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 Post subject: Re: This 'n' that
Post #21 Posted: Fri Oct 09, 2015 2:03 pm 
Honinbo

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tiger314 wrote:
Bill Spight wrote:
My impression is that most go tournaments in the West use area scoring, and most tournament players are aware that eliminating dame before winning a ko is advantageous.

As far as I know, with the exception of Britain, France and the Congress, Europe still uses territory scoring for the majority of tournaments. This does create areas where half the tournaments around are area scored and half are territory scored. Poor people living there have to learn the endgame twice :cry: .


Thanks for the info. :)

End of game procedures may differ for different rule sets, but with some exceptions, correct play by territory scoring is also correct by area scoring. :)

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 Post subject: Re: This 'n' that
Post #22 Posted: Sun Oct 11, 2015 1:10 pm 
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Problems with my theory. The environment.

As I said, I considered part of the environment part of the ko ensemble. For instance, if the environment consists of a number of simple gote with swing values G0 ≥ G1 ≥ G2 ≥ . . . , in deciding whether to take or win a ko I might compare G0 with K - Gn + Gn+1 - Gn+2 + . . . , where K is the swing value of the ko, and the value of n depended on the ko threat situation. In my mind G0 was the swing value of the largest play on the board besides the ko, and therefore K - Gn + . . . was the swing value of the ko ensemble. Kos did not have values independent of the rest of the board.

There is nothing particularly wrong with this theory. After all, it led me to an understanding of komonster. :) But it is unwieldy in practice. How deeply do you look into the environment? 8 moves? 10 moves? (This is related to the famous magic number 7, plus or minus 2 that John Fairbairn often brings up. :)) As a practical matter, at some point you have to stop. (The fact that the environment does not just consist of simple gote is another matter.)

You can estimate the value of Gn - Gn+1 + Gn+2 - . . . by (Gn)/2. So we can decide whether to take or win the ko or not by comparing G0 with K - (Gn)/2, or with K - Gn + (Gn+1)/2, etc. Which estimate we use is up to us. OC, if the difference between Gn and Gn+1 is significant, then we should not use (Gn)/2, as it will probably be an overestimate.

Another problem I discovered with this framework is that it makes the analysis of approach kos difficult.

Fast forward to 1994, when I attended a talk by Professor Berlekamp in which he presented the idea of komaster (which he had developed in the '90s). The komaster is able to win the ko, but is not komonster. After the talk I sent him a note about komonster effects (without using the term) and suggesting a possible modification of his methods. By using the idea of komaster, however, Berlekamp had been able to evaluate approach kos and 10,000 year kos.

The methodology used by Berlekamp, called thermography, utilizes the concept of temperature, or a tax on making a play. For non-ko positions it gets the same results as traditional go evaluation, and also provides additional information. My theory departed from traditional go evaluation, so that is a plus for thermography. :)

It turns out that thermography can be adapted to my approach. For instance, if we decide to stop the analysis at Gn and use (Gn)/2, just set the temperature, t, to (Gn)/2 and treat the larger gote as hot plays. Thus, where my theory says to win the ko if K > G0 + (G2)/2, change that to K > G0 + t. :) This means that G0 is no longer considered part of the environment. The environment consists of G2 and smaller plays. It is a kind of foreground/background distinction.

In 1998 I used the idea of an environment with temperature to redefine thermography and extend it to the evaluation of multiple kos and superkos. :D

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

My two main guides in life:
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Everything with love. Stay safe.

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 Post subject: Re: This 'n' that
Post #23 Posted: Mon Oct 12, 2015 3:54 am 
Dies with sente

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Bill Spight wrote:
I started writing a book about it in 1989 ...
The original position is worth 0.75 for White ...
In 1998 I used the idea of an environment with temperature to redefine thermography and extend it to the evaluation of multiple kos and superkos.

ONAG is nice and precise. "Winning Ways" is funny and handwaving. "Mathematical Go" is not a pleasure to read for a mathematician. It starts saying too much before giving definitions. I wouldnt mind a current book that is precise.

Your posts are unreadable for me since the background is missing. "Worth 0.75" - in which valuation system?

ONAG describes the disjunctive sum. But the existence of kos means that go positions do not neatly decompose as disjunctive sums. Is there a mathematically precise definition of thermography that applies to go?

