Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-03 Thread Hideki Kato
David Fotland: [EMAIL PROTECTED]:
Many Faces does not use null move, but does extensive caching of life and
death and other tactical results.

The problem of such caching scheme is when and how programs can make 
correctly the cache be dirty (ie, invalid).  It may be very hard even 
for human players.

-gg (Hideki)

-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of terry mcintyre
Sent: Tuesday, October 02, 2007 9:21 AM
To: computer-go
Subject: Re: [computer-go] IEEE Spectrum article by Deep Blue creator


- Original Message 

From: Don Dailey [EMAIL PROTECTED]


I think [Hsu] is betting on null move proving - but I'm real skeptical that
 it will be effective in Computer Go.   It will indeed reduce the tree
 significantly, but this comes at a qualitative price that is not so bad
 in Chess but is a lot in Go.


Hsu also discusses the gains from caching life-and-death analysis of groups.
I suspect that
this will greatly reduce computational effort, once an efficient mechanism
is implemented.
Existing monte carlo programs cache information about playable/non playable
points; when
augmented with knowledge about life and death, search should more quickly
home in on crucial 
lines of play.

I've been playing against Mogo the last few weeks. It has a very interesting
style of play, and it 
often does quite well in tactical analysis, but sometimes it misses a key
move and fails to kill or
fails to preserve a large group - game over! A good life-and-death cache
would be a definite improvement.

Caching parts of trees works better in Go, since well-defined sections of
the board can sometimes be 
partitioned from the rest of the board. Where such partitions leak, analysis
is likely to be critical; 
for example, ladders and ladder breakers can extend across the board;
invasions often depend on 
cutting points halfway across the board. 


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RE: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-03 Thread David Fotland
It's a very difficult problem, but I have something that works reasonably
well.

David

 -Original Message-
 From: [EMAIL PROTECTED] 
 [mailto:[EMAIL PROTECTED] On Behalf Of Hideki Kato
 Sent: Wednesday, October 03, 2007 12:27 AM
 To: computer-go
 Subject: Re: [computer-go] IEEE Spectrum article by Deep Blue creator
 
 
 David Fotland: [EMAIL PROTECTED]:
 Many Faces does not use null move, but does extensive 
 caching of life 
 and death and other tactical results.
 
 The problem of such caching scheme is when and how programs can make 
 correctly the cache be dirty (ie, invalid).  It may be very hard even 
 for human players.
 
 -gg (Hideki)
 
 -Original Message-
 From: [EMAIL PROTECTED]
 [mailto:[EMAIL PROTECTED] On Behalf Of terry 
 mcintyre
 Sent: Tuesday, October 02, 2007 9:21 AM
 To: computer-go
 Subject: Re: [computer-go] IEEE Spectrum article by Deep Blue creator
 
 
 - Original Message 
 
 From: Don Dailey [EMAIL PROTECTED]
 
 
 I think [Hsu] is betting on null move proving - but I'm 
 real skeptical that
  it will be effective in Computer Go.   It will indeed 
 reduce the tree
  significantly, but this comes at a qualitative price that 
 is not so 
 bad  in Chess but is a lot in Go.
 
 
 Hsu also discusses the gains from caching life-and-death analysis of 
 groups. I suspect that this will greatly reduce 
 computational effort, 
 once an efficient mechanism is implemented.
 Existing monte carlo programs cache information about 
 playable/non playable
 points; when
 augmented with knowledge about life and death, search should 
 more quickly
 home in on crucial 
 lines of play.
 
 I've been playing against Mogo the last few weeks. It has a very 
 interesting style of play, and it often does quite well in tactical 
 analysis, but sometimes it misses a key move and fails to kill or
 fails to preserve a large group - game over! A good 
 life-and-death cache
 would be a definite improvement.
 
 Caching parts of trees works better in Go, since 
 well-defined sections 
 of the board can sometimes be partitioned from the rest of 
 the board. 
 Where such partitions leak, analysis is likely to be critical;
 for example, ladders and ladder breakers can extend across the board;
 invasions often depend on 
 cutting points halfway across the board. 
 
