Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Rémi Coulom

Ingo Althöfer wrote:

Hello all, two questions.

(i) Do there exist strong 9x9-go programs on Monte-Carlo base
for Japanese rules?

(ii) Having available only programs for Chinese rules, but playing
in a tournament with Japanese rules, which special tricks and
settings should be used to maximise winning chances? (This is meant
especially in the light of MC's tendency to win games by 0.5
points according to the rules implemented.)

Ingo.
  

Hi Ingo,

The standard trick is to pass as soon as your opponent passes. For this 
to work, you need to take a one-point security margin with the komi. You 
should also score seki the Japanese way.


That is how Crazy Stone played the UEC Cup and the matches at FIT2008. 
In fact, for the UEC cup, Crazy Stone did not understand seki, so I took 
a bigger security margin with the komi. But a bigger security margin is 
not good for 9x9.


Rémi
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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Don Dailey
On Thu, 2008-11-06 at 09:19 +0100, Ingo Althöfer wrote:
 Hello all, two questions.
 
 (i) Do there exist strong 9x9-go programs on Monte-Carlo base
 for Japanese rules?
 
 (ii) Having available only programs for Chinese rules, but playing
 in a tournament with Japanese rules, which special tricks and
 settings should be used to maximise winning chances? (This is meant
 especially in the light of MC's tendency to win games by 0.5
 points according to the rules implemented.)

I've thought about those questions myself from time to time.  Let me
think out loud concerning this.   I am by know means an expert in
Japanese scoring or even GO in general, so I'm just giving some thoughts
here and a plan for building a Japanese simple bot that you can be
free to criticize:

It seems to me the primary difference between the two is knowing when to
stop playing and of course scoring dead groups.   The Chinese style bots
do not technically need to know about scoring.  

You can look at the combined statistics at the end of the games for a
given point to get a sense of whether that point is still in play or
whether it's a forgone conclusion.  You can do the same to determine
dead groups.   I don't know how well that works in all cases, but I have
used it and it works pretty well.  

But we also want to recognize dame,  and not play to dame points early
in the game even if it doesn't affect the final Chinese outcome.   So
here is my idea:

  1. If ALL the stones of a particular group belong to the opponent with
high certainty,  they are dead.   

  2. If there are open spaces that belong to you or the opponent with
high certainty don't move to them.   

  3. If an uncertain point is touching stones of both colors and both
colors have high certainty for the color they belong to, it is probably
dame and you shouldn't move to them.   

example:   White has a stone on d4 that is clearly alive.
   Black has a stone on f4 that is clearly alive.  
   An empty point on e4 is highly uncertain.   
   Do not play to e4 - it is probably dame.

   question:  Is that a reasonably good rule or does it need some work?
 

  4. If you have no moves other than these cases, you should pass.   

You can test this idea by playing a bot on KGS under Japanese rules.
You may have to tweak what you consider your uncertainty margin.   Also,
I'm not considering seki here but we would want to find a way to cope
with that. 

- Don



 Ingo.


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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Jason House
I think simplistic handling of Japanese rules should play dame points  
that connect chains. This avoids some problems that can arise where  
ownership probability drops after the opponent plays the dame, and a  
point of territory must get filled.


Even if not technically required, I can imagine bots acting like  
beginners and get nervous over imagined vulnerabilites.


Sent from my iPhone

On Nov 6, 2008, at 9:12 AM, Don Dailey [EMAIL PROTECTED] wrote:


On Thu, 2008-11-06 at 09:19 +0100, Ingo Althöfer wrote:

Hello all, two questions.

(i) Do there exist strong 9x9-go programs on Monte-Carlo base
for Japanese rules?

(ii) Having available only programs for Chinese rules, but playing
in a tournament with Japanese rules, which special tricks and
settings should be used to maximise winning chances? (This is meant
especially in the light of MC's tendency to win games by 0.5
points according to the rules implemented.)


I've thought about those questions myself from time to time.  Let me
think out loud concerning this.   I am by know means an expert in
Japanese scoring or even GO in general, so I'm just giving some  
thoughts

here and a plan for building a Japanese simple bot that you can be
free to criticize:

It seems to me the primary difference between the two is knowing  
when to
stop playing and of course scoring dead groups.   The Chinese style  
bots

do not technically need to know about scoring.

