

Bot games have one thing in common---the number of possible
situations and games is far higher than any of us can grasp.
Therefore both games will entertain and thrill humans (and
computers <grin>) for a long time to come.

Hans-Georg

Raffles

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May 27, 1997, 3:00:00 AM5/27/97
to

Zoltan Mark wrote:

>
> Gerry Forbes wrote:
>
> > >Now Professor Elwyn Berlekamp has upped the ante by offering
> > >US$5,000,000 to the first computer program that can beat a 5-dan
> > >player, which is equivalent to a strong expert player.
> >
> > Completely untrue. If you equate a 9-dan with 2700 Elo and give
> > 100 points for each dan, then a 5-dan would be Fide Master
> > strength, two levels above a strong expert. Since the differentiation
> > between dans is probably less than 100 points, a 5-dan would
> > probably be more like a strong International Master/weak GM.
>
> Just as a remark on comparing the upper ranks of these games. I remember reading a book
> some years ago that claimed that in a given sense Go is 'deeper' than chess, and offered
> the following measurement for 'depth'.
>
> You can set up a chain of players in either game using three rules:
> 1. the first player is a complete beginner, with an understanding of basic rules only;
> 2. two consecutive players relate to each other in strength in such a way that each
> player wins against the previous one 3/4 of the time - 3 games out of 4;
> 3. the last player in the chain is the best you can have, in other words, you stretch
> the chain to be as long as it possibly can.
>
> Depth of a given game is then simply the length of the chain one can make for that game.
> Unfortunately, I do not remember the exact numbers from the book, but the claim was that
> in Go you can set up a much longer such chain than in chess.
<snip>

> while basketball has something like 20+

A chess playing colleague of mine read an article in a chess mag (in the
UK) that used a similar system. The difference being; the chain went
from an absolute beginner to the best human expert, not from beginner to
the best player possible. The complexities I remember are 18 for chess
and 40 for go! Quite surprising. Perhaps more surprising is that these
figures would make basketball more complex than chess! Mind you I don't
see how you could come up with the "perfect" basketball team. I mean if
you have a machine that can do full path analysis on go or chess then
that would constitute a perfect player, but I don't see an equivalent in
basketball.

Other figures I remember are 8 for backgammon and 12 for draughts
(checkers). I seem to remember scrabble was in double figures too!

The article was a year or two ago. I am pretty sure about the chess and
go figures, no so sure about the draughts and b/g.

Raffles

PS Remove anti-spam '#' from my addr if you mail me


A chess playing colleague of mine read an article in a chess mag (in the
UK) that used a similar system. The difference being; the chain went
from an absolute beginner to the best human expert, not from beginner to
the best player possible. The complexities I remember are 18 for chess
and 40 for go! Quite surprising. Perhaps more surprising is that these
figures would make basketball more complex than chess! Mind you I don't
see how you could come up with the "perfect" basketball team. I mean if
you have a machine that can do full path analysis on go or chess then
that would constitute a perfect player, but I don't see an equivalent in
basketball.

Other figures I remember are 8 for backgammon and 12 for draughts
(checkers). I seem to remember scrabble was in double figures too!

The article was a year or two ago. I am pretty sure about the chess and
go figures, no so sure about the draughts and b/g.

Raffles

PS Remove anti-spam '#' from my addr if you mail me

Mark Boon

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May 28, 1997, 3:00:00 AM5/28/97
to

In article <338b3c0f...@snews.zippo.com>,
no_mail_please-H...@cis.compuserve.com (Hans-Georg Michna)
wrote:

> Zoltan,
>
> how can you know the perfect first move, or any perfect move,
> without knowing all possible games?
>

Alpha-beta search, for example. You'll need to know only the square-root
of all possible games. Maybe God knows much better algorithms than
AB-search.

--
Mark Boon

tes...@xs4all.nl

Kenneth Sloan

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May 28, 1997, 3:00:00 AM5/28/97
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In article <338b3c0f...@snews.zippo.com>,

Hans-Georg Michna <no_mail_please-H...@cis.compuserve.com> wrote:
>Zoltan,
>
>how can you know the perfect first move, or any perfect move,
>without knowing all possible games?

A perfectly reasonable question - which has many answers.
(There are other answers - but these three ought to do.)

================================================================
ANSWER 1. - the Breadth-First answer

Suppose you generate all possible games of length 30-ply (or less).

Suppose further that analysis of these games demonstrates that 1. a3
allows White to force a win in fewer than 30 ply.

In that case, it will be unnecessary to consider *any* game of length
31-ply, or longer.
================================================================

================================================================
ANSWER 2. - the Depth-First answer

Suppose you generate the chess tree (graph, actually) depth-first.

In that case, it turns out that you can often prove (not guess,
not hope - PROVE) that some sub-trees which have not yet
been generated are IRRELEVANT.

This means that you can come to the correct conclusion about the
perfect first move (and can KNOW that you will come to the correct
conclusion) without exploring these sub-trees. These sub-trees
describe "possible games" which you need not know.

(see "Alpha-Beta Search", and also perhaps "Hashing")
================================================================

================================================================
ANSWER 3. - the NIM answer

Suppose that someone creates an effective evaluation function
for chess similar to that already developed for the game of
NIM. In principle, this may be possible - our failure to do
so so far argues persuasively that one should not bet heavily
on the possibility - but the possibility remains, however slight.

In that case, you can choose the perfect first move by simply
creating a 1-ply deep tree, evaluating the resulting positions,
and selecting one of the moves with the maximal value.
================================================================

--
Kenneth Sloan sl...@cis.uab.edu
Computer and Information Sciences (205) 934-2213
University of Alabama at Birmingham FAX (205) 934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/info/faculty/sloan/

Toni D. Anderson

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May 28, 1997, 3:00:00 AM5/28/97
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If there can be only one perfect move on the board, it must be in the
middle :^)

Hans-Georg Michna <no_mail_please-H...@cis.compuserve.com>
wrote in article <338b3c0f...@snews.zippo.com>...


> Zoltan,
>
> how can you know the perfect first move, or any perfect move,
> without knowing all possible games?
>

> Hans-Georg
>

Anders Thulin

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May 28, 1997, 3:00:00 AM5/28/97
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In article <3383C03D.4618@remove_this_segment.erols.com>,

Zoltan Mark <mzoltan@remove_this_segment.erols.com> wrote:
>
>Depth of a given game is then simply the length of the chain one can make for that game.