 
   _
 
 Building a website is a piece of cake.
 Yahoo! Small Business gives you all
 http://us.rd.yahoo.com/evt=48251/*http://smallbusiness.yahoo
.com/webhosting
/?p=PASSPORTPLUS the tools to get online.
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Sylvain Gelly
Hi,

 Has anyone else done scaling experiments with 19x19 and UCT?


I did some months ago, and reported them in that list with the title
19x19 Go, scalability with time vs handicap
(http://www.mail-archive.com/computer-go%40computer-go.org/msg02775.html)

The results are old, but now everyone can do those experiments as
you all have the newest binaries ;) (you can only do the experiments
with time but not number of simulations, so you would have to run
on the same type of machines).

Cheers,
Sylvain
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Alain Baeckeroot
Le mardi 2 octobre 2007 16:46, Ian Osgood a écrit :
 Greetings,

 I noticed that the following link was recently added to the Computer
 Go Wikipedia article.

 http://www.spectrum.ieee.org/oct07/5552 Cracking Go, by Feng-hsiung
 Hsu, IEEE Spectrum magazine, October 2007.

 He claims it should be possible to build a Go machine stronger than
 any human player.

 Ian

Unless i missed something in this 4 pages article, there is nothing in it !
Just vague phrase, and assumption that brute force (ala deep blue) _may_ give 
a strong go machine.

I think classical, MC and UCT programmers have contributed much more to 
computer go than this respectable researcher.

Alain.

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread A van Kessel
 I think he is betting on null move proving - but I'm real skeptical that
 it will be effective in Computer Go.   It will indeed reduce the tree

IMHO null-move mixes badly with ko-tactics, effectively doubling
(or squaring ? ;-) the tree size.
It might be of some use in solving local sub-problems.

It still has the scent of alpha-beta-with-some-evaluation-function,
which is probably not the right paradigm for go.

We'll see.
AvK
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread terry mcintyre
- Original Message 
From: Don Dailey [EMAIL PROTECTED]

I think [Hsu] is betting on null move proving - but I'm real skeptical that
 it will be effective in Computer Go.   It will indeed reduce the tree
 significantly, but this comes at a qualitative price that is not so bad
 in Chess but is a lot in Go.



Hsu also discusses the gains from caching life-and-death analysis of groups. I 
suspect that
this will greatly reduce computational effort, once an efficient mechanism is 
implemented.
Existing monte carlo programs cache information about playable/non playable 
points; when
augmented with knowledge about life and death, search should more quickly home 
in on crucial 
lines of play.

I've been playing against Mogo the last few weeks. It has a very interesting 
style of play, and it 
often does quite well in tactical analysis, but sometimes it misses a key move 
and fails to kill or
fails to preserve a large group - game over! A good life-and-death cache would 
be a definite improvement.

Caching parts of trees works better in Go, since well-defined sections of the 
board can sometimes be 
partitioned from the rest of the board. Where such partitions leak, analysis is 
likely to be critical; 
for example, ladders and ladder breakers can extend across the board; invasions 
often depend on 
cutting points halfway across the board. 
 



   

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Don Dailey
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I don't believe null move pruning will be  effective in Go.  The basic
principle of null move pruning has been described in a couple of ways:

  1. threat analysis
  2. bounds checking.

It does both things - this is more about how to think about it.  In
bounds checking you are relying on the null move assumption which is
that it's always bad to give up a move.   This assumption is more true
in Go than it is in chess so that is one argument in favor of null move
pruning.

The null move test is to play 2 moves in a row for one side and consider
the result an upper bound.  (or conversely to consider the result a
lower bound for the other side.)

In order to be a reduction of effort, the null move is combined with a
reduced depth search.   That's where the trouble begins with Go.  More
about that in a second.

The other way to think about null move pruning is as a threat test.
If I am given 2 moves in a row and I still can't create any problems for
my opponent, the assumption is that I have no threats.   This is of
course combined with a depth reduction effort - the assumption being
that with 2 moves in a row, I should be able to create trouble even at a
reduced depth.   A dangerous assumption in GO!