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 Post subject: Re: This 'n' that
Post #24 Posted: Mon Oct 12, 2015 9:31 am 
Honinbo

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vier wrote:
Your posts are unreadable for me since the background is missing. "Worth 0.75" - in which valuation system?

Click Here To Show Diagram Code
[go]$$B AGA rules.
$$ -------------------
$$ | . # O C C C O O O |
$$ | X O O C O O O X X |
$$ | X X O C O X X X C |
$$ | C X O O . b a X C |
$$ | C X . . X X X X C |
$$ | C X O O O O O X C |
$$ | X O O B B O X W . |
$$ | X X O C O O X X X |
$$ | C X . . C O O O . |
$$ -------------------[/go]


Because the number of Black stones and White stones on the board are equal, the area count and territory count are the same, even if the value for individual points may differ. For convenience and the familiarity of the readers I will use the territory count. The marked points and circled stones indicate territory. Black has 10 points, White has 11. Using probabilistic semantics we can evaluate point “a” as 0.75 point for Black and “b” as 0.5 point. Adding those to the rest of Black’s territory yields 11.25. The ko stone in the top left corner is usually valued as 1/3 point for White. By komonster analysis its value is 1 point for White, which gives White 12 points for a net value of 0.75 for White.

Why is the ko worth 1 point for White? Again, using probabilistic semantics, half the time Black will fill the ko for 0 points of territory, and half the time White will win the ko, as in the next diagram.

Click Here To Show Diagram Code
[go]$$B AGA rules.
$$ -------------------
$$ | W C O . . . O O O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |
$$ | . X O O . . . X . |
$$ | . X . . X X X X . |
$$ | . X O O O O O X . |
$$ | X O O X X O X O . |
$$ | X X O . O O X X X |
$$ | . X . . . O O O . |
$$ -------------------[/go]


Because White is komonster he does not have to fill the ko (before the end of play), so the marked point is one point of territory and White gets one point for the captured stone, for a total of two points. The original ko is worth the average, or 1 point for White.

(Historical note: Counting the marked point for White was a possibility for the Japanese rules before they were codified. Both Honinbo Shusai and Go Seigen favored doing that. :))

Quote:
ONAG describes the disjunctive sum. But the existence of kos means that go positions do not neatly decompose as disjunctive sums. Is there a mathematically precise definition of thermography that applies to go?


The "Extended thermography" paper is where I redefine thermography in terms of play in an environment.

Some references:

Berlekamp, “The economist’s view of combinatorial games,” in Games of No Chance, Richard J. Nowakowski (ed.), Cambridge University Press(1996)

Spight, “Extended thermography for multiple kos in go,” in Lecture Notes in Computer Science, 1558: Computers and Games, Van den Herik and Iida (eds.), Springer (1999)

Spight, “Go thermography: The 4/19/98 Jiang-Rui endgame,” in More Games of No Chance, Richard J. Nowakowski (ed.), Cambridge University Press (2002)

Siegel, Aaron, Combinatorial Game Theory, American Mathematical Society (2013)

Edit: I almost forgot.

Berlekamp, "Baduk+coupons," and

Spight, "Evaluating kos: A review of the research," both in

Proceedings: ICOB 2006: The 4th International Conference on Baduk, Myongji University and Korean Society for Baduk Studies (2006)

I don't know how easily available those proceedings are.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

My two main guides in life:
My mother and my wife. :)

Everything with love. Stay safe.

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 Post subject: Re: This 'n' that
Post #25 Posted: Mon Oct 12, 2015 1:13 pm 
Dies with sente

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Bill Spight wrote:
Berlekamp, “The economist’s view of combinatorial games”
Spight, “Extended thermography for multiple kos in go”
Spight, “Go thermography: The 4/19/98 Jiang-Rui endgame”
Siegel, Aaron, Combinatorial Game Theory, AMS (2013)
Berlekamp, "Baduk+coupons," and
Spight, "Evaluating kos: A review of the research," both in
Proceedings: ICOB 2006: The 4th International Conference on Baduk, Myongji University and Korean Society for Baduk Studies (2006)

I don't know how easily available those proceedings are.

Thanks! I found the Korean proceedings at
http://www.earticle.net/search/pub/?org=106&jour=252
with the two papers mentioned at
http://www.earticle.net/article.aspx?sn=27269 and
http://www.earticle.net/article.aspx?sn=27268

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 Post subject: Re: This 'n' that
Post #26 Posted: Mon Oct 12, 2015 11:47 pm 
Honinbo

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Click Here To Show Diagram Code
[go]$$ Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | . O O . O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O . O X |
$$ | . . . O . O O X X |
$$ | . . . . O X . X . |
$$ ------------------[/go]


Black to play. What result with best play?