This makes that depth very dependent on time and external factors.
Today, say, Qubic is deep, tomorrow it has been solved, and all
players are at the same level, and depth is gone.

Furthermore, the depth is limited to nr of players. I invent a new
game, and don't tell anyone about it. Depth 1, no matter what.

It seems that this metric is not so much a statement about the game
per se, as a statement of current proficiency, and involvement in the
game.

--
Anders Thulin Anders...@lejonet.se 013 - 23 55 32
Telia Engineering AB, Teknikringen 6, S-583 30 Linkoping, Sweden

Hans-Georg Michna

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May 28, 1997, 3:00:00 AM5/28/97
to

Kenneth, Mark,

ok, I see I have to modify my question just slightly.

How can you know the perfect first move, or most perfect moves,
without knowing many more games than are currently known or
calculable?

Hans-Georg

epes...@elmer.tci.com

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May 28, 1997, 3:00:00 AM5/28/97
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>
> >I'll remember your prediction. Wanna bet? Their prize money is pretty safe.
> >2050 is more close to target, unless quantum computers come out in force, in
> >which case maybe 2025.
> >
> >: amateur threw the match for his percentage of the prize!"). And


> >: you will go over the game with your friend and shake your head and
> >: Tsktsk.
> >

> >Yeah.. but I saw the Deep Blue victory coming from a mile away. The small
> >branching level of chess and the single minded goal makes it prey to easy
> >attacks like brute force. It's even possible that Deep Blue has gotten to the
> >point where it can Draw/Win 99.9999% of games against GM players, which will
> >make it real frustrating for Kasparov to regain his title.
>
> Title? What title? The only thing on the line was IBM's money. It's

You know what I mean. His reputation, his status in the chess world. He
isn't even 'official' champion of the world (he backed out of FIDE). But
in this case I think it is safe to say that perception is reality. To the
public, this *was* the champion match of the world.

> quite obvious that all you know about this match is from the press.

No, I watched it quite closely. You can say what you like, but this event
damaged championship chess quite a bit.

It was a propoganda match for sure, but just because it was a propoganda
match doesn't say it was meaningless.

> is avoiding negotiations for a real World Championship match. Not
> only do you not understand anything about chess, but you didn't even
> bother to read what I had written. I completely destroyed the notion
> of a "single minded goal" but here you are bringing it up again.

You thought you destroyed the notion of a 'single minded goal'. I think
you miss what I am trying to say.

Chess has a defined ending, a 'cut in stone' finality to it. You mate the
King, and you are done. To support this goal, you can build tablebases.
You can do a complete search of all the king's moves in a check.

How you get there is based on simple heuristics of material and
positional factors (100-1000 rules) and lots of alfa-beta search. At any
point you can find a forced mate, and then the game is over.

Go has no such defined ending. Left to your own devices, you can play
inside your own territory, play inside enemy territory (throw stones
away) get into loss loops, etc.

*This* is what I mean by single-minded goal. And this is only one of many
reasons why go won't fall to simple alfa-beta search.

> Haven't you ever wondered why Deep Blue's win in the first game of
> the 1996 match was described as the first time a computer had beaten
> a world champion in a game played under "classical chess tournament
> conditions"? It's because Kasparov had lost to a chess program in a
> 25 minute game! There are DOZENS of GMs who are better suited to
> playing computers than Kasparov, especially after he psychs himself
> out with his own hype! They don't play ridiculous anti-machine anti-
> chess; they know that they can play normal openings where the computer

Right, but their days are numbered. And I have yet to see whether or not
one can take on Deep Blue. Rumors are that lots of GMs got slaughtered in
the trials with Deep Blue's smaller cousin (only one processor)

> >They are going to need a substantially different approach with Go, which is
> >going to have to involve *real* AI. It is computationally as hard as such
> >tasks as learning languages, symbolic understanding, etc.
> >
> >A good analog is the strength of neuro-chess versus the strength of deep blue
.
> >Neuro-chess tries to 'learn' chess from first principles and training, etc.
> >It loses dismally even against programs like gnu chess at the first level.
> >Ed
> >
> >
> Of course a different approach will be needed, but there are sub-
> stantial improvements that can be made without using "real AI". I
> downloaded Turbogo and beat it by over 80 points when giving it 9
> stones. Apparently the registered version is "considerably stronger"
> but I doubt that it would give me any problems. The fact that go
> programs are so weak is, paradoxically, an indication that my pre-
> diction will be closer than yours, since it indicates that go

Optimistic programmers were saying in the fifties that simple problems
like English, planning, common-sense, etc. would be the first problems
that would be 'solved' by computers. That they are the last isn't a
surprise, since just because they are easy for humans doesn't mean they
are easy for computers.

> programmers are still clueless about how to approach the problem.

No... Hand-Talk is at 4 kyu (7 kyu really). And he is hitting barriers due
to the fact that the hard problems behind go aren't solved.

> As soon as one of them (and there will be new programmers with
> fresh ideas now that chess is "conquered") has a good idea progess
> will come exponentially.


I doubt it. In fact, I would say that chess isn't solved by a long shot.
It just was unfortunate to be 8x8. Being so small, it just fell victim to
ol' Moore's law. Make it 16x16 (or 19 x 19!) and see how strong deep blue
is!

Ed

-------------------==== Posted via Deja News ====-----------------------
http://www.dejanews.com/ Search, Read, Post to Usenet

J. Kroll

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May 28, 1997, 3:00:00 AM5/28/97
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On Tue, 27 May 1997, T Mark Hall wrote:
> in this are to be applauded. I last played Chess in a club where
> everyone else treated the game, and it is only a game, as a semi-

yes yes and a violin is only a toy made of hollow wood and four strings...

> is such a minority interest that it does not deserve publicity, I cannot

> condemn those who say that it is "better" than Chess in order to attract

You think it's okay to lie in order to spread your board game?

> both games must appeal to people with a commonality of interest. It
> would perhaps be better, considering the number of newsgroups that this
> was originally sent to, to ask why you wish to belittle Go so much.

Do I belittle Go so much?

> Fear, perhaps?

I'm sick of liars... perhaps?


