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This 'n' that

https://lifein19x19.com/viewtopic.php?t=12327

Page 59 of 71

Re: This 'n' that

Posted: Sat Jun 05, 2021 3:20 am
by Gérard TAILLE
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | . . . . X . . . . |
$$ | . a O O X . . . . |
$$ | . . O X X . . . . |
$$ | . O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . X . . . . . . . |
$$ | . X . . . . . . . |
$$ | X X . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Let me give you my analyse of black strategy by provoquing the ko, in a ideal environment without any ko threat.

1) Black starts the ko, white plays once in the environment and Black plays twice, and then White plays in the corner to win the ko, and then Black plays in the environment again
score1 = -t + t + t + t/2 - 5 = 3t/2 - 5
2) Black play in the corner and white give up the corner by playing in the environment
score2 = -t - t/2 + 22 = -3t/2 + 22

White chooses to give up the corner if :
score2 <= score1 <=> -3t/2 + 22 <= 3t/2 - 5 <=> t >= 9

3) The initial temperature being equal to t1 <= 9 assume black wait until temperature drops to t2 before starting the ko
score3 = (t1 - t2)/2 + 3t2/2 - 5 = t1/2 + t2 - 5
In order to reach the best score black must choose t2 to increase score3 as far as possible. As a consequence black chooses t2 = t1 and reaches the score1.

what conclusion in an ideal enviroment without ko threat? As soon as temperature drops under t= 9 Black should provoque the ko as soon as possible.

Note : it is quite interesting to study some non ideal environment u >= v >= t, with two gote points u et v and an ideal environment t. Depending of the values u,v,t it may be better for black to delay her move in the corner.

Robert : in your theory, did you take into consideration such local situation? If yes can you tell us what was your results?

Re: This 'n' that

Posted: Sat Jun 05, 2021 3:31 am
by Bill Spight
RobertJasiek wrote:
Bill Spight wrote:In 1998 I redefined and expanded thermography to cover multiple kos and superkos by basing it on play in an ideal environment.
Do you mean an arbitrarily dense "rich environment"?
In my paper, I used Berlekamp's terminology. I have since refined the concept to that of an ideal enivornment, because playing first in a dense environment does not always produce a result of t/2. The slight change is not worth a paper in itself.

Re: This 'n' that

Posted: Sat Jun 05, 2021 3:52 am
by Bill Spight
Gérard TAILLE wrote:what conclusion in an ideal enviroment without ko threat? As soon as temperature drops under t= 9 Black should provoque the ko as soon as possible.
Since we agree that a White play in the corner gains only 1 point there in regular go, why shouldn't Black wait to play in the corner? Assuming a temperature drop between the top plays in the rest of the board, why not play elsewhere and pick up the difference?

Re: This 'n' that

Posted: Sat Jun 05, 2021 4:02 am
by Gérard TAILLE
Bill Spight wrote:
Gérard TAILLE wrote:what conclusion in an ideal enviroment without ko threat? As soon as temperature drops under t= 9 Black should provoque the ko as soon as possible.
Since we agree that a White play in the corner gains only 1 point there in regular go, why shouldn't Black wait to play in the corner? Assuming a temperature drop between the top plays in the rest of the board, why not play elsewhere and pick up the difference?
Look at my previous example Bill:
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . X X X X X X O . . . . . . . . |
$$ | . a O O X O O O O u O . . . . . . . . |
$$ | . . O X X X X X X X O . . . . . . . . |
$$ | . O O X X . O O O v O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X O O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . . . . . . t . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
the environment is the following:
Three gote points u, v, w with the values 4, 3½, 3 and I assume the remaining environment being an ideal environment at temperature t = 2½.

Can you reach a better result for black than playing immediatly in the corner at "a"?

Re: This 'n' that

Posted: Sat Jun 05, 2021 4:35 am
by Bill Spight
Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:what conclusion in an ideal enviroment without ko threat? As soon as temperature drops under t= 9 Black should provoque the ko as soon as possible.
Since we agree that a White play in the corner gains only 1 point there in regular go, why shouldn't Black wait to play in the corner? Assuming a temperature drop between the top plays in the rest of the board, why not play elsewhere and pick up the difference?
Look at my previous example Bill:
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . X X X X X X O . . . . . . . . |
$$ | . a O O X O O O O u O . . . . . . . . |
$$ | . . O X X X X X X X O . . . . . . . . |
$$ | . O O X X . O O O v O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X O O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . . . . . . t . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
the environment is the following:
Three gote points u, v, w with the values 4, 3½, 3 and I assume the remaining environment being an ideal environment at temperature t = 2½.

