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 Post subject: Re: Engame value of ko
Post #21 Posted: Wed Dec 09, 2020 12:50 pm 
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Gérard TAILLE wrote:
It seems we have now a common understanding.
Click Here To Show Diagram Code
[go]$$Wc
$$ -----------------
$$ | a X b X . . . |
$$ | X O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]


A white move at "a" not only gains nothing but may be a mistake and must be avoid unless white can use this move as a ko threat between temperature 1/3 and 7/9. The expected local sequence shoud be the black sente exchange black b white a which must occur as soon as temperature drops to 1/3.


Well, in the Fujisawa-Son game Son as Black filled a ko in the other corner instead of filling the one with this shape. It didn't matter in that game, but I think that that is generally best, because Black may have the chance to win this ko.

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 Post subject: Re: Engame value of ko
Post #22 Posted: Wed Dec 09, 2020 2:18 pm 
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Bill Spight wrote:
Above temperature ⅓ there is the ko threat matter which you have discussed. Below temperature ⅓ the inclined mast indicates that White should wait until the ambient temperature reaches 0, if possible, and Black should make the play as early as possible. (In real life there are no plays on the go board between temperature ⅓ and temperature 0 -- although I have constructed one or two -- so the question is moot.)

I never saw an area with a miai value less than 1/3 and I will be interested to analyse some of these.
Can you show us such position Bill?
Each time I tried to find such position I finally failed due to sente/gote consideration which modify the intitial evaluation like our last example where the miai value 5/9 was not correct.

Here is another example
Click Here To Show Diagram Code
[go]$$Bc
$$ -----------------
$$ | O 1 . X . . . |
$$ | . O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

:b1: looks like gaining 1/9 but it is sente and OC white will answer by taking the ko. In the absence of ko threat it is loss for black and :b1: is a mistake.

The other solution would be to assume black is komaster.
In this case the black move :b1: looks like the first move in a corridor where black can follow by taking the other ko. That means that black :b1: value is ¾.
As you see I failed here to build a 1/9 miai value.

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 Post subject: Re: Engame value of ko
Post #23 Posted: Wed Dec 09, 2020 3:03 pm 
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Gérard TAILLE wrote:
Bill Spight wrote:
Above temperature ⅓ there is the ko threat matter which you have discussed. Below temperature ⅓ the inclined mast indicates that White should wait until the ambient temperature reaches 0, if possible, and Black should make the play as early as possible. (In real life there are no plays on the go board between temperature ⅓ and temperature 0 -- although I have constructed one or two -- so the question is moot.)

I never saw an area with a miai value less than 1/3 and I will be interested to analyse some of these.
Can you show us such position Bill?
Each time I tried to find such position I finally failed due to sente/gote consideration which modify the intitial evaluation like our last example where the miai value 5/9 was not correct.

Here is another example
Click Here To Show Diagram Code
[go]$$Bc
$$ -----------------
$$ | O 1 . X . . . |
$$ | . O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

:b1: looks like gaining 1/9 but it is sente and OC white will answer by taking the ko. In the absence of ko threat it is loss for black and :b1: is a mistake.

The other solution would be to assume black is komaster.
In this case the black move :b1: looks like the first move in a corridor where black can follow by taking the other ko. That means that black :b1: value is ¾.
As you see I failed here to build a 1/9 miai value.


If Black is komaster the miai value of :b1: is 4/9.

Click Here To Show Diagram Code
[go]$$Bc Black komaster
$$ -----------------
$$ | O 1 . X . . . |
$$ | 3 O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

In 2 moves Black moves to a position worth ⅓, with a temperature of ⅓.

Click Here To Show Diagram Code
[go]$$Wc Black komaster
$$ -----------------
$$ | O 1 . X . . . |
$$ | . O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

In 1 move White move to a position worth -1.

Each move gains on average 1⅓/3 = 4/9.

:)

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 Post subject: Re: Engame value of ko
Post #24 Posted: Wed Dec 09, 2020 4:09 pm 
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Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote:
Above temperature ⅓ there is the ko threat matter which you have discussed. Below temperature ⅓ the inclined mast indicates that White should wait until the ambient temperature reaches 0, if possible, and Black should make the play as early as possible. (In real life there are no plays on the go board between temperature ⅓ and temperature 0 -- although I have constructed one or two -- so the question is moot.)