You can look at the combined statistics at the end of the games for a
given point to get a sense of whether that point is still in play or
whether it's a forgone conclusion.  You can do the same to determine
dead groups.   I don't know how well that works in all cases, but I  
have

used it and it works pretty well.

But we also want to recognize dame,  and not play to dame points early
in the game even if it doesn't affect the final Chinese outcome.   So
here is my idea:

 1. If ALL the stones of a particular group belong to the opponent  
with

high certainty,  they are dead.

 2. If there are open spaces that belong to you or the opponent with
high certainty don't move to them.

 3. If an uncertain point is touching stones of both colors and both
colors have high certainty for the color they belong to, it is  
probably

dame and you shouldn't move to them.

   example:   White has a stone on d4 that is clearly alive.
  Black has a stone on f4 that is clearly alive.
  An empty point on e4 is highly uncertain.
  Do not play to e4 - it is probably dame.

  question:  Is that a reasonably good rule or does it need some work?


 4. If you have no moves other than these cases, you should pass.

You can test this idea by playing a bot on KGS under Japanese rules.
You may have to tweak what you consider your uncertainty margin.
Also,

I'm not considering seki here but we would want to find a way to cope
with that.

- Don




Ingo.

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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Don Dailey
On Thu, 2008-11-06 at 10:44 -0500, Jason House wrote:
 I think simplistic handling of Japanese rules should play dame
 points  
 that connect chains. This avoids some problems that can arise where  
 ownership probability drops after the opponent plays the dame, and a  
 point of territory must get filled.

I'm trying to think of a counter example where my rule will not work.
Of course this has to be understood within the context of the playing
strength of the bot itself, so we don't expect extremely sophisticated
handling of special cases.  

In my example, both black and white have clearly live stones and there
is an empty point touching both of them.  Assuming that the map is
correct of course and both groups are alive,  then I suppose a
connecting move could cause a weaker group to live.   So that suggests
another rule -  in addition to the original condition of at least 1
white and black live group touching,  there should be no connections to
a group that is not alive.  

A group that is alive passes some thresehold of certainty.
Otherwise, it is not-alive but not dead.   The threshold might be
something like 90 - 95% or something but some experimentation would be
required to find a good value for this.

- Don


 
 Even if not technically required, I can imagine bots acting like  
 beginners and get nervous over imagined vulnerabilites.


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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Erik van der Werf
IIRC under official Japanese rules at the end of the game all groups
with liberties shared between opposing colours are by definition in
seki. Therefore eventually (before counting) all dame have to be
filled.

Further, playing dame points is almost equally bad under Chinese rules
as it is under Japanese rules. So, if you have a strong 'Chinese'
engine no special tricks are needed at least until you reach the
endgame. The only thing that is severely penalized under Japanese
rules is playing needless defensive moves inside your own territory
while the opponent is passing.

Erik



On Thu, Nov 6, 2008 at 4:44 PM, Jason House [EMAIL PROTECTED] wrote:
 I think simplistic handling of Japanese rules should play dame points that
 connect chains. This avoids some problems that can arise where ownership
 probability drops after the opponent plays the dame, and a point of
 territory must get filled.

 Even if not technically required, I can imagine bots acting like beginners
 and get nervous over imagined vulnerabilites.

 Sent from my iPhone

 On Nov 6, 2008, at 9:12 AM, Don Dailey [EMAIL PROTECTED] wrote:

 On Thu, 2008-11-06 at 09:19 +0100, Ingo Althöfer wrote:

 Hello all, two questions.

 (i) Do there exist strong 9x9-go programs on Monte-Carlo base
 for Japanese rules?

 (ii) Having available only programs for Chinese rules, but playing
 in a tournament with Japanese rules, which special tricks and
 settings should be used to maximise winning chances? (This is meant
 especially in the light of MC's tendency to win games by 0.5
 points according to the rules implemented.)

 I've thought about those questions myself from time to time.  Let me
 think out loud concerning this.   I am by know means an expert in
 Japanese scoring or even GO in general, so I'm just giving some thoughts
 here and a plan for building a Japanese simple bot that you can be
 free to criticize:

 It seems to me the primary difference between the two is knowing when to
 stop playing and of course scoring dead groups.   The Chinese style bots
 do not technically need to know about scoring.