White to play. What result with best play?

Enjoy! :)

(Board edited later.)

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

My two main guides in life:
My mother and my wife. :)

Everything with love. Stay safe.


Last edited by Bill Spight on Wed Oct 14, 2015 9:26 am, edited 2 times in total.
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 Post subject: Re: This 'n' that
Post #27 Posted: Tue Oct 13, 2015 7:40 am 
Oza

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Universal go server handle: skydyr
Online playing schedule: When my wife is out.
Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?

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 Post subject: Re: This 'n' that
Post #28 Posted: Tue Oct 13, 2015 9:29 am 
Honinbo

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skydyr wrote:
Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?


You show a number of variations, but do not explicitly answer the questions. :)

For extra credit, evaluate the three gote and the ko. :)

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

My two main guides in life:
My mother and my wife. :)

Everything with love. Stay safe.

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 Post subject: Re: This 'n' that
Post #29 Posted: Tue Oct 13, 2015 9:30 am 
Honinbo

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My apologies to anyone who tried the 9x10 board. It has its own charm, though. :D More later.

Edit: I have skipped the discussion of the 9x10 board position, despite its charm. ;)

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

My two main guides in life:
My mother and my wife. :)

Everything with love. Stay safe.


Last edited by Bill Spight on Thu Oct 29, 2015 9:18 am, edited 1 time in total.
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 Post subject: Re: This 'n' that
Post #30 Posted: Tue Oct 13, 2015 10:59 am 
Oza

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Universal go server handle: skydyr
Online playing schedule: When my wife is out.
Bill Spight wrote:
skydyr wrote:
Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?


You show a number of variations, but do not explicitly answer the questions. :)

For extra credit, evaluate the three gote and the ko. :)

The leftmost play at A7 is 4 points gote for either side.
The next one over at D7 is 5 points gote for either side.
The lower play at G1 is 2 points gote for either side. However, if black takes it, it creates a 5 point ko threat for black.
The ko, if white fills it, saves 6 points and creates a one point sente followup. If black fills it, he takes all 7 points, but he does so over two moves, so each move is 3.5 points. However, the two left side plays are miai-ish and both more valuable than 3.5 points.

Click Here To Show Diagram Code
[go]$$ :w4: at marked, :w6: at :w1: White by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 2 O X . X . |
$$ | X X O X O X 7 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 W X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]


I suppose the crux of it is that the ko is worth less than either of the two plays on the left, but that they can be used as ko threats because they are almost miai, being a net gain of 1 point for the first side to play and more valuable than an individual move for black in the ko. Also, the total value of the two moves is equal to the total value of the ko and G7.

White has an advantage in the ko in being able to finish it in one move rather than two, as can be seen when white fills the ko for the first move and wins, but black can't take the ko first and win. So, as mentioned earlier, black has to play out the miai-ish moves on the left first. Once black starts that, though, white's play to fill the ko is 7 points vs. 4 points for the gote at A7.

Black starts out 3 points ahead without counting any of the moves, so white has to gain 4 points on black to win but has no ko threats. However, due to the ko, black is 3.5 points behind white locally, and really only half a point ahead before play commences. The key for black is to clear the ko threats first, while white needs to fill first due to the lack of ko threats.

Click Here To Show Diagram Code
[go]$$ Best for black, victory by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W Best for white, victory by 1\n :b2: and :w3: can be exchanged
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]

If white lets black play at :w1:, black can trade A7 for G1 and the ko threat is enough to win the ko later.

It's hard to use words to explain what's going on, I find. Perhaps it's best to say that every other move on the board affects the value of the ko, or that there's a value that's attached to the ko threat black can create, but it's very hard to define.

Maybe the best way is to say that the two sides appear equal, but white needs to remove the value of the potential ko threat while black needs to create it. However, playing the move that creates the threat isn't valuable enough to play so it needs to be dealt with indirectly. This seems to miss the single/double move required for the ko though.

Did I miss anything? How would you explain this?

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 Post subject: Re: This 'n' that
Post #31 Posted: Tue Oct 13, 2015 11:19 am 
Honinbo

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skydyr wrote:
Bill Spight wrote:
skydyr wrote:
Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?