Can you reach a better result for black than playing immediatly in the corner at "a"?
That does not answer the general question. :)

BTW, I do not know of an ideal environment in regular go at t = 2½. It is possible to construct an ideal environment in chilled go at chilled temperature 1½, however. If there is no ko fight aside from this one, which we know that White is going to win, anyway, correct play in chilled go should be the same as correct play in regular go. Since we can construct an actual ideal environment for chilled go, why not use it?

Re: This 'n' that

Posted: Sat Jun 05, 2021 5:18 am
by Bill Spight
RobertJasiek wrote:
Bill Spight wrote:In 1998 I redefined and expanded thermography to cover multiple kos and superkos by basing it on play in an ideal environment.
Do you mean an arbitrarily dense "rich environment"?
For the problem where the rich environment is not ideal, Berlekamp used one with a delta of 0.01 point, such that, as a practical matter a ko fight would hardly ever result in a result different from that in an ideal environment. If necessary he would resort to an even smaller delta. :)

Re: This 'n' that

Posted: Sat Jun 05, 2021 5:57 am
by Bill Spight
Or, we can construct an ideal environment with temperature 2 in regular go, so why no try that, with appropriate changes to your example, to avoid a sizable temperature drop? (We will start at temperature 3½ instead of 4. :))
Click Here To Show Diagram Code
[go]$$B Corner first
$$ ---------------------------------------
$$ | 5 2 7 8 X X X X X X O . . . . . . . . |
$$ | 4 1 O O X . O O O 6 O . . . . . . . . |
$$ | 3 . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O v O . . . . . . . . |
$$ | 9 O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Wm10 Black has captured 2 stones in the ko fight
$$ ---------------------------------------
$$ | B 1 B O X X X X X X O . . . . . . . . |
$$ | 3 B O O X . O O O O O . . . . . . . . |
$$ | B 5 O X X X X X X X O . . . . . . . . |
$$ | . O O X X X W W W 2 O . . . . . . . . |
$$ | X O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X C W W 4 O . . . . . . . . |
$$ | C X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X W W 6 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O 7 O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X W W 8 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O 9 O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
If I have counted correctly, the net result is +14 for Black.

Now let Black play first in the largest play on the board.
Click Here To Show Diagram Code
[go]$$B Largest play first
$$ ---------------------------------------
$$ | 7 4 9 0 X X X X X X O . . . . . . . . |
$$ | 6 3 O O X C W W W 1 O . . . . . . . . |
$$ | 5 . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O 2 O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O 8 O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Bcm11 Black has captured 2 stones in the ko fight
$$ ---------------------------------------
$$ | B 2 B O X X X X X X O . . . . . . . . |
$$ | 4 B O O X C W W W X O . . . . . . . . |
$$ | B 6 O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O O O . . . . . . . . |
$$ | 1 O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O O O . . . . . . . . |
$$ | C X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X W W 3 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X W W 5 O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X W W 7 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O 8 O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Again, if I have counted correctly, Black is 14 points ahead, the same as when she starts in the corner. Note that in the second sequence Black played twice in the ideal environment before White won the ko.

I'm taking a break now. More later. :)

Re: This 'n' that

Posted: Sat Jun 05, 2021 5:59 am
by Gérard TAILLE
Bill Spight wrote:
That does not answer the general question. :)

BTW, I do not know of an ideal environment in regular go at t = 2½. It is possible to construct an ideal environment in chilled go at chilled temperature 1½, however. If there is no ko fight aside from this one, which we know that White is going to win, anyway, correct play in chilled go should be the same as correct play in regular go. Since we can construct an actual ideal environment for chilled go, why not use it?
OK Bill if ideal environment notion do not simplify the reasoning we had better to not use it.
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | . . . . X . . . . |
$$ | . a O O X . . . . |
$$ | . . O X X . . . . |
$$ | . O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . X . . . . . . . |
$$ | . X . . . . . . . |
$$ | X X . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Let's add the following (quasi ideal?) environment : the 8 following pure gote points : 4, 3½,3, 2½, 2, 1½, 1, ½.