 You can look at the combined statistics at the end of the games for a
 given point to get a sense of whether that point is still in play or
 whether it's a forgone conclusion.  You can do the same to determine
 dead groups.   I don't know how well that works in all cases, but I have
 used it and it works pretty well.

 But we also want to recognize dame,  and not play to dame points early
 in the game even if it doesn't affect the final Chinese outcome.   So
 here is my idea:

  1. If ALL the stones of a particular group belong to the opponent with
 high certainty,  they are dead.

  2. If there are open spaces that belong to you or the opponent with
 high certainty don't move to them.

  3. If an uncertain point is touching stones of both colors and both
 colors have high certainty for the color they belong to, it is probably
 dame and you shouldn't move to them.

   example:   White has a stone on d4 that is clearly alive.
  Black has a stone on f4 that is clearly alive.
  An empty point on e4 is highly uncertain.
  Do not play to e4 - it is probably dame.

  question:  Is that a reasonably good rule or does it need some work?


  4. If you have no moves other than these cases, you should pass.

 You can test this idea by playing a bot on KGS under Japanese rules.
 You may have to tweak what you consider your uncertainty margin.   Also,
 I'm not considering seki here but we would want to find a way to cope
 with that.

 - Don



 Ingo.

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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Mark Boon
Although what Don writes is all correct, I understood the question to  
be rather different. It's not a matter of being able to determine the  
right score at the end or the right way to play, it's a matter of  
determining the right score after each playout. For performance  
reasons MC programs will cut corners there which could be taken  
advantage of when playing by Japanese rules because the after the  
playout it is prone to getting the wrong score in certain situations.


Mark

On 6-nov-08, at 12:12, Don Dailey wrote:


On Thu, 2008-11-06 at 09:19 +0100, Ingo Althöfer wrote:

Hello all, two questions.

(i) Do there exist strong 9x9-go programs on Monte-Carlo base
for Japanese rules?

(ii) Having available only programs for Chinese rules, but playing
in a tournament with Japanese rules, which special tricks and
settings should be used to maximise winning chances? (This is meant
especially in the light of MC's tendency to win games by 0.5
points according to the rules implemented.)


I've thought about those questions myself from time to time.  Let me
think out loud concerning this.   I am by know means an expert in
Japanese scoring or even GO in general, so I'm just giving some  
thoughts

here and a plan for building a Japanese simple bot that you can be
free to criticize:

It seems to me the primary difference between the two is knowing  
when to
stop playing and of course scoring dead groups.   The Chinese style  
bots

do not technically need to know about scoring.

You can look at the combined statistics at the end of the games for a
given point to get a sense of whether that point is still in play or
whether it's a forgone conclusion.  You can do the same to determine
dead groups.   I don't know how well that works in all cases, but I  
have

used it and it works pretty well.

But we also want to recognize dame,  and not play to dame points early
in the game even if it doesn't affect the final Chinese outcome.   So
here is my idea:

  1. If ALL the stones of a particular group belong to the opponent  
with

high certainty,  they are dead.

  2. If there are open spaces that belong to you or the opponent with
high certainty don't move to them.

  3. If an uncertain point is touching stones of both colors and both
colors have high certainty for the color they belong to, it is  
probably

dame and you shouldn't move to them.

example:   White has a stone on d4 that is clearly alive.
   Black has a stone on f4 that is clearly alive.
   An empty point on e4 is highly uncertain.
   Do not play to e4 - it is probably dame.

   question:  Is that a reasonably good rule or does it need some  
work?



  4. If you have no moves other than these cases, you should pass.

You can test this idea by playing a bot on KGS under Japanese rules.
You may have to tweak what you consider your uncertainty margin.
Also,

I'm not considering seki here but we would want to find a way to cope
with that.

- Don




Ingo.

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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Don Dailey
On Thu, 2008-11-06 at 17:10 +0100, Erik van der Werf wrote:
 IIRC under official Japanese rules at the end of the game all groups
 with liberties shared between opposing colours are by definition in
 seki. Therefore eventually (before counting) all dame have to be
 filled.
 