You show a number of variations, but do not explicitly answer the questions. :)

For extra credit, evaluate the three gote and the ko. :)

The leftmost play at A7 is 4 points gote for either side.
The next one over at D7 is 5 points gote for either side.
The lower play at G1 is 2 points gote for either side. However, if black takes it, it creates a 5 point ko threat for black.
The ko, if white fills it, saves 6 points and creates a one point sente followup. If black fills it, he takes all 7 points, but he does so over two moves, so each move is 3.5 points. However, the two left side plays are miai-ish and both more valuable than 3.5 points.

Click Here To Show Diagram Code
[go]$$ :w4: at marked, :w6: at :w1: White by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 2 O X . X . |
$$ | X X O X O X 7 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 W X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]


I suppose the crux of it is that the ko is worth less than either of the two plays on the left, but that they can be used as ko threats because they are almost miai, being a net gain of 1 point for the first side to play and more valuable than an individual move for black in the ko. Also, the total value of the two moves is equal to the total value of the ko and G7.

White has an advantage in the ko in being able to finish it in one move rather than two, as can be seen when white fills the ko for the first move and wins, but black can't take the ko first and win. So, as mentioned earlier, black has to play out the miai-ish moves on the left first. Once black starts that, though, white's play to fill the ko is 7 points vs. 4 points for the gote at A7.

Black starts out 3 points ahead without counting any of the moves, so white has to gain 4 points on black to win but has no ko threats. However, due to the ko, black is 3.5 points behind white locally, and really only half a point ahead before play commences. The key for black is to clear the ko threats first, while white needs to fill first due to the lack of ko threats.

Click Here To Show Diagram Code
[go]$$ Best for black, victory by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W Best for white, victory by 1\n :b2: and :w3: can be exchanged
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]

If white lets black play at :w1:, black can trade A7 for G1 and the ko threat is enough to win the ko later.

It's hard to use words to explain what's going on, I find. Perhaps it's best to say that every other move on the board affects the value of the ko, or that there's a value that's attached to the ko threat black can create, but it's very hard to define.

Maybe the best way is to say that the two sides appear equal, but white needs to remove the value of the potential ko threat while black needs to create it. However, playing the move that creates the threat isn't valuable enough to play so it needs to be dealt with indirectly. This seems to miss the single/double move required for the ko though.

Did I miss anything? How would you explain this?


Thanks. :)

Actually, things are simpler than you suppose. :)

Also, to compare the ko with swing values of the gote, you take 2/3 of the ko swing, which gives you 4 2/3, slightly less than the swing value of the largest gote, and more than the swing value of the second largest gote.

I'll save further discussion for a while, to give others, if any, a chance to respond. :)

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 Post subject: Re: This 'n' that
Post #32 Posted: Tue Oct 13, 2015 11:42 am 
Oza

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Bill Spight wrote:
Actually, things are simpler than you suppose. :)

Also, to compare the ko with swing values of the gote, you take 2/3 of the ko swing, which gives you 4 2/3, slightly less than the swing value of the largest gote, and more than the swing value of the second largest gote.

I'll save further discussion for a while, to give others, if any, a chance to respond. :)


I eagerly await your more detailed explanation. Why 2/3, for example, and do you see the threat black can create as relevant or not?

Wouldn't evaluating at 2/3 imply that white should start with the 5 point move, black takes the 4 2/3 point ko, white takes the 4 point move, and black takes the 2 point move and wins due to the threat? Alternatively, white takes the 5, black the ko, white the 2, then black the 4, and white retakes to win, or black finishes the ko, and white takes the 4 to win, but then how do you value the G7 gote to get things to add up?

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 Post subject: Re: This 'n' that
Post #33 Posted: Tue Oct 13, 2015 12:02 pm 
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skydyr wrote:
Bill Spight wrote:
Actually, things are simpler than you suppose. :)

Also, to compare the ko with swing values of the gote, you take 2/3 of the ko swing, which gives you 4 2/3, slightly less than the swing value of the largest gote, and more than the swing value of the second largest gote.

I'll save further discussion for a while, to give others, if any, a chance to respond. :)


I eagerly await your more detailed explanation. Why 2/3, for example, and do you see the threat black can create as relevant or not?