J. Kroll

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May 28, 1997, 3:00:00 AM5/28/97
to

On Tue, 27 May 1997, Alberto Rezza wrote:

> >>We (in the West) are sick of arrogant Go players saying that Go is better
> >>that Chess when we all know what they really mean.

> No poster in the thread ever said anything about go being "better"


> or "more difficult" than chess. I have become much stronger in go than
> in chess, perhaps go was easier for me!

Many people did... I was just responding to someone else who also wasn't
thrilled by incessant go propoganda.

> Chess may well be more difficult than go - for humans.
> Fact is, go is much more difficult than chess - for computers.
> Kroll seems to know something about programming, yet he refuses
> to understand this.

Why do you think I don't understand this? I think Go is definitely within
the realm of computers... maybe not yet because we don't know the right
techniques and maybe our hardware isn't fast enough. I've got an algorythm
that beats me at one ply, but then I rather dislike Go so I stopped
working since I'd have to be a stronger player in order to make a
sufficiently stronger program...

> Perhaps, after DB-Kasparov, he is the one with an inferiority
> complex...

Personal attacks aren't particularly necessary or appropriate...


David Mechner

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May 30, 1997, 3:00:00 AM5/30/97
to

Raffles wrote:
> A chess playing colleague of mine read an article in a chess mag (in the
> UK) that used a similar system. The difference being; the chain went
> from an absolute beginner to the best human expert, not from beginner to
> the best player possible. The complexities I remember are 18 for chess
> and 40 for go! Quite surprising. Perhaps more surprising is that these
> figures would make basketball more complex than chess! Mind you I don't
> see how you could come up with the "perfect" basketball team. I mean if
> you have a machine that can do full path analysis on go or chess then
> that would constitute a perfect player, but I don't see an equivalent in
> basketball.
>
> Other figures I remember are 8 for backgammon and 12 for draughts
> (checkers). I seem to remember scrabble was in double figures too!
>
> The article was a year or two ago. I am pretty sure about the chess and
> go figures, no so sure about the draughts and b/g.

Calling this a measure of depth or complexity seems quite wrong. It
seems that this is a measure of the inherent skill-leverage of the
game. If a game allows a player with only a slight advantage of skill
to consistently win, it doesn't mean the game is "deeper" in anything
like the normal english language sense. Imagine a children's game:
each player picks a number, then the players compare numbers, and the
person who picked the higher number wins. If child A can count one
higher than child B, he can win 100% of the time, and this game has a
potentially infinte "complexity" (as defined in the article referred
to above).

-David

p.s. for people who think "number of possible games" is a measure of
complexity, sell your go set! this children's game is infinitely more
complex than go.
--
David A. Mechner Center for Neural Science
mec...@cns.nyu.edu 4 Washington Place, New York, NY 10003
212.998.3941 http://tilla.cs.nyu.edu/~mechner/


Hans-Georg Michna

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May 31, 1997, 3:00:00 AM5/31/97
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mec...@tilla.cs.nyu.edu (David Mechner) wrote:

>Calling this a measure of depth or complexity seems quite wrong. ...

David,

I agree. The measure is more one of the "luck factor" or
"reproducible outcome". A game that had no luck factor would
have indefinitely many player strength levels. An IQ test comes
to mind, where the "luck factor" is rather low.

But this has nothing to do with anything one would normally
associate with the word "depth".

Let's not forget that, while Go has more fields and many more
possible games than chess, these numbers for chess are
nonetheless indefinite, for all practical purposes. The fact has
no practical meaning.

Hans-Georg

Jared Roach

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Jun 1, 1997, 3:00:00 AM6/1/97
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In article <sqnn2pc...@tilla.cs.nyu.edu>,

David Mechner <mec...@cns.nyu.edu> wrote:
>
>Calling this a measure of depth or complexity seems quite wrong. It
>seems that this is a measure of the inherent skill-leverage of the
>game. If a game allows a player with only a slight advantage of skill
>to consistently win, it doesn't mean the game is "deeper" in anything
>like the normal english language sense.

It does not "mean" it, but it is difficult to deny that it is
evidence leaning in that direction.

>Imagine a children's game:
>each player picks a number, then the players compare numbers, and the
>person who picked the higher number wins. If child A can count one
>higher than child B, he can win 100% of the time, and this game has a
>potentially infinte "complexity" (as defined in the article referred
>to above).

I don't think this game has infinite complexity. I have several
arguments.

This is actually a binary game. Assume a real number domain.
The first player picks a number which divides the number line into two
equal halves. Without loss of generality assume this number to be zero.
The probability of the second player picking the same number is zero (if
it isn't, then there will be 3 moves for the other player - big deal).
Since the first player's move is irrelevant, The game is a one
move game in which the second player chooses one of two options: positive,
or negative. The second player wins if they choose positive. The second
player can ensure a win by choosing "infinity." Or at least a draw if you
want to quibble over details tangential to the issue at hand.

>-David
> >p.s. for people who think "number of possible games" is a measure of
>complexity, sell your go set! this children's game is infinitely more
>complex than go.

Since there are only two possible games here (three if you count
the tie), perhaps David could point out which are the 358 or so
intersections of the Go board that are illegal for black's first (and
only) move? And if I can get a satisfactoy response, I'll not only sell
my Go board, but I'll give it away.

So how many skill levels are involved in this game? Obviously,
all people who know what infinity is will be in the same (top) skill
group, leaving people who have yet to learn that word. My guess is that
there are very few people for whom the largest number known is not
1,2,3,4,5,6,7,8,9,10,100,1000,1 million, 1 billion, 1 trillion, or
infinity. So the number of skill levels is small.

Furthermore, set down all the players who do not know what
infinity is at the games of strategy that are the main subject of debate
in this context (chess, go, backgammon, some others). Chances are that
all such players will be quite weak - likely to be "off the low end of the
ratings scales." Such players are likely to be less than 20k in go, for
example. When they play each other games of Go, they will likely stratify
into the same levels that they do in the "bigger than" game.
These levels of complexity will likely be found in all games, and
thus can be "subtracted out" as a baseline. I think we _can_ have a
meaningful discussion using the concept of counting skill level
stratifications as a measure of complexity. I think trivial
counter-examples such as the one David raises are not excpetions, and if
they are, further analysis will reveal that they are excpetions that prove
the rule.