I never saw an area with a miai value less than 1/3 and I will be interested to analyse some of these.
Can you show us such position Bill?
Each time I tried to find such position I finally failed due to sente/gote consideration which modify the intitial evaluation like our last example where the miai value 5/9 was not correct.

Here is another example
Click Here To Show Diagram Code
[go]$$Bc
$$ -----------------
$$ | O 1 . X . . . |
$$ | . O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

:b1: looks like gaining 1/9 but it is sente and OC white will answer by taking the ko. In the absence of ko threat it is loss for black and :b1: is a mistake.

The other solution would be to assume black is komaster.
In this case the black move :b1: looks like the first move in a corridor where black can follow by taking the other ko. That means that black :b1: value is ¾.
As you see I failed here to build a 1/9 miai value.


If Black is komaster the miai value of :b1: is 4/9.

Click Here To Show Diagram Code
[go]$$Bc Black komaster
$$ -----------------
$$ | O 1 . X . . . |
$$ | 3 O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

In 2 moves Black moves to a position worth ⅓, with a temperature of ⅓.

Click Here To Show Diagram Code
[go]$$Wc Black komaster
$$ -----------------
$$ | O 1 . X . . . |
$$ | . O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

In 1 move White move to a position worth -1.

Each move gains on average 1⅓/3 = 4/9.

:)


Obvioulsy you assume here that black has only one ko threat and black is unable de delay resolving the ko while the temperature of the environment drops. OK in this case I agree on the figue 4/9 providing you play the correct moves for black:

Click Here To Show Diagram Code
[go]$$Bc Black komaster
$$ -----------------
$$ | O 1 b X . . . |
$$ | a O X X . . . |
$$ | O O O X . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------[/go]

First of all white must first take the ko with :w2: in order to force black to use her ko threat and retake the ko. Obviouly you play that way by assuming black is komaster so, let's forget about that.
Secondly, unless black has other ko threats, black :b3: must not be played at "a" but at "b".

What about a position with a miai value less than 1/3. Did you find one?

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 Post subject: Re: Engame value of ko
Post #25 Posted: Wed Dec 09, 2020 5:24 pm 
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Gérard TAILLE wrote:
What about a position with a miai value less than 1/3. Did you find one?


Click Here To Show Diagram Code
[go]$$Wc White komaster
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . O O O O |
$$ . . . X X X X O . |
$$ . . X X O O O . . |
$$ . . X . X . . . . |
$$ ------------------[/go]


:cool: ;-)

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 Post subject: Re: Engame value of ko
Post #26 Posted: Thu Dec 10, 2020 7:38 am 
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Bill Spight wrote:
Gérard TAILLE wrote:
What about a position with a miai value less than 1/3. Did you find one?


Click Here To Show Diagram Code
[go]$$Wc White komaster
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . O O O O |
$$ . . . X X X X O . |
$$ . . X X O O O . . |
$$ . . X . X . . . . |
$$ ------------------[/go]


:cool: ;-)


If I analysed correctly, the position is sente for black and the score is -4. But the point is that white can play and gain 1/5 point in reverse sente provided white is komaster (5 ko threats).
You found here a beautiful position Bill. :clap: :clap: :clap:


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 Post subject: Re: Engame value of ko
Post #27 Posted: Fri Dec 11, 2020 5:06 am 
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Bill Spight wrote:
Gérard TAILLE wrote:
Eventually this white "a" black "b" exchange looks like a reversible play and we can verify that point by the following difference game:

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

the two positions are equivalent and we can conclude that the white "a" black "b" exchange reverses for both players.


Kos do not add and subtract, although what Berlekamp dubbed placid kos typically do so in terms of average counts. We cannot say that these two kos sum to 0, even though their mast values do so and they have the same temperature.


Bill, I do not understand in which cases I can use or not difference game when ko are implied.
In many occasions you use yourself such difference game (see for example https://lifein19x19.com/viewtopic.php?p=260154#p260154) so it is not clear for me what is correct or not.

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 Post subject: Re: Engame value of ko
Post #28 Posted: Fri Dec 11, 2020 6:41 am 
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Gérard TAILLE wrote:
Bill, I do not understand in which cases I can use or not difference game when ko are implied.
In many occasions you use yourself such difference game (see for example https://lifein19x19.com/viewtopic.php?p=260154#p260154) so it is not clear for me what is correct or not.