Wouldn't evaluating at 2/3 imply that white should start with the 5 point move, black takes the 4 2/3 point ko, white takes the 4 point move, and black takes the 2 point move and wins due to the threat? Alternatively, white takes the 5, black the ko, white the 2, then black the 4, and white retakes to win, or black finishes the ko, and white takes the 4 to win, but then how do you value the G7 gote to get things to add up?


Why 2/3? Because the swing for a gote takes 2 moves, while the swing for a simple ko takes 3 moves. This may be easier to understand in terms of how much each move gains on average. A gote move gains 1/2 of the swing; a ko move gains 1/3 of the swing.

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 Post subject: Re: This 'n' that
Post #34 Posted: Wed Oct 14, 2015 9:24 am 
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Quote:
Click Here To Show Diagram Code
[go]$$ Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | . O O . O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O . O X |
$$ | . . . O . O O X X |
$$ | . . . . O X . X . |
$$ ------------------[/go]


Black to play. What result with best play?


Click Here To Show Diagram Code
[go]$$B Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O 7 O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Result: Black +1

Click Here To Show Diagram Code
[go]$$B Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 4 O O 2 O X . X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]


Result: Black +1

Quote:
White to play. What result with best play?


Click Here To Show Diagram Code
[go]$$W Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]


Result: White +1

Click Here To Show Diagram Code
[go]$$W Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 2 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O 7 O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Result: White +1

:)

Is it better to take the largest gote or to play in the ko? It does not matter. :)

Obviously, I constructed the board that way, but the position is not particularly unusual. On a larger board, with more plays in the environment, it would look even more normal. That was my point, to show a fairly normal position where playing the ko was equivalent to taking the largest gote.

How much does taking the largest gote gain? If Black takes it the local result is 0, if White takes it it is 5 points for White. We may write that as {0|−5}. Black moves to positions to the left of the bar and White moves to positions to the right of the bar. The score is from Black's point of view, so 5 points for White is −5 points for Black. The value of the original gote position is −5/2, or −2.5, and each move in the gote gains 2.5.

The ko is a little tricky to evaluate. First suppose that White wins the ko.

Click Here To Show Diagram Code
[go]$$W Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | . O O . O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X . X . |
$$ ------------------[/go]


:w1: wins the ko and later :w3: - :b4: is a sente sequence, which we assume that White will be able to play. The local result is 0.

Now suppose that Black takes and wins the ko.

Click Here To Show Diagram Code
[go]$$B Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | . O O . O X C X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X W X . |
$$ | . . O . O X W X X |
$$ | . O . O O O 1 W X |
$$ | . . . O . O O X X |
$$ | . . . . O X . X . |
$$ ------------------[/go]


The local result is 7 points for Black, the three :wc: stones plus the empty point, :ec:.

The original ko position is worth −2 1/3, and each move in the ko gains 2 1/3 points.

2 1/3 is a little less than 2.5, yet the two plays are in this case equivalent. As I mentioned earlier, a small komonster effect is normal. :)

Gotta run. More later. :)

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 Post subject: Re: This 'n' that
Post #35 Posted: Wed Oct 14, 2015 5:33 pm 
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OK. The above study illustrates the equation,

Code:
K = G + t


where K is the swing value of the ko, G is the swing value of the largest gote, and t is the (ambient) temperature of the environment. The ko and gote are the only plays hotter than the environment. That is, K > 3t and G > 2t. K = 7 and G = 5, so t = 2. If the ambient temperature is 2, then the player to move is indifferent between taking the gote and making a ko move. If t > 2 then the player takes the gote; if t < 2 then the player makes a ko play.

It may not be obvious why we may consider the temperature to be 2 on this board. After all, we can read the whole play out at temperature 0. Well, we can do that, but it would have been tedious and error-prone for me to provide a realistic environment at temperature 2 that it would have been impractical to read out. So I took a short cut. ;)

Click Here To Show Diagram Code
[go]$$ Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | . O O . O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O . O X |
$$ | . . . O . O O X X |
$$ | . . . . O X . X . |
$$ ------------------[/go]


The swing values for the second and third hottest gote are 4 and 2, respectively. If we takes the second largest gote as the hottest play in the environment, then the temperature is 2, which is how much a play in that gote gains.