Note also that the "bigger than" game is SOLVED. It is hard to
believe that a solved game is more complex. it is also hard to believe
that such a game has more skill levels than an unsolved game.

Intuition and common sense are sometimes dangerous,
but my intuition and common sense tell me that "bigger than" is neither
complex nor full of skill levels.

Strangely enough, I actually agree with David, to an extent. IIt
just seems that he chose an unfortunate "counterexample." There was
considerable discussion in this newsgroup (rec.games.go) about a year ago
on this subject, and much of what has been posted recently is quite
redundant with what has been said before, suggesting that we could save a
lot of bandwidth if we were just to content ourselves with using DejaNews
rather than rehashing already hashed out stuff.

But to rehash myself, it is my feeling that the most intriguing
"counterexample" is to take any game with at least two skill levels such
that the odds of the stronger player winning when two players play each
other, one from each skill level, are greater than 50% and less than 100%.
Furthermore, assume that at least one of these two skill levels actually
represents an infinite and continuous gradation of skills that have
been grouped by choosing a discrete boundary to form the two skill levels.
One can then construct a game with an arbitrarily high number of
skill levels by defining the new game as a "best of N" competition of the
basic underlying game. As N increases towrds infinity, the number of
skill levels increases towards infinity.
In practice, it is difficult to meet the assumptions necessary for
such a game (consider, for example, the effect of a finite world
population), but it is nevertheless interesting "food for thought."
I'd refute this here, but rather than waste more bandwidth, I
recommend DejaNews.

It remains my feeling that there _is_ a correpondence
between number of skill levels and "complexity." I will readily agree
that it is a nebulous connection, but _it_ _is_ _there_.

It is a testimony to the nastiness of the net that I feel I have
to add this paragraph. I view this thread and related discussion as a
platonic and socratic dialog. If anything is interpreted as insulting,
demaeaning or threatening it should be reinterpreted in light of its
actual intent which contained not a drop of ire. I not only respect
David's opinions, but I like him.

Cheers,
Jared


--------------------------------------------------------
"You are the move you make." -YES

Jared Roach, AGA 3D
Seattle, WA

ro...@u.washington.edu
http://weber.u.washington.edu/~roach/


Kevin Whyte

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Jun 1, 1997, 3:00:00 AM6/1/97
to

>Raffles wrote:
>> A chess playing colleague of mine read an article in a chess mag (in the
>> UK) that used a similar system. The difference being; the chain went
>> from an absolute beginner to the best human expert, not from beginner to
>> the best player possible. The complexities I remember are 18 for chess
>> and 40 for go! Quite surprising. Perhaps more surprising is that these
>> figures would make basketball more complex than chess! Mind you I don't
>> see how you could come up with the "perfect" basketball team. I mean if
>> you have a machine that can do full path analysis on go or chess then
>> that would constitute a perfect player, but I don't see an equivalent in
>> basketball.
>>
>> Other figures I remember are 8 for backgammon and 12 for draughts
>> (checkers). I seem to remember scrabble was in double figures too!
>>
>> The article was a year or two ago. I am pretty sure about the chess and
>> go figures, no so sure about the draughts and b/g.

Perhaps this should be an FAQ? This comes up reasonably often, and
is reasonably convincing at first, but has a clear flaw. The flaw can
be seen as follows: consider the game "super-go" where two players
play a best of three match of go games. The winner of one game of
super-go is then the winner of a 3 game match of go. Clearly the
game super-go is not any "deeper" or more complex than go, just longer.
It has substantially more "skill levels" than go, though.

I don't know if there's a good way to fix this system. I've thought
about this some, and it's messy. My basic thoughts are below. I
have a more precise mathematical formulation/semi-solution to the
problem, but it's too technical to be of general interest. I'd be
happy to explain/discuss it via e-mail with anyone intersted.

A basic assumption behind elo ratings, aga/igs/nngs etc ratings,
go handicaps, etc. is that if I know A beats B with probability p1
and B beats C with probability p2 then I can compute the probability
that A beats C just from p1 and p2. Of course, in real life this
is false - we all know of examples of players A, B, and C where A
usually beats B, B beats C, and C beats A. It should be clear that
this phenomenon will thwart any attempt to assign ratings. It
also isn't really important in the larger scheme of things - this
only happens when A,B, and C are relatively close in ability - you
won't find a pro 9-dan who just can't beat a certain 1 kyu.

What does this have to do with complexity? Well, if we switch
from "go" to "super-go" the function that computes p(A beats C)
from p(A beats B) and p(B beats C) changes. If we insist that one
play long enough matches of game-1 and game-2 so that the functions
are the same, and then measure "skill levels" for matches of those
lengths, we would have something a lot more reasonable. In practice
this will be difficult to compute exactly, but we can get close.
The ratings data from various games should provide us enough info
to (more or less) estimate the functions, and away we go.

Kevin Whyte
kwh...@math.uchicago.edu

Barry Phease

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Jun 2, 1997, 3:00:00 AM6/2/97
to

Kevin Whyte wrote:
>
> >Raffles wrote:
> >> A chess playing colleague of mine read an article in a chess mag (in the
> >> UK) that used a similar system. The difference being; the chain went
> >> from an absolute beginner to the best human expert, not from beginner to
> >> the best player possible. The complexities I remember are 18 for chess
> >> and 40 for go!

>

> Perhaps this should be an FAQ? This comes up reasonably often, and
> is reasonably convincing at first, but has a clear flaw. The flaw can
> be seen as follows: consider the game "super-go" where two players
> play a best of three match of go games. The winner of one game of
> super-go is then the winner of a 3 game match of go. Clearly the
> game super-go is not any "deeper" or more complex than go, just longer.
> It has substantially more "skill levels" than go, though.
>

What you say is true but there is another way of looking at it. Go is
equivalent in this scheme to some variant of "superchess". 3 games of
chess played in a match would give a similar "probability ladder" as
go. The difference is that THESE 3 GAMES HAVE TO BE PLAYED
SIMULTANEOUSLY.

Everyone can agree that simultaneous chess is more complex than a single
game.