 Further, playing dame points is almost equally bad under Chinese rules
 as it is under Japanese rules. So, if you have a strong 'Chinese'
 engine no special tricks are needed at least until you reach the
 endgame. The only thing that is severely penalized under Japanese
 rules is playing needless defensive moves inside your own territory
 while the opponent is passing.

The dame rule I assumed was needed for an MC bot playing because of the
way MC bots play badly when winning or losing. The idea was to
focus on what fights were left on the board so that you don't lose due
to a Japanese technicality.

But it's now not clear to me that my rule would fix that.   Maybe it
should be left out.I'm also not sure how my rule would affect seki
positions. 
   

- Don

 


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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Jason House

On Nov 6, 2008, at 11:09 AM, Don Dailey [EMAIL PROTECTED] wrote:


On Thu, 2008-11-06 at 10:44 -0500, Jason House wrote:

I think simplistic handling of Japanese rules should play dame
points
that connect chains. This avoids some problems that can arise where
ownership probability drops after the opponent plays the dame, and a
point of territory must get filled.


I'm trying to think of a counter example where my rule will not work.
Of course this has to be understood within the context of the playing
strength of the bot itself, so we don't expect extremely sophisticated
handling of special cases.


Consider a miai to connect a chain with two liberties. It's easy to  
get the ownership correct in all heavy playouts. If one of the two  
miai points is dame, your rule would say not to play it. If the  
opponent plays there, the chain ends up in atari...








In my example, both black and white have clearly live stones and there
is an empty point touching both of them.  Assuming that the map is
correct of course and both groups are alive,  then I suppose a
connecting move could cause a weaker group to live.   So that suggests
another rule -  in addition to the original condition of at least 1
white and black live group touching,  there should be no connections  
to

a group that is not alive.

A group that is alive passes some thresehold of certainty.
Otherwise, it is not-alive but not dead.   The threshold might be
something like 90 - 95% or something but some experimentation would be
required to find a good value for this.

- Don




Even if not technically required, I can imagine bots acting like
beginners and get nervous over imagined vulnerabilites.

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RE: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread David Fotland
Many Faces of Go's Monte Carlo engine plays strongly using Japanese rules.
It's required for sales in American and japan (as AI Igo).  I don't use
Remi's trick, since there are sometimes points remaining when your opponent
passes when playing against weaker players.

David

 -Original Message-
 From: [EMAIL PROTECTED] [mailto:computer-go-
 [EMAIL PROTECTED] On Behalf Of Rémi Coulom
 Sent: Thursday, November 06, 2008 1:02 AM
 To: computer-go
 Subject: Re: [computer-go] Monte-Carlo and Japanese rules
 
 Ingo Althöfer wrote:
  Hello all, two questions.
 
  (i) Do there exist strong 9x9-go programs on Monte-Carlo base
  for Japanese rules?
 
  (ii) Having available only programs for Chinese rules, but playing
  in a tournament with Japanese rules, which special tricks and
  settings should be used to maximise winning chances? (This is meant
  especially in the light of MC's tendency to win games by 0.5
  points according to the rules implemented.)
 
  Ingo.
 
 Hi Ingo,
 
 The standard trick is to pass as soon as your opponent passes. For this
 to work, you need to take a one-point security margin with the komi. You
 should also score seki the Japanese way.
 
 That is how Crazy Stone played the UEC Cup and the matches at FIT2008.
 In fact, for the UEC cup, Crazy Stone did not understand seki, so I took
 a bigger security margin with the komi. But a bigger security margin is
 not good for 9x9.
 
 Rémi
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RE: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread dave.devos
What if the playout uses the AGA rule of paying 1 point for a pass and 
requiring white to pass last (so the game does not end by two passes if black 
plays the second pass).
Wouldn't the score then be equivalent to the japanese score?
 
Dave



Van: [EMAIL PROTECTED] namens Mark Boon
Verzonden: do 6-11-2008 17:11
Aan: computer-go
Onderwerp: Re: [computer-go] Monte-Carlo and Japanese rules



Although what Don writes is all correct, I understood the question to 
be rather different. It's not a matter of being able to determine the 
right score at the end or the right way to play, it's a matter of 
determining the right score after each playout. For performance 
reasons MC programs will cut corners there which could be taken 
advantage of when playing by Japanese rules because the after the 
playout it is prone to getting the wrong score in certain situations.