Even in Chess null move pruning can be a problem.  It fails most
spectacularly in endings and in slow attacks.  A slow attack might be a
clever knight move, that puts the program one move closer to marching
the knight to a critical square on the other side of the board.   There
are direct threats, there are threats of threats, and threats of threats
of threats and so on.Null move pruning (with depth reduction) is
GREAT at finding the most direct threats, but cannot see more distant
threats.

Unfortunately,  Go is much like a chess endgame or a slow attack in this
regard.   A single seemingly innocent move is a powerful but very LONG
TERM threat from a finite and limited search point of view.   Null move
pruning with reductions would fail to consider these moves.

The scalable solution is recursive null move pruning, which will pick up
all threats eventually if you search deeply enough.   This will work in
GO, but I'm quite confident that you will need several extra ply of
depth to see the same tactics a brute force search would find - and the
extra speed is not enough to buy that back.   And this will be a very
common thing - not like in chess where it still happens, but is
relatively rare.

It's possible that it could made to work if the evaluation function is
really powerful about recognizing long term threat potential - it would
have to be really good at statically recognizing life and death as well
as being able to sense that life is in trouble.   However that's the
problem with are trying to solve - this kind of evaluation does not yet
exist.

- - Don




Don Dailey wrote:
 I know Hsu from my computer chess days.Of course most of us probably
 realize he was on the Deep Blue team.
 
 I think he is betting on null move proving - but I'm real skeptical that
 it will be effective in Computer Go.   It will indeed reduce the tree
 significantly, but this comes at a qualitative price that is not so bad
 in Chess but is a lot in Go.
 
 I would like to see that kind of hardware (which was described in the
 article) applied to 19x19 GO using UCT combined with more research on
 UCT, that could produce something that plays in the Dan range, although
 I'm very skeptical it will be in the high Dan range, certainly not the
 stronger than any human player.
 
 Having said that,  one must be very careful about making predictions,
 lest one ends up with egg on their face.  Computer chess started with
 wild optimism, then extreme pessimism then big surprise!  I clearly
 remember the days when it was ludicrous to imagine chess computers ever
 touching even the weak masters.  It was just not possible and a simple
 calculation on a paper napkin proved that it could never happen.  Woops!
  In those days you were considered an idealistic fool if you were
 optimistic but it turns out the optimistic ones were the most realistic
 and the ones who were objectively reasonable and pragmatic were the
 fools.
 
 I never did scaling experiments on 19x19 with UCT, but I have no reason
 to believe it would not show the same amazing scaling curve.   Lazarus
 is so weak at 19x19 that it would take a few doublings of speed to get
 competitive with reasonably good programs.
 
 Has anyone else done scaling experiments with 19x19 and UCT?
 
 - Don
 
 
 Ian Osgood wrote:
 Greetings,
 
 I noticed that the following link was recently added to the Computer Go
 Wikipedia article.
 
 http://www.spectrum.ieee.org/oct07/5552 Cracking Go, by Feng-hsiung Hsu,
 IEEE Spectrum magazine, October 2007.
 
 He claims it should be possible to build a Go machine stronger than any
 human player.
 
 Ian
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Don Dailey
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 It still has the scent of alpha-beta-with-some-evaluation-function,
 which is probably not the right paradigm for go.

No matter how you slice it, the problem is evaluation.  I'm a strong
believe in tree search,  but it must be combined with knowledge in the
right proportions.

UCT is a very clever tree search algorithm, very smart because it's
incredibly selective and yet it uses on the fly experience to simulate
GO knowledge.   I think it also happens to simulate how we humans play
better than even the pure knowledge and pattern approach.   Humans use
pattern knowledge at a low level and imagination at a high level and
good UCT implementations simulate this well in my opinion.