--
Barry Phease

mailto:Bar...@es.co.nz

http://www.es.co.nz/~barryp/home.html

Patrick Juola

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Jun 2, 1997, 3:00:00 AM6/2/97
to

In article <5mqm0l$7...@nntp5.u.washington.edu> ro...@u.washington.edu (Jared Roach) writes:
>In article <sqnn2pc...@tilla.cs.nyu.edu>,

>>Imagine a children's game:
>>each player picks a number, then the players compare numbers, and the
>>person who picked the higher number wins. If child A can count one
>>higher than child B, he can win 100% of the time, and this game has a
>>potentially infinte "complexity" (as defined in the article referred
>>to above).
>
> I don't think this game has infinite complexity. I have several
>arguments.
>
> This is actually a binary game. Assume a real number domain.

This is where your analysis fails. A real number domain is the
ultimate extension of the game's complexity.

More succinctly,

>The second player can ensure a win by choosing "infinity."

What if (by construction), the second player doesn't know about
the "number" infinity -- and thus can't choose it?

> Note also that the "bigger than" game is SOLVED. It is hard to
>believe that a solved game is more complex. it is also hard to believe
>that such a game has more skill levels than an unsolved game.

Only because most of the readership of this group is already at the
top of the ladder. Somewhere, space aliens may be reading this
group and wondering how we can consider chess to be "complex."

If you accept that "intermediate stages" is a valid measure of complexity,
"bigger than" is indeed an infinitely complex game. This argues that
"intermediate states" is not a particularly meaningful measure of
complexity.

-kitten

edwa...@cc5.crl.aecl.ca

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Jun 2, 1997, 3:00:00 AM6/2/97
to

In a previous article, ro...@u.washington.edu (Jared Roach) wrote:
->In article <sqnn2pc...@tilla.cs.nyu.edu>,
->David Mechner <mec...@cns.nyu.edu> wrote:
->>
->>Calling this a measure of depth or complexity seems quite wrong. It
->>seems that this is a measure of the inherent skill-leverage of the
->>game. If a game allows a player with only a slight advantage of skill
->>to consistently win, it doesn't mean the game is "deeper" in anything
->>like the normal english language sense.
->
-> It does not "mean" it, but it is difficult to deny that it is
->evidence leaning in that direction.
->
->>Imagine a children's game:
->>each player picks a number, then the players compare numbers, and the
->>person who picked the higher number wins. If child A can count one
->>higher than child B, he can win 100% of the time, and this game has a
->>potentially infinte "complexity" (as defined in the article referred
->>to above).
->
-> I don't think this game has infinite complexity. I have several
->arguments.
->
-> This is actually a binary game. Assume a real number domain.
->The first player picks a number which divides the number line into two
->equal halves. Without loss of generality assume this number to be zero.
->The probability of the second player picking the same number is zero (if
->it isn't, then there will be 3 moves for the other player - big deal).
-> Since the first player's move is irrelevant, The game is a one
->move game in which the second player chooses one of two options: positive,
->or negative. The second player wins if they choose positive. The second
->player can ensure a win by choosing "infinity." Or at least a draw if you
->want to quibble over details tangential to the issue at hand.
->
-> >-David
->> >p.s. for people who think "number of possible games" is a measure of
->>complexity, sell your go set! this children's game is infinitely more
->>complex than go.
->
-> Since there are only two possible games here (three if you count
->the tie), perhaps David could point out which are the 358 or so
->intersections of the Go board that are illegal for black's first (and
->only) move? And if I can get a satisfactoy response, I'll not only sell
->my Go board, but I'll give it away.
->
-> So how many skill levels are involved in this game? Obviously,
->all people who know what infinity is will be in the same (top) skill
->group, leaving people who have yet to learn that word. My guess is that
->there are very few people for whom the largest number known is not
->1,2,3,4,5,6,7,8,9,10,100,1000,1 million, 1 billion, 1 trillion, or
->infinity. So the number of skill levels is small.
->
-> Furthermore, set down all the players who do not know what
->infinity is at the games of strategy that are the main subject of debate
->in this context (chess, go, backgammon, some others). Chances are that
->all such players will be quite weak - likely to be "off the low end of the
->ratings scales." Such players are likely to be less than 20k in go, for
->example. When they play each other games of Go, they will likely stratify
->into the same levels that they do in the "bigger than" game.
-> These levels of complexity will likely be found in all games, and
->thus can be "subtracted out" as a baseline. I think we _can_ have a
->meaningful discussion using the concept of counting skill level
->stratifications as a measure of complexity. I think trivial
->counter-examples such as the one David raises are not excpetions, and if
->they are, further analysis will reveal that they are excpetions that prove
->the rule.
->
-> Note also that the "bigger than" game is SOLVED. It is hard to
->believe that a solved game is more complex. it is also hard to believe
->that such a game has more skill levels than an unsolved game.
->
-> Intuition and common sense are sometimes dangerous,
->but my intuition and common sense tell me that "bigger than" is neither
->complex nor full of skill levels.
->
-> Strangely enough, I actually agree with David, to an extent. IIt
->just seems that he chose an unfortunate "counterexample." There was
->considerable discussion in this newsgroup (rec.games.go) about a year ago
->on this subject, and much of what has been posted recently is quite
->redundant with what has been said before, suggesting that we could save a
->lot of bandwidth if we were just to content ourselves with using DejaNews
->rather than rehashing already hashed out stuff.
->
-> But to rehash myself, it is my feeling that the most intriguing
->"counterexample" is to take any game with at least two skill levels such
->that the odds of the stronger player winning when two players play each
->other, one from each skill level, are greater than 50% and less than 100%.
->Furthermore, assume that at least one of these two skill levels actually
->represents an infinite and continuous gradation of skills that have
->been grouped by choosing a discrete boundary to form the two skill levels.
-> One can then construct a game with an arbitrarily high number of
->skill levels by defining the new game as a "best of N" competition of the
->basic underlying game. As N increases towrds infinity, the number of
->skill levels increases towards infinity.
-> In practice, it is difficult to meet the assumptions necessary for
->such a game (consider, for example, the effect of a finite world
->population), but it is nevertheless interesting "food for thought."
-> I'd refute this here, but rather than waste more bandwidth, I
->recommend DejaNews.
->
-> It remains my feeling that there _is_ a correpondence
->between number of skill levels and "complexity." I will readily agree
->that it is a nebulous connection, but _it_ _is_ _there_.
->
-> It is a testimony to the nastiness of the net that I feel I have
->to add this paragraph. I view this thread and related discussion as a
->platonic and socratic dialog. If anything is interpreted as insulting,
->demaeaning or threatening it should be reinterpreted in light of its
->actual intent which contained not a drop of ire. I not only respect
->David's opinions, but I like him.
->
-> Cheers,
-> Jared
->
->
->--------------------------------------------------------
->"You are the move you make." -YES
->
->Jared Roach, AGA 3D
->Seattle, WA
->
->ro...@u.washington.edu
->http://weber.u.washington.edu/~roach/
->

Infinity is not a number, eliminating 99% of the argument above.
Geoff

Jared Roach

unread,
Jun 3, 1997, 3:00:00 AM6/3/97
to

Patrick,

Do actually believe that the "bigger then" game is complex? I
wasn't sure from your posting. I remain convinced that my analysis does
not fail.