Mark

On 6-nov-08, at 12:12, Don Dailey wrote:

 On Thu, 2008-11-06 at 09:19 +0100, Ingo Althöfer wrote:
 Hello all, two questions.

 (i) Do there exist strong 9x9-go programs on Monte-Carlo base
 for Japanese rules?

 (ii) Having available only programs for Chinese rules, but playing
 in a tournament with Japanese rules, which special tricks and
 settings should be used to maximise winning chances? (This is meant
 especially in the light of MC's tendency to win games by 0.5
 points according to the rules implemented.)

 I've thought about those questions myself from time to time.  Let me
 think out loud concerning this.   I am by know means an expert in
 Japanese scoring or even GO in general, so I'm just giving some 
 thoughts
 here and a plan for building a Japanese simple bot that you can be
 free to criticize:

 It seems to me the primary difference between the two is knowing 
 when to
 stop playing and of course scoring dead groups.   The Chinese style 
 bots
 do not technically need to know about scoring.

 You can look at the combined statistics at the end of the games for a
 given point to get a sense of whether that point is still in play or
 whether it's a forgone conclusion.  You can do the same to determine
 dead groups.   I don't know how well that works in all cases, but I 
 have
 used it and it works pretty well.

 But we also want to recognize dame,  and not play to dame points early
 in the game even if it doesn't affect the final Chinese outcome.   So
 here is my idea:

   1. If ALL the stones of a particular group belong to the opponent 
 with
 high certainty,  they are dead.

   2. If there are open spaces that belong to you or the opponent with
 high certainty don't move to them.

   3. If an uncertain point is touching stones of both colors and both
 colors have high certainty for the color they belong to, it is 
 probably
 dame and you shouldn't move to them.

 example:   White has a stone on d4 that is clearly alive.
Black has a stone on f4 that is clearly alive.
An empty point on e4 is highly uncertain.
Do not play to e4 - it is probably dame.

question:  Is that a reasonably good rule or does it need some 
 work?


   4. If you have no moves other than these cases, you should pass.

 You can test this idea by playing a bot on KGS under Japanese rules.
 You may have to tweak what you consider your uncertainty margin.   
 Also,
 I'm not considering seki here but we would want to find a way to cope
 with that.

 - Don



 Ingo.
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RE: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread dave.devos
And of course black should pay 1 point for each extra handicap stone. 
http://www.britgo.org/rules/compare.html#coun
 
Dave



Van: [EMAIL PROTECTED] namens [EMAIL PROTECTED]
Verzonden: do 6-11-2008 19:28
Aan: computer-go
Onderwerp: RE: [computer-go] Monte-Carlo and Japanese rules


What if the playout uses the AGA rule of paying 1 point for a pass and 
requiring white to pass last (so the game does not end by two passes if black 
plays the second pass).
Wouldn't the score then be equivalent to the japanese score?
 
Dave



Van: [EMAIL PROTECTED] namens Mark Boon
Verzonden: do 6-11-2008 17:11
Aan: computer-go
Onderwerp: Re: [computer-go] Monte-Carlo and Japanese rules



Although what Don writes is all correct, I understood the question to 
be rather different. It's not a matter of being able to determine the 
right score at the end or the right way to play, it's a matter of 
determining the right score after each playout. For performance 
reasons MC programs will cut corners there which could be taken 
advantage of when playing by Japanese rules because the after the 
playout it is prone to getting the wrong score in certain situations.

Mark

On 6-nov-08, at 12:12, Don Dailey wrote:

 On Thu, 2008-11-06 at 09:19 +0100, Ingo Althöfer wrote:
 Hello all, two questions.

 (i) Do there exist strong 9x9-go programs on Monte-Carlo base
 for Japanese rules?

 (ii) Having available only programs for Chinese rules, but playing
 in a tournament with Japanese rules, which special tricks and
 settings should be used to maximise winning chances? (This is meant
 especially in the light of MC's tendency to win games by 0.5
 points according to the rules implemented.)