In my opinion, UCT is the best thing we have right now.  If UCT had not
been discovered, then Hsu's approach is perfectly reasonable and would
be the best known try although it would surely produce weak play.   But
I think he is capable of making a piece of hardware using alpha beta
that will beat the current best programs.

I have done experiments with patterns that suggest that it would be
possible to build a heavily pruned tree which could be used in a global
searcher using ordinary alpha beta pruning.   The amount of pruning
possible (in a reasonably fast way) is hard to determine, I never found
enough to make a global searcher very feasible in 19x19.   The idea is
to use patterns to find moves that have very low probability of being
playable.For a scalable alpha beta searcher the probability of being
playable would have to be considered by depth (prune more near leaf nodes.)

So I personally believe a feasible alpha/beta searcher is possible, if a
high quality evaluation function is combined with a highly selective
global search in a pragmatic way.One has to be very aggressive about
finding moves that can be thrown out and this is tough problem.  It's
not hard to find a few moves that can be pruned, but it's difficult to
eliminate the MAJORITY of moves without throwing out the baby with the
bathwater.

- - Don



 
 We'll see.
 AvK
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Phil G
 The null move test is to play 2 moves in a row for one side and consider
 the result an upper bound.  (or conversely to consider the result a
 lower bound for the other side.)


I take it that without a good evaluation function to distinguish the value of a 
move with other moves one or two ply down into the tree, especially in the 
early game, that null move prune is ineffective for pruning the tree. And 
worse, if the evaluation function is wrong.
 
Also, is it just me that a good evaluation function early in the game is 
difficult to write? 
 
On a slight different topic, for those of you with experience writing an 
evaluation function for an alpha-beta search, do you use the number of total 
moves played to weight different parts of the evaluation function? For example, 
it is easier towards the end of the game to know the certainly of certain 
points and use that as the evaluation function. But at the beginning of the 
game, an estimate of territory seems to be a better function (in light of not 
knowing the certain of any or few points). How do you merge these functions as 
the game transitions between middle game to end game? (and as different parts 
of the board are in various stages too).

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Jason House
On 10/2/07, Phil G [EMAIL PROTECTED] wrote:

 Also, is it just me that a good evaluation function early in the game is
 difficult to write?



I think it's doable.  It's just not trivial.  Simple pattern matching should
give a reasonable approximation for corner spats at the start of the game.
Feeding group safety into an overall evaluation should be able to give
tenuki plays.  Books on opening theory seem relatively straightforward.

I've neither coded it into my bot or mastered it in my play...  So it could
be tougher than I think it is ;)
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread terry mcintyre
From my conversations with dan-level players, analysis in the fuseki is not 
broad. They'll consider a handful of moves at any point - should I play in the 
open corner first, or respond to an approach move, or make my own approach 
move? Candidate moves are chosen from a small set of patterns - mostly 3rd and 
4th line plays. The evaluation function is approximate - do I have more 
influence and profit than my opponent or not?

Behind this higher-level analysis is an understanding of tactics - a good 
player knows not only that a particular play is joseki and another is not, but 
knows why; knows how to follow up to gain local advantage; how to give up a 
little to gain something more. If this sort of knowledge could be grafted 
together with the extensive search capabilities of computer programs, 
especially on the multicore architectures now becoming available, dan-level 
programs should be in reach.




   

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Ian Osgood


On Oct 2, 2007, at 10:33 AM, Phil G wrote:


On a slight different topic, for those of you with experience  
writing an evaluation function for an alpha-beta search, do you use  
the number of total moves played to weight different parts of the  
evaluation function? For example, it is easier towards the end of  
the game to know the certainly of certain points and use that as  
the evaluation function. But at the beginning of the game, an  
estimate of territory seems to be a better function (in light of  
not knowing the certain of any or few points). How do you merge  
these functions as the game transitions between middle game to end  
game? (and as different parts of the board are in various stages too).