In article <5mu421$h...@news.ox.ac.uk> you write:

>> [The bigger than game] is actually a binary game. Assume a real
>> number domain.
>


>This is where your analysis fails. A real number domain is the
>ultimate extension of the game's complexity.

Actually, I don't think it matters, for purposes of the discussion
at hand. I shouldn't have made the distinction, as it adds needless
complexity (??!!!??!!=:) to the discussion at hand. Real number line,
integers, whatever. See the end of this post for what is probably a
better game to illustrate this point.

>
>
>>The second player can ensure a win by choosing "infinity."
>

>What if (by construction), the second player doesn't know about
>the "number" infinity -- and thus can't choose it?

I assume you wrote this before reading my entire posting.
Otherwise the criticism doesn't make sense, as I addressed it. Perhaps I
was not sufficiently clear. If so, I apologize.

>> Note also that the "bigger than" game is SOLVED. It is hard to
>>believe that a solved game is more complex. it is also hard to believe
>>that such a game has more skill levels than an unsolved game.
>

>Only because most of the readership of this group is already at the
>top of the ladder. Somewhere, space aliens may be reading this
>group and wondering how we can consider chess to be "complex."

Most people that play strategy games know what infinity is. It is
somewhat meaningless to extend the discussion to include people who do not
play strategy games.
Also, unmentioned in my original post is the fact that most who do
not know what infinity is are on an extremely steep learning curve so
that their level of play improves from game to game, making a statistical
analysis of their skill almost impossible. Again, it is reasonable,
although perhaps not necessary, to exclude such people from analysis.

Also, I found no claim on your part that levels of skill were
completely independent from the complexity of game. Do you beleive that
they are?

>If you accept that "intermediate stages" is a valid measure of complexity,
>"bigger than" is indeed an infinitely complex game. This argues that
>"intermediate states" is not a particularly meaningful measure of
>complexity.

I do not understand what you mean. After subtracting the
background noise of imbeciles, poorly educated children, people who do not
know the rules, and people who haven't had a beginner's introduction on
how to win a game, you'll be lucky to find more than one skill level. I
find it hard to believe that you actually read my post before responding.
Surely it is reasonable to subtract out the background noise.
This is common sense. Certainly one would do this for chess, go, and
backgammon, which really are the games of interest in the forums where
debate has arisen.
"Bigger than," as I stated before, is an unfortunate
counterexample. If you wish to pursue this type of counterexample, find a
better game, as otherwise you are hurting the "anti-intermediate states"
argument.

I won't necerssarily disagree with your statement that
"intermediate states" is not particularly meaningful. See for example, my
posts of about a year ago in the newsgroups.

They definitely are meaningful, but perhaps not _particularly_
meaningful. They are probably not useful, primarily due to difficulties
in quantification.

Also note that "complexity" is poorly defined. We may very well
be thinking of different things when we use this word. Again, I refer you
to my old posts for extensive discussion on this point.

Best Wishes,
Jared

btw: Maybe the following is a better game for this type of "anti-levels
of skill" argument:

Have a neutral referee generate an ordered and infinte (or
arbitrarily large) list of unbreakable code words (or numbers). The
player who can name the code with the greatest cardinal wins.
The referee reveals a different code to everyone on the
planet, creating over 5 billion skill levels, each with a 100% chance of
beating any lower skill level.

I'll leave it as an exercise to the readership to refute this game
as a counterexample.
I'm pretty sure a much better counterexample can be found.


btbtw, Oh yeah. I'd be amazed if any space aliens intelligent enough o
have to power to read these posts would not also have enough intelligence
to understand the human psyche well enough to understand why we think
chess is complex.

Hans-Georg Michna

unread,
Jun 4, 1997, 3:00:00 AM6/4/97
to

Barry Phease <bar...@es.co.nz> wrote:

>What you say is true but there is another way of looking at it. Go is
>equivalent in this scheme to some variant of "superchess". 3 games of
>chess played in a match would give a similar "probability ladder" as
>go. The difference is that THESE 3 GAMES HAVE TO BE PLAYED
>SIMULTANEOUSLY.

Barry,

simultaneous play is a possibility, but not necessary. You could
just as well define n subsequent games, where n may have to be
3, 4 or 5 to match Go. The principle is the same.

Hans-Georg

Jared Roach

unread,
Jun 5, 1997, 3:00:00 AM6/5/97
to

In article <2JUN97....@cc5.crl.aecl.ca>,
<edwa...@cc5.crl.aecl.ca> wrote:

>Infinity is not a number, eliminating 99% of the argument above.

Webster's has among the definitions of infinity:

1) an indefinitely great number or amount
2) a transfinite number (as aleph-null)

However, it is acceptable to me for one to define infinity in such
a way that it "is not a number." Even if you use a definition that it is
a number (which I think is reasonable), you can simply add a rule to the
"bigger than" game that outlaws the use of "infinity." To actually make
the "bigger than" game work, it should be noted that rules must be
carefully crafted to deal with exactly what is meant by a number. For
example, everyone would agree that "two" is a legal move, but how about
"one plus one?" This gets tricky when one (or both!) players choose "one
plus the number my opponent chooses." Are you allowed to use exponential
(or other shorthand) notations? Is there a limit on the amount of time a
player has to vocalize their move?