 I've thought about those questions myself from time to time.  Let me
 think out loud concerning this.   I am by know means an expert in
 Japanese scoring or even GO in general, so I'm just giving some 
 thoughts
 here and a plan for building a Japanese simple bot that you can be
 free to criticize:

 It seems to me the primary difference between the two is knowing 
 when to
 stop playing and of course scoring dead groups.   The Chinese style 
 bots
 do not technically need to know about scoring.

 You can look at the combined statistics at the end of the games for a
 given point to get a sense of whether that point is still in play or
 whether it's a forgone conclusion.  You can do the same to determine
 dead groups.   I don't know how well that works in all cases, but I 
 have
 used it and it works pretty well.

 But we also want to recognize dame,  and not play to dame points early
 in the game even if it doesn't affect the final Chinese outcome.   So
 here is my idea:

   1. If ALL the stones of a particular group belong to the opponent 
 with
 high certainty,  they are dead.

   2. If there are open spaces that belong to you or the opponent with
 high certainty don't move to them.

   3. If an uncertain point is touching stones of both colors and both
 colors have high certainty for the color they belong to, it is 
 probably
 dame and you shouldn't move to them.

 example:   White has a stone on d4 that is clearly alive.
Black has a stone on f4 that is clearly alive.
An empty point on e4 is highly uncertain.
Do not play to e4 - it is probably dame.

question:  Is that a reasonably good rule or does it need some 
 work?


   4. If you have no moves other than these cases, you should pass.

 You can test this idea by playing a bot on KGS under Japanese rules.
 You may have to tweak what you consider your uncertainty margin.   
 Also,
 I'm not considering seki here but we would want to find a way to cope
 with that.

 - Don



 Ingo.
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RE: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Jeff Nowakowski
On Thu, 2008-11-06 at 09:43 -0800, David Fotland wrote:
 Many Faces of Go's Monte Carlo engine plays strongly using Japanese rules.

So what do you do in the playouts?  Do you score with area or territory?
Does your program play optimally where different rules would result in
different winner?

-Jeff

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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Michael Williams

I'm sure he meant, Does your program play optimally in trivial situations where 
different rules would result in a different winner?

I'm not sure if your last answer also applies to that, more specific question.


David Fotland wrote:

I score with area, and adjust for Japanese rules.  It doesn't play optimally
under and rule set :)

David


-Original Message-
From: [EMAIL PROTECTED] [mailto:computer-go-
[EMAIL PROTECTED] On Behalf Of Jeff Nowakowski
Sent: Thursday, November 06, 2008 11:57 AM
To: computer-go
Subject: RE: [computer-go] Monte-Carlo and Japanese rules

On Thu, 2008-11-06 at 09:43 -0800, David Fotland wrote:

Many Faces of Go's Monte Carlo engine plays strongly using Japanese

rules.

So what do you do in the playouts?  Do you score with area or territory?
Does your program play optimally where different rules would result in
different winner?

-Jeff

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Re: [computer-go] Monte-Carlo and Japanese rules

2008-11-06 Thread Darren Cook
 (ii) Having available only programs for Chinese rules, but playing
 in a tournament with Japanese rules, which special tricks and
 settings should be used to maximise winning chances? (This is meant
 especially in the light of MC's tendency to win games by 0.5
 points according to the rules implemented.)

The difference I've noticed most in analyzing strong 9x9 games (in
Japanese rules using a bot playing in Chinese rules) is a half-point ko
at the end of the game.

In Chinese rules, once all the dame have been filled in, if one side has
no ko threats he has to pass, and the opponent fills the ko and gets an
extra point. In Japanese rules passing does not cost anything. So the
score ends up one point different. In these games what tends to happen
is the Chinese-rule-monte-carlo bot, playing for its 0.5pt win, ends up
choosing the wrong move 20 moves from the end of the game.

If that is as clear as mud let me know and I'll try to hunt up an
example game.

Darren

-- 
Darren Cook, Software Researcher/Developer
http://dcook.org/mlsn/ (English-Japanese-German-Chinese-Arabic
open source dictionary/semantic network)
http://dcook.org/work/ (About me and my work)
http://dcook.org/blogs.html (My blogs and articles)
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