Black plays immediatly in the corner:
Score1 = -4 + 3½ + 3 + 2½ - 2 + 1½ - 1 + ½ -5 = -1
Black waits one move before playing in the corner
Score2 = 4 - 3½ - 3 + 2½ + 2 + 1½ - 1 + ½ - 5 = -2

You see that black loses one point if she waits a move before playing in the corner

Re: This 'n' that

Posted: Sat Jun 05, 2021 6:35 am
by Bill Spight
Gérard TAILLE wrote:
Bill Spight wrote:
That does not answer the general question. :)

BTW, I do not know of an ideal environment in regular go at t = 2½. It is possible to construct an ideal environment in chilled go at chilled temperature 1½, however. If there is no ko fight aside from this one, which we know that White is going to win, anyway, correct play in chilled go should be the same as correct play in regular go. Since we can construct an actual ideal environment for chilled go, why not use it?
OK Bill if ideal environment notion do not simplify the reasoning we had better to not use it.
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | . . . . X . . . . |
$$ | . a O O X . . . . |
$$ | . . O X X . . . . |
$$ | . O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . X . . . . . . . |
$$ | . X . . . . . . . |
$$ | X X . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Let's add the following (quasi ideal?) environment : the 8 following pure gote points : 4, 3½,3, 2½, 2, 1½, 1, ½.

Black plays immediatly in the corner:
Score1 = -4 + 3½ + 3 + 2½ - 2 + 1½ - 1 + ½ -5 = -1
Black waits one move before playing in the corner
Score2 = 4 - 3½ - 3 + 2½ + 2 + 1½ - 1 + ½ - 5 = -2

You see that black loses one point if she waits a move before playing in the corner
If you can read everything out, you do not need any theory. :)

Re: This 'n' that

Posted: Sat Jun 05, 2021 7:09 am
by Bill Spight
Now that we have found an equilibrium position, we can fiddle with it. ;)
Click Here To Show Diagram Code
[go]$$B Reduce the top play
$$ ---------------------------------------
$$ | . . . . X X X X X X O . . . . . . . . |
$$ | . . O O X B O O O u O . . . . . . . . |
$$ | . . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O v O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Now it is better to create the ko in the corner.
Click Here To Show Diagram Code
[go]$$B Reduce the second largest play
$$ ---------------------------------------
$$ | . . . . X X X X X X O . . . . . . . . |
$$ | . . O O X . O O O u O . . . . . . . . |
$$ | . . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X C O O v O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Now it is better to take the largest play first.
Click Here To Show Diagram Code
[go]$$B All same same
$$ ---------------------------------------
$$ | . . . . X X X X X X O . . . . . . . . |
$$ | . . O O X X X O O u O . . . . . . . . |
$$ | . . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X X O O v O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X X O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
And in this particular ideal environment, playing in the environment is better, right?

Re: This 'n' that

Posted: Sat Jun 05, 2021 7:24 am
by RobertJasiek
Bill Spight wrote:I have since refined the concept to that of an ideal enivornment, because playing first in a dense environment does not always produce a result of t/2.
What is your definition of your 'ideal environment' and why / how does it avoid the odd parity problem of not exactly t/2?
resort to an even smaller delta.
Of course. Siegel lets it converge to 0 :)

Re: This 'n' that

Posted: Sat Jun 05, 2021 7:29 am
by Bill Spight
RobertJasiek wrote:
Bill Spight wrote:I have since refined the concept to that of an ideal enivornment, because playing first in a dense environment does not always produce a result of t/2.
What is your definition of your 'ideal environment' and why / how does it avoid the odd parity problem of not exactly t/2?

By definition, an environment of simple gote is ideal if playing in it alone yields a result of t/2 no matter who plays first. That is the basic idea of button go. :)

Also, for whatever position you are considering, the environment should contain a simple gote of the same size as that position and all subpositions.