It may be that, given suitable answers to these rules questions,
the optimal play is "googleplex." Ther are indeed relatively few numbers
that can be vocalized without the use of shorthand in a limited period of
time (or at all, for that matter). The vast majority of these numbers
would only be known to people who also knew of a larger number, so most
vocalizable numbers would never actually be played. Even without
infinity, the number of skill levels of "greater than" is quite limited.

These issues, of course, are all tangential to the main argument.
Many of them can be bridged by the use of the game I mentioned in my last
post as a better counterexample than the "bigger than" game.

I am pretty sure that with mild effort, anyone can rework the
argument of the post that Geoff quotes so that only a few percent is
eliminated, much less than the 99% that he (at least on first pass)
beleives to be invalidated. In any case, whatever of the argument is left
after all of this "invalidating" should remain convincing, even if it is
only 1%.

Eliminating infinity actually strengthens my argument by
eliminating one of the possible plays, reducing both the number of skill
levels and the complexity of the game. (But see below, as I claim that
there is only one skill level, whether or not infinity is used as a legal
move.)

Again, one of the keys to recognizing trivial games such as this
as the chaff that they are is to eliminate skill levels that arise from
players who don't the the rules to the game as well as from players who
don't have a basic introduction to the game's strategy. One might
arbitrarily but reasonably define a "basic" introduction as an hour's
worth of some kind of learning experience. The informational content of
the learning experience to be provided by someone at least as skilled as a
"master" of the game in question.
I am pretty sure that given an hour with anyone without a
communication or learning disability that I could teach them how to become
the world's best "greater than" player. "Best" in the "equal to or
greater than" sense.
To reiterate: After subtracting out noise, "Greater than" has
just one skill level. This is consistent with it not being a complex game.

Oh yeah: Can we please edit our posts so that at least we create
more new material than we quote? The phrase "Where's the beef?" comes to
mind.

-Jared

--------------------------------------------------------


"You are the move you make." -YES

Jared Roach, AGA 3D

Jared Roach

unread,
Jun 5, 1997, 3:00:00 AM6/5/97
to

In article <339590ab...@snews.zippo.com>,

Hans-Georg Michna <no_mail_please-H...@cis.compuserve.com> wrote:
>
>simultaneous play is a possibility, but not necessary. You could
>just as well define n subsequent games, where n may have to be
>3, 4 or 5 to match Go. The principle is the same.

The principle is certainly not the same. In order for "levels of
skill" to be used as a measure of complexity, the complexity measure must
be defined in such a way that it is insensitive to counterintuitive
alterations in the rules of a game that apparently increase the number of
levels of skill without increasing its complexity.
One approach to defining the measure of complexity to bridge this
difficulty is to only use it to measure "minimum mutually dependent
games." For example, after playing a round of blackjack with a fresh
deck, one's strategy in a subsequent round with a fresh deck will not be
dependent on the moves played in the previous round. Thus "levels of
skill" should not be used to measure the complexity of a game defined as
Super-Fresh-Deck-Blackjack. Such a game should be split to its smallest
grouping of mutually dependent moves before it is analyzed for skill
levels and/or complexity.
There is an argument of "learning from game to game" and/or
"psyching out the opponent" that claims that it is actually impossible to
have games played completely independently from each other. This _is_ an
interesting line of reasoning. We spent a lot of time on it when this
thread came up about a year ago.
In short, Barry is being quite reasonable that the Super-Chess
game in question should be played simultaneously or in a such a manner
that the games are all dependent on each other (i.e. Fairy Chess).
Of course, Super-Chess then loses its value as a counterexample,
and instead becomes a supportive example, as both the levels of skill and
the levels of complexity will increase.

Hans-Georg Michna

unread,
Jun 5, 1997, 3:00:00 AM6/5/97
to

ro...@u.washington.edu (Jared Roach) wrote:

Jared,

I see your point. Subsequent games could alter the character of
the game by introducing psychic factors, for example.
Interesting.

But it's all theory anyway. Super chess will not be played
widely. It's a good mental experiment though.

Hans-Georg

Michael J. Scudder

unread,
Jun 6, 1997, 3:00:00 AM6/6/97
to

Someone who knows more than I may want to add to this thread, but I
believe there was a 'game' among mathematicians at conferences some time
ago which was to write an expression that fit on a 3 by 5 card which
denoted the largest finite number among the contestants. With
mathematicians trying hard the numbers got very big, making a googleplex
look ludicrously small. This game could be considered to have a large
number of skill levels :-).

EMail: SCU...@CS.UMASS.EDU Phone: (413)545-9788
SMail: Mike Scudder, COINS Dept., Even a fool, when he keeps silent,
Univ of Mass, Amherst, MA 01003 is considered wise. Proverbs 17:28

Jared Roach

unread,
Jun 6, 1997, 3:00:00 AM6/6/97
to

In article <339829...@acsiom.org>,

Michael J. Scudder <scu...@acsiom.org> wrote:
>Someone who knows more than I may want to add to this thread, but I
>believe there was a 'game' among mathematicians at conferences some time
>ago which was to write an expression that fit on a 3 by 5 card which
>denoted the largest finite number among the contestants. With
>mathematicians trying hard the numbers got very big, making a googleplex
>look ludicrously small. This game could be considered to have a large
>number of skill levels :-).

This, I think, is an excellent example to consider in this thread.
I think there are two lines of thought flowing away form here:

1) Is this game complex? If so, how complex? Commensurately complex with
the number of skill levels?

2) How many skill levels are there?

I don't know if the game is complex or not, largely because we
haven't really decided what we mean by "complex."

However, it may be that there are, in fact, very few skill levels
to this game.
Suppose the game were to be played for high stakes over many years
and the results of all games were available for analysis by the world's
experts. Furthermore, suppose a reasonable dissemination of this
analysis. Again, subtract out the "noise" of people who haven't had at
least an hour's worth of competent instruction in the game. These seem
like reasonable prerequisites to apply before we allow "levels of skill"
to be used as a measure of complexity. Certainly, these assumptions can
be met by Go, Chess, and Backgammon, as well as many other games of
interest to this thread.
I think many "counter-examples" will fail these tests. It was
these tests that I had in mind when soliciting a rebuff to my "Codes with
Cardinals" counter-example that I mentioned at the end of an earlier post.

Oh yeah, one quick question: How small are you allowed to write
on the card? Can you use photolithography or other technology-intensive
writing techniques?