First, let us look at the case where Black to play can take the ko. As we can see from the sequences in the previous note, all of the plays change hands. At temperature 0 we have this equation:

Code:
7 = 5 + 4 − 2 = 5 + 2


Check. :)

Now let us look at the case where White to play can win the ko. In each sequence White gets the second hottest gote, so it does not figure into the calculations. At temperature 0 we have this equation:

Code:
7 = 5 + 2


Check. :)

The trick is to have the third largest gote be half the size of the second largest gote. Doing so yields an effective temperature in our equation of 2. (This is the trick behind button go, BTW. :D ) On a larger board I could have had a more normal environment with plays having swing values of 4, 3, 2, and 1, to the same effect, but the space on the 9x9 is cramped, so I used that trick. ;)

Aside from the equation, what is the takeaway from all this? Note that the player to move makes a ko play when t is small enough (and K > G). To put it another way, when G is significantly hotter than 2t. OC, we may see that G is significantly hotter than 2t by inspection, but there is a time when we expect G to be hotter than 2t, when the opponent has just played a ko threat and we have to decide whether to answer it or not. If neither player has any other threats at that point, then the above comparison may be our guide.

Now, when I was learning go the rule of thumb was this. Answer a ko threat when G > 2K/3, that is, when a play in the threat gains more than a play in the ko, on average. But often we should ignore such a threat. G > K − t is a better guide. (And it is even better to take other threats into account if possible, as we shall see. :D )

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 Post subject: Re: This 'n' that
Post #36 Posted: Thu Oct 15, 2015 8:45 am 
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Hey, Bill. I don't mean to detract from the discussion, but I was wondering if you ever considered writing a book on this material. The topic seems deep enough that you'd have enough material.

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 Post subject: Re: This 'n' that
Post #37 Posted: Thu Oct 15, 2015 10:04 am 
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Kirby wrote:
Hey, Bill. I don't mean to detract from the discussion, but I was wondering if you ever considered writing a book on this material. The topic seems deep enough that you'd have enough material.


Thanks, Kirby. I appreciate the encouragement. :)

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 Post subject: Re: This 'n' that
Post #38 Posted: Thu Oct 15, 2015 11:44 am 
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Bill Spight wrote:
Kirby wrote:
Hey, Bill. I don't mean to detract from the discussion, but I was wondering if you ever considered writing a book on this material. The topic seems deep enough that you'd have enough material.


Thanks, Kirby. I appreciate the encouragement. :)


No problem... I'll take that as a "Yes" :-)

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Post #39 Posted: Fri Oct 16, 2015 8:55 am 
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To continue the discussion of ko and the environment I need to move to larger boards. :) So today let me introduce a new topic:

Sente and gote

In a way, I was fortunate that the second go book I bought was Korschelt's The Theory and Practice of Go. (The first was Edward Laker's, Go and Go-Moku.) For some strange reason through the double translation from Japanese to German to English, sente became Upper Hand. However, Korschelt was clear that good players tried to take and keep Upper Hand. ;) So I avoided the beginner's trap of following White around the board. :) OC, that meant that a lot of my groups died, but ç'est la vie! ;) Or ç'est la guerre.

Later on, when I was around 3 kyu, I learned that good players also tried to get the Last Play (tedomari) not just at the end of the game, but at earlier stages of the game, as well, such as the opening. OC, if you get the last play of the opening, you give up sente, so those two principles are apparently at odds. There is a go proverb that attempts to reconcile them by saying "Tedomari is worth sente." Sorry folks, but, unlike most go proverbs, that one is just misleading. I'll explain why in a later note. :)

Now, the idea of taking and keeping sente hearkens to the meaning of sente as the initiative. (I think that that would have been a better translation, even though one meaning of te is hand. ;))

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 Post subject: Re: This 'n' that
Post #40 Posted: Fri Oct 16, 2015 10:27 am 
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Quote:
"Tedomari is worth sente."


I've never come across this in any language. Is it perchance a western invention, Bill?

Quote:
OC, if you get the last play of the opening, you give up sente,


I await the promised explanation, but I don't mind admitting that I for one do not yet see why "OC". Imagine an alleyway with Batman at one end and the Joker in the middle. If Robin gets the last big point by blocking the other end of the alley, Batman and Robin surely have the initiative (i.e. sente). The Joker has to respond. But if the Joker's accomplice got to the end point of the alley before Robin, the pressure's off. In general it seems that a tedomari in the opening does imply a threat or a follow up. Because the board is so open at this stage, the opponent can naturally decide to ignore the tedomari's threats, but that doesn't seem automatically to confer the initiative on him. At best he may get a local initiative, but the whole-board initiative surely still rests with the guy who got the tedomari.

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