Re: This 'n' that

Posted: Sat Jun 05, 2021 7:37 am
by Gérard TAILLE
Bill Spight wrote:Or, we can construct an ideal environment with temperature 2 in regular go, so why no try that, with appropriate changes to your example, to avoid a sizable temperature drop? (We will start at temperature 3½ instead of 4. :))
Click Here To Show Diagram Code
[go]$$B Corner first
$$ ---------------------------------------
$$ | 5 2 7 8 X X X X X X O . . . . . . . . |
$$ | 4 1 O O X . O O O 6 O . . . . . . . . |
$$ | 3 . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O v O . . . . . . . . |
$$ | 9 O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O w O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Wm10 Black has captured 2 stones in the ko fight
$$ ---------------------------------------
$$ | B 1 B O X X X X X X O . . . . . . . . |
$$ | 3 B O O X . O O O O O . . . . . . . . |
$$ | B 5 O X X X X X X X O . . . . . . . . |
$$ | . O O X X X W W W 2 O . . . . . . . . |
$$ | X O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X C W W 4 O . . . . . . . . |
$$ | C X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X W W 6 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O 7 O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X W W 8 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O 9 O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
If I have counted correctly, the net result is +14 for Black.

Now let Black play first in the largest play on the board.
Click Here To Show Diagram Code
[go]$$B Largest play first
$$ ---------------------------------------
$$ | 7 4 9 0 X X X X X X O . . . . . . . . |
$$ | 6 3 O O X C W W W 1 O . . . . . . . . |
$$ | 5 . O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O 2 O . . . . . . . . |
$$ | . O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O 8 O . . . . . . . . |
$$ | . X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X O O . O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X O O . O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O . O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Bcm11 Black has captured 2 stones in the ko fight
$$ ---------------------------------------
$$ | B 2 B O X X X X X X O . . . . . . . . |
$$ | 4 B O O X C W W W X O . . . . . . . . |
$$ | B 6 O X X X X X X X O . . . . . . . . |
$$ | . O O X X X O O O O O . . . . . . . . |
$$ | 1 O X X X X X X X X O . . . . . . . . |
$$ | . X X . X X . O O O O . . . . . . . . |
$$ | C X . . X X X X X X O . . . . . . . . |
$$ | X X . . . . X W W 3 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . , . . X W W 5 O . . . . , . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . X W W 7 O . . . . . . . . |
$$ | . . . . . . X X X X O . . . . . . . . |
$$ | . . . . . . . X O 8 O . . . . . . . . |
$$ | . . . . . . . X X X X . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Again, if I have counted correctly, Black is 14 points ahead, the same as when she starts in the corner. Note that in the second sequence Black played twice in the ideal environment before White won the ko.

I'm taking a break now. More later. :)
OK Bill let's try to generalise.
Consider the environment of pure gote areas g1 >= g2 >= g3 >= g4 ....

Black plays immediatly in the corner:
score1 = -g1 + g2 + g3 + g4 - g5 + g6 - g7 ...
Black waits one move before playing in the corner:
score2 = g1 - g2 - g3 + g4 + g5 + g6 - g7 ...

score2 - score1 = 2 (g1 - g2 + g3 - g5)
score2 >= score1 <=> g1 - g2 >= g3 - g5
In my example I have g1 - g2 = ½ and g3 - g5 = 1 => black cannot wait
In your example you have g1 - g2 = ½ and g3 - g5 = ½ => black can play immediatly or can wait
In you consider a regular serie of gote moves then you have g1 - g2 > g3 - g5 and black cannot wait one move.

In you take the environment 4½, 3, 2½, 2, 1½, 1, ½
you can see that g1 - g2 > g3 - g5 and you must wait one move before playing in the corner which is just common sense when you see the big gap between g1 and g2.

Re: This 'n' that

Posted: Sat Jun 05, 2021 10:00 am
by Bill Spight
Here is an SGF file for a chilled go environment with chilled temperature 1½. OC, when the chilled temperature is less than 0, neither player will play. :) The ½ point territory is marked by ∆.



All roads lead to Rome. :)

Re: This 'n' that

Posted: Sat Jun 05, 2021 10:33 am
by Gérard TAILLE
Bill Spight wrote:Here is an SGF file for a chilled go environment with chilled temperature 1½. OC, when the chilled temperature is less than 0, neither player will play. :) The ½ point territory is marked by ∆.



All roads lead to Rome. :)
yes Bill with g1 - g2 = g3 - g5 = 0 it is indifferent to play immediatly in the corner or to wait one move.
We can see clearly the problem with the definition of an "ideal" environment. If the temperature do not drop then black can always wait before playing in the corner. As soon as the temperature may drop (t becomes t-0.01 or whatever you want) you have to compare g1 - g2 to g3 - g5 in order to know if you have to play immediatly in the corner.
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