And to use this opportunity to broaden the discussion: Is Trivial
Pursuit (or another suitably defined game of knowledge) complex? How
many skill levels do such games have? By mixing the elements of luck and
knowledge, it would seem to be possible to design such a game with an
arbitrarily large number of skill levels (subject to finite constraints
like the world population size).
I think discussion along these lines will start to get at
"different kinds of complexity." The complexity of "knowledge" (or the
ability to remember - i.e. size of RAM/ROM) on one side,
and the complexity of "analysis" on the other. The "levels of skill" in a
game probably results as a function of both "knowledge" and "analysis."
If I had my way, I would not consider the "knowledge" portion to be
complex. If this is done, then I think that "levels of skill" will indded
be dependent on the complexity (i.e. "analysis" factor) of a game, and
thus be a measure of complexity. However, since "levels of skill" will
also depend on at least one other factor (i.e. ability to remember, or
knowledge), it will have decreased utility as a measure of complexity.

Clearly, Chess, Go, and Backgammon have both knowledge and
analysis components.

Onward!
-Jared

--------------------------------------------------------


"You are the move you make." -YES

Jared Roach, AGA 3D

Yueqi Zhu

unread,
Jun 6, 1997, 3:00:00 AM6/6/97
to

Is it possible that I finish my first game of it this lifetime
to know which skill level I am at?:)

Yueqi Zhu


In article <339829...@acsiom.org> scu...@acsiom.org writes:
>Someone who knows more than I may want to add to this thread, but I
>believe there was a 'game' among mathematicians at conferences some time
>ago which was to write an expression that fit on a 3 by 5 card which
>denoted the largest finite number among the contestants. With
>mathematicians trying hard the numbers got very big, making a googleplex
>look ludicrously small. This game could be considered to have a large
>number of skill levels :-).
>

Bogomolov

unread,
Jun 8, 1997, 3:00:00 AM6/8/97
to

Pardon me, but WHAT IS GO?
I would really love to KNOW.
(hey, that rhymes! ... sort of)

Can you tell me the rules, PLEASE?
And how the game is played?

Thanks in advance,
F.B.

(not much of a poem, though)
oh, well...

Michael Sullivan

unread,
Jun 8, 1997, 3:00:00 AM6/8/97
to

In article <3391F8ED...@es.co.nz>, Barry Phease <bar...@es.co.nz> wrote:

>What you say is true but there is another way of looking at it. Go is
>equivalent in this scheme to some variant of "superchess". 3 games of
>chess played in a match would give a similar "probability ladder" as
>go. The difference is that THESE 3 GAMES HAVE TO BE PLAYED
>SIMULTANEOUSLY.

>Everyone can agree that simultaneous chess is more complex than a single
>game.

Yes, it is, but I wonder how much more. I suspect I could play 3
simultaneous go games within 2-3 stones of my single game strength. And
I've had no practice against players better than about 10kyu. I imagine
that teaching pros who have ample opportunity to play simuls, have a much
smaller gap between their simul strength and single game strength.

But even then -- in "super chess" those three games are independent --
whereas all the go moves in a given game must be considered together. A
more appropriate "super chess" would be analogous to bughouse (pieces from
one board can be placed on another according to various sets of rules).
It's unclear to me whether bughouse or similar variants are actually more
complex than a single game of chess (or simul games). Not enough people
play them seriously.


Michael

David Mechner

unread,
Jun 8, 1997, 3:00:00 AM6/8/97
to

Jared wrote:
> <edwa...@cc5.crl.aecl.ca> wrote:
>
> >Infinity is not a number, eliminating 99% of the argument above.
>
> Webster's has among the definitions of infinity:
>
> 1) an indefinitely great number or amount
> 2) a transfinite number (as aleph-null)

Sorry, use "integer" instead of "number". Infinity isn't an integer,
and there's no ambiguity (algorithms aren't allowed).

Now, imagine 100 4-year-olds that, as it happens, can count only as
high as 1, 2, ... 100. I don't think this scenario beggars
imagination. You will then be able to demonstrate 100 "skill levels"
at the "bigger number" game, making it more complex than go.

But don't get in an uproar! I agree, go is more complex than the
number game. My whole point is that "number of skill levels" as
defined eariler in the thread isn't a meaningful measure of
complexity. Call it proof by counterexample.

-David

ze...@wam.umd.edu

unread,
Jun 8, 1997, 3:00:00 AM6/8/97
to

Bogomolov wrote:
>
> Pardon me, but WHAT IS GO?
> Can you tell me the rules, PLEASE?
> And how the game is played?

Take a look at http://www.sentex.net/~mmcadams/goweb.html#basic

Dan Amodeo

hsel

unread,
Jun 9, 1997, 3:00:00 AM6/9/97
to

Bogomolov wrote:
>
> Pardon me, but WHAT IS GO?
> I would really love to KNOW.
> (hey, that rhymes! ... sort of)
>
> Can you tell me the rules, PLEASE?
> And how the game is played?
>
> Thanks in advance,
> F.B.
>
> (not much of a poem, though)
> oh, well...

Good question, hey I like that poem, very poetic.

What is GO? Well, it is Japanese word for Wei Qi(very Original Chinese
term) - the game of ancient Chinese tactical war arts, no strategies,
only tactics. If you like strategic game, try chess. I guess GO means
Good for Orientals, in fact they are best at it. :)

B.J. Herbison

unread,
Jun 9, 1997, 3:00:00 AM6/9/97
to Bogomolov

Bogomolov wrote:
> Pardon me, but WHAT IS GO?
> I would really love to KNOW.

From David Scholefield's Go Page
( http://www.port80.co.uk/personal/david/go.html ):

Go is an oriental board game played on a 19 by 19 grid,
with players placing black and white `stones' alternately
on the intersections. The aim of the game is to surround
as much territory on the board as possible.

The basic rules and strategy (enough to play the first dozen or
more games) can be described over the board in under a minute.

Pointers to compete rules, tutorials, and several other online
sources of information can be found at
http://www.herbison.com/herbison/bj_go.html .

B.J.
--
B.J. Herbison HighGround Systems, Inc.
bher...@HighGround.com +1 508 263-5588 x126 FAX: -5565
1300 Massachusetts Avenue Boxborough, MA 01719-2203
At home: b...@herbison.com http://www.herbison.com/herbison/bj.html