Phil


This problem crops up in computer chess. The middlegame evaluation  
differs markedly from endgame evaluation. For example, in the former  
you wish to keep the king protected whereas in the endgame it becomes  
a mobile, active piece.  One technique is to perform both  
evaluations, then combine them continuously weighted on how much the  
current position is middle-game-like or endgame-like. For  
example, it could be a linear combination dependent on the amount of  
material left on the board. In Go, it could be some other measure of  
the progress of the game, such as stone density or move number. It is  
important that the evaluations be combined continuously instead of  
via a sudden cutoff or threshold, in order to avoid border effects.


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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Christoph Birk

Hsu wrote:
If we assume the top Go players calculate about as deeply as the top 
chess players do, the result should be a machine that plays Go as well 
as Deep Blue played chess.


I don't think this assumption holds.
A high level player reads 25-30 ply sequences (very low branching, but
not a ladder, of course).

Christoph
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Don Dailey
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I don't think he was talking about this kind of reading,  strong chess
players also  read in this sense.Especially in the end games where
you might envision then next 10 moves or more (which is 20 ply or more.)

It's harder to do in chess (because the pieces don't always stay put),
but it's still done quite a bit.


- - Don



Christoph Birk wrote:
 Hsu wrote:
 If we assume the top Go players calculate about as deeply as the top
 chess players do, the result should be a machine that plays Go as well
 as Deep Blue played chess.
 
 I don't think this assumption holds.
 A high level player reads 25-30 ply sequences (very low branching, but
 not a ladder, of course).
 
 Christoph
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Christoph Birk

On Tue, 2 Oct 2007, Don Dailey wrote:

I don't think he was talking about this kind of reading,  strong chess
players also  read in this sense.


What other kind of reading is there? I was am talking about the
common term (in Go and Chess) reading ahead.


It's harder to do in chess (because the pieces don't always stay put),
but it's still done quite a bit.


Yes it is ... that's why humans cannot read as deep in Chess as they
can in Go. That's my point.

Christoph

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Don Dailey
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He wasn't talking about reading at all.   I was being nice when I said
he wasn't talking about that kind of reading - giving you the benefit of
the doubt.

- - Don


Christoph Birk wrote:
 On Tue, 2 Oct 2007, Don Dailey wrote:
 I don't think he was talking about this kind of reading,  strong chess
 players also  read in this sense.
 
 What other kind of reading is there? I was am talking about the
 common term (in Go and Chess) reading ahead.
 
 It's harder to do in chess (because the pieces don't always stay put),
 but it's still done quite a bit.
 
 Yes it is ... that's why humans cannot read as deep in Chess as they
 can in Go. That's my point.
 
 Christoph
 
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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Heikki Levanto
On Tue, Oct 02, 2007 at 12:27:28PM -0400, Don Dailey wrote:
 I don't believe null move pruning will be  effective in Go.  The basic
 principle of null move pruning has been described in a couple of ways:
 
   1. threat analysis
   2. bounds checking.

In go terms, doesn't that translate to something like understanding sente?
And to the problems of local sente vs. global sente?

-H

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Heikki Levanto
On Tue, Oct 02, 2007 at 06:02:53PM +0200, Alain Baeckeroot wrote:
 Unless i missed something in this 4 pages article, there is nothing in it !
 Just vague phrase, and assumption that brute force (ala deep blue) _may_ give 
 a strong go machine.
 
 I think classical, MC and UCT programmers have contributed much more to 
 computer go than this respectable researcher.

I wouldn't put it as strongly, but I also noticed that MC and UCT and suclike
techniques were not mentioned at all.

I am not sure how that affects the predictions. On one hand, the article
seems overly optimistic, but on the other hand, it does not consider the
latest techniques that have shown some real promise, indicating that it may
be underestimating the future programs... Maybe there are other inventions
coming up in the near future that make the optimism more justified? 

-H



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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Heikki Levanto
On Tue, Oct 02, 2007 at 10:33:09AM -0700, Phil G wrote:
 Also, is it just me that a good evaluation function early in the game is
 difficult to write? 

No, it is not you. The rest of people can be divided in two groups. Some
believe such a function is easy to write. Let them come forth and show their
results! The rest of us believe such a function is (almost?) impossible to
write.