First, if there is no ko fight there is no problem. For instance:

Click Here To Show Diagram Code
[go]$$Wc Kosumi vs. Monkey jump 1, White first
$$ --------------------------------
$$ | . . B 1 . . O | X B W 2 W . . |
$$ | X X 4 W . . O | X . B 5 3 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

:b6: fills ko.

Also, in general, G - G = 0, even if G is not a combinatorial game. But G - G must be finite. Obviously this lies outside the scope of CGT, but mirror play will lead to 0 if G - G is finite.

Also, 3 copies of a simple ⅓ point ko add to 1 or -1. And 3 copies of any simple ko likewise add to an integer.

We may assume any ko fight away. For instance, the final evaluation of Three Points without Capturing assumes no ko fight, although a ko fight may be possible.

Another idea, which I think Martin Mueller came up with, is to assume that one player is not only komaster, but komonster, so that ko fights are futile. For instance, if Black is komonster White can win a ko but cannot take one. And if Black takes a ko she wins it. This generally does not apply in real life, but it offers limits. For instance, if Black is komonster but White wins the difference game, the difference game is good for White. OC, if the komonster wins the difference game that does not mean much.

Even though ko fights were possible in the examples you linked to, I believe that I avoided them. Maybe I goofed, and avoiding them was not always reasonable, but I thought so. This was early on in our discussions, and I wanted to avoid complicated explanations. I would not have chosen your example to start out with, but there we were. ;)

As for this combination:

Click Here To Show Diagram Code
[go]$$Wc
$$ -----------------
$$ | . X . X . O O O X |
$$ | X O X X . O O X . |
$$ | O O O X . O X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]


Click Here To Show Diagram Code
[go]$$Wc
$$ -----------------
$$ | 1 X 2 X . O O O X |
$$ | X O X X . O O X . |
$$ | O O O X . O X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]

The result is -1 without a ko fight, as the position after :b2: is 0 on the board by mirror go.

Click Here To Show Diagram Code
[go]$$Wc
$$ -----------------
$$ | . X 2 X . O O O X |
$$ | X O X X . O O X 1 |
$$ | O O O X . O X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]

The same is true when White takes this ko.

Click Here To Show Diagram Code
[go]$$Bc
$$ -----------------
$$ | 2 X 1 X . O O O X |
$$ | X O X X . O O X . |
$$ | O O O X . O X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]

The same is true with this sequence.

Click Here To Show Diagram Code
[go]$$Bc Possible ko fight
$$ -----------------
$$ | 2 X . X . O O O X |
$$ | X O X X . O O X 1 |
$$ | O O O X . O X X X |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]

But in this case there is a possible ko fight.

If we assume that Black has no ko threat, then Black fills the ko and then White does, too. With that assumption this is fine as a difference game, IMO. But really, there is no theory to back this up. :(

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 Post subject: Re: Engame value of ko
Post #29 Posted: Sun Feb 12, 2023 1:54 am 
Judan

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INTRODUCTION

What are the move value, gains and count?

Click Here To Show Diagram Code
[go]$$B Initial position
$$ ---------------
$$ | . X . X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Transformation to a follow-up:

Click Here To Show Diagram Code
[go]$$W Transformation
$$ ---------------
$$ | 1 X 2 X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Click Here To Show Diagram Code
[go]$$B Prisoners = -1, count = -2/3
$$ ---------------
$$ | O X X X . X .
$$ | . O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


The prisoner difference is -1 and the ko has the count 1/3 so the follow-up position has the count -1 + 1/3 = -2/3.

Now, Bill has used this count of the follow-up to derive the alleged count -2/3 of the initial position.

Click Here To Show Diagram Code
[go]$$B Miai?
$$ ---------------
$$ | W X B X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


His argument has been that the circled stones could be exchanged in either order in a sente-like sequence so would be miai and therefore the initial position would inherit the count -2/3 from its sente-like follower.

However, "miai" is only an informal term. In the transformation above, Black need not play at 2 but he has the alternative option of playing elsewhere and fighting the stage ko. There is no a priori justification why the initial count would have to be determined by the basic ko fight due to the connection Black 2.