-H

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread steve uurtamo
 I wouldn't put it as strongly, but I also noticed that MC and UCT and suclike
 techniques were not mentioned at all.

to be fair to the article, in fact they were.  you just have to click on all of 
the
links in the article to see it.

s.





   

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Darren Cook
 I wouldn't put it as strongly, but I also noticed that MC and UCT and suclike
 techniques were not mentioned at all.
 
 to be fair to the article, in fact they were.  you just have to click on all 
 of the
 links in the article to see it.

For others, like me, who missed the link, it is here:
  http://www.spectrum.ieee.org/oct07/5552/monte

But this is just talking about monte carlo; no mention of UCT, which (as
Don said earlier in this thread) is the best (global) search algorithm
we have right now, and it would be dangerous to ignore it.

Darren

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread steve uurtamo
 For others, like me, who missed the link, it is here:
   http://www.spectrum.ieee.org/oct07/5552/monte

 But this is just talking about monte carlo; no mention of UCT, which (as
 Don said earlier in this thread) is the best (global) search algorithm
 we have right now, and it would be dangerous to ignore it.

actually, direct search is better, for instance, on 3x3 boards.

the relevant issue is 19x19 boards.

s.





  

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Re: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread Don Dailey
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Christoph Birk wrote:
 On Tue, 2 Oct 2007, Don Dailey wrote:
 He wasn't talking about reading at all.   I was being nice when I said
 he wasn't talking about that kind of reading - giving you the benefit of
 the doubt.
 
 Please explain what he meant by calculating about as deeply.


Hsu thinks in terms of chess programming and from the article he was
comparing the depth of the search of Chess to Go,  trying to make a case
that with modern hardware you would be able to search to the same depths
that Deep Blue used to search in chess.So a chess search normally
iterates until it runs out of time - searching 1 ply, then 2, then 3 etc.

So when he says as deeply he means that if Deep blue did a 12 ply
search (for instance) he thought a Go program might manage a 12 ply
search (I disagree, but that's beside the point.)

Of course 12 ply doesn't really mean exactly 12 ply - it means a highly
selective search where you might look up to 20 or 30 ply with extensions
and quiescence.I'm using 12 ply as an example, I don't know how deep
Deep Blue actually searched.

In Chess it is very common for good players to look very deeply in
tactical situations and endgames.  There is nothing special about
searching this deeply in chess, it's done in most 2 player games of
perfect information and of course in Go it's called reading.

- - Don




 Thank you,
 Christoph
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RE: [computer-go] IEEE Spectrum article by Deep Blue creator

2007-10-02 Thread David Fotland
Many Faces does not use null move, but does extensive caching of life and
death and other tactical results.

-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of terry mcintyre
Sent: Tuesday, October 02, 2007 9:21 AM
To: computer-go
Subject: Re: [computer-go] IEEE Spectrum article by Deep Blue creator


- Original Message 

From: Don Dailey [EMAIL PROTECTED]


I think [Hsu] is betting on null move proving - but I'm real skeptical that
 it will be effective in Computer Go.   It will indeed reduce the tree
 significantly, but this comes at a qualitative price that is not so bad
 in Chess but is a lot in Go.


Hsu also discusses the gains from caching life-and-death analysis of groups.
I suspect that
this will greatly reduce computational effort, once an efficient mechanism
is implemented.
Existing monte carlo programs cache information about playable/non playable
points; when
augmented with knowledge about life and death, search should more quickly
home in on crucial 
lines of play.

I've been playing against Mogo the last few weeks. It has a very interesting
style of play, and it 
often does quite well in tactical analysis, but sometimes it misses a key
move and fails to kill or
fails to preserve a large group - game over! A good life-and-death cache
would be a definite improvement.

Caching parts of trees works better in Go, since well-defined sections of
the board can sometimes be 
partitioned from the rest of the board. Where such partitions leak, analysis
is likely to be critical; 
for example, ladders and ladder breakers can extend across the board;
invasions often depend on 
cutting points halfway across the board. 


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