The initial position allows a basic ko fight or a stage ko fight. The ko(s) can be fought differently. Such kos can be 'active' or 'hyperactive', their move value, gains or count can depend on the environment and possibly its ko threats. Due to different fights (here: basic ko fight or stage ko fight) in different environments, the initial values can differ. There need not be only one move value, only one black gain, only one white gain and only one count.

BASIC KO FIGHT

If there is the basic ko fight, the initial count is -2/3 indeed, the move value is 1/3 and each gain is 1/3.

STAGE KO FIGHT

However, if there is the stage ko fight, we must not use the initial count -2/3 of the basic ko fight and must not derive the gain (-2/3 - (-3)) / 3 = 7/9 from this abused initial count and the count -3 of the settled white follower after three successive white plays.

Instead, for the stage ko fight, we must calculate its own values.

Click Here To Show Diagram Code
[go]$$B Stage ko fight, Black starts, count = -1/3
$$ ---------------
$$ | . X 1 X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


If Black starts in the stage ko fight, the local sequence comprises one play. It does not comprise two plays (with White answering by capturing the ko) because the gain 1/3 of White's ko capture would be smaller than the move value calculated then. Black's start results, after the only one play, in the count -1/3 for the ko with its black ko stone.

Click Here To Show Diagram Code
[go]$$W Stage ko fight, White starts, Black 2 and 4 elsewhere
$$ ---------------
$$ | 1 5 3 X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Click Here To Show Diagram Code
[go]$$W Prisoners = -2, count = -3
$$ ---------------
$$ | O O O X . X .
$$ | C O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


The stage ko fight and White's start result in the prisoner difference -2 and the count -3.

Now, for the stage ko fight, we know that Black's start leads to 1 black excess play and the count -1/3 while White's start leads to 3 white excess plays and the count -3. The tally of both numbers of excess plays is 1 + 3 = 4. We also use the difference of resulting counts to calculate the move value and count of the initial position in the case of a stage ko fight:

Move value = (-1/3 - (-3)) / 4 = 2/3.

We can derive the count from Black's or White's follower:

Count = -1/3 - 1 * 2/3 = -3 + 3 * 2/3 = -1.

Gain of Black's play: -1/3 - (-1) = 2/3.

The gains of White's plays need not all be the same. First, we would have to determine the counts after White 1 and White 3 in the stage ko fight.

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 Post subject: Re: Engame value of ko
Post #30 Posted: Mon Feb 13, 2023 12:30 am 
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I disagree. I think it is completely uneccessary to count the position where white plays 3 times. It will just never happen, unless it is used as a ko threat in another ko. The reasoning is similar to any other connect and die: white will just never capture there, unless its big for black to answer, because back can never prevent white from capturing.

As such, this position is much more like a connect and die then like a usual stage ko (in which black could protect the first stage without self-atari).

Th only point of ko remaining is that if white captures, black protects and then white tenuki it is actually worse for white than not capturing to begin with(not in terms of counts, but ko threats, white would allow black to take the ko first later. One more reason why white would never start playing there unless the global temperature is so low, that both players will continue playing locally

Your count on the other hand makes it seem like a move in the „stage ko“ would be worth twice as much as a move in the simple ko remaining after white and black play, which might just make white believe it was good to play there once the ambient temperature is 0,5. This would be a mistake, as black could later potentially take the ko first

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 Post subject: Re: Engame value of ko
Post #31 Posted: Mon Feb 13, 2023 12:55 am 
Judan

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We can distinguish two views:

1) Usual practical playing advice.

2) Theoretical evaluation covering all cases.

***

You are concerned with (1), which is fine. I have approached (2), which is also fine (I have omitted the komonster cases though).

For (1), the stage ko fight is rare (or maybe even non-existent; don't know yet). For (1), your observation "make white believe it was good to play there once the ambient temperature is 0,5. This would be a mistake, as black could later potentially take the ko first" is useful.

***

For (2), we must consider the basic ko fight and the stage fight.

Possible reason why this stage go fight might never be played: White chooses the wrong option on move 2, due to which the initial count would be 1. White prefers move 2 in Dia. 2 so that the smaller, more favourable initial count is 2/3.

Possible reason why this stage go fight might be fought nevertheless: construct an environment so that the stage ko fight is correct for both players. Are other kos elsewhere necessary for that? Maybe the colour-reversed copy?

Compare the thermographs of both options from White's perspective. At all temperatures, does the basic ko fight dominate the stage ko fight, that is, does White achieve the smaller global count?

Can ko fights elsewhere and ko bans influence this?


Edited.

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Post #32 Posted: Mon Feb 13, 2023 2:14 am 
Judan

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Here is the proof of the existence of a possible stage ko fight in perfect play. The file is meant to be on a 6x6 board. Download the file to view! Therefore, evaluation of the stage ko fight is also necessary.


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 Post subject: Re: Engame value of ko
Post #33 Posted: Mon Feb 13, 2023 11:36 pm 
Judan

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RobertJasiek wrote:
"miai" is only an informal term.


While I may be right about this,...

Quote:
[...] Move value = (-1/3 - (-3)) / 4 = 2/3. [...] Count = -1/3 - 1 * 2/3 = -3 + 3 * 2/3 = -1. [...]


...I may be wrong about this.

Apparently, hyperactive kos must not be simply evaluated referring to swing divided by tally. Instead, some more general theory must be applied: general ko thermography in its algebraic or graphical representations. I need to learn it and will make another attempt later.

Like for stage kos in the middle of the board, I have already noticed that consistency demands possible transfers of initial positions of a corner stage ko, whose counts are related by adjusting virtual prisoners.

Click Here To Show Diagram Code
[go]$$B Count -2/3
$$ ---------------
$$ | . X . X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Click Here To Show Diagram Code
[go]$$B Count -4/9
$$ ---------------
$$ | O X . X . X .
$$ | . O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


These two counts are related. When imagining transferring it from the first initial position with its postulated count -2/3, add the prisoner difference -1 to the second initial position so its modified count is -1 4/9. Now, if we find, as Bill has suggested, that a play gains 7/9, we have a consistent relation of the values:

-2/3 - 7/9 = -1 4/9.

We must understand thermography so that hopefully its application generates these counts and the gain for at least some (komaster) case.


Edited.

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 Post subject: Re: Engame value of ko
Post #34 Posted: Thu Feb 16, 2023 1:47 am 
Judan

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Bill used to say: "Draw the thermographs to determine the values!" The difficulty, however, is to know how to do so at all and correctly. After a week of studying mathematical theory about thermography, I am becoming increasingly aware of what I have always suspected: it is very difficult! Drawing is one means - algebraic calculation is another means. Either way, one must rely on the right numbers.

Standard ko thermography (too euphemistically advertised by its name 'generalised thermography') makes in particular these assumptions:
- Each play is compensated by 1 point in favour of its player so one can play out filling territory.
- The imagined environment of simple gotes or coupons has the temperature t with arbitrarily many such moves of the same value.
- Cyclic positions are 'simple' if for the initial position and each follow-up position only basic kos occur, there are no long cycles of alternating [board-]plays, Black has at most one basic ko capture, White has at most one basic ko capture.

As it turns out, a 2-stage ko in the corner is not too bad as it is a 'simple' cyclic position. Ko thermography is difficult and thermographs start at -1 (instead of 0) but we do not need those extra difficult additions for multiple kos or long cycles.

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 Post subject: Re: Engame value of ko
Post #35 Posted: Sat Feb 18, 2023 5:07 am 
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RobertJasiek wrote:
INTRODUCTION

What are the move value, gains and count?

Click Here To Show Diagram Code
[go]$$B Initial position
$$ ---------------
$$ | . X . X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Transformation to a follow-up:

Click Here To Show Diagram Code
[go]$$W Transformation
$$ ---------------
$$ | 1 X 2 X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Click Here To Show Diagram Code
[go]$$B Prisoners = -1, count = -2/3
$$ ---------------
$$ | O X X X . X .
$$ | . O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


The prisoner difference is -1 and the ko has the count 1/3 so the follow-up position has the count -1 + 1/3 = -2/3.

Now, Bill has used this count of the follow-up to derive the alleged count -2/3 of the initial position.

Click Here To Show Diagram Code
[go]$$B Miai?
$$ ---------------
$$ | W X B X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


His argument has been that the circled stones could be exchanged in either order in a sente-like sequence so would be miai and therefore the initial position would inherit the count -2/3 from its sente-like follower.

However, "miai" is only an informal term. In the transformation above, Black need not play at 2 but he has the alternative option of playing elsewhere and fighting the stage ko. There is no a priori justification why the initial count would have to be determined by the basic ko fight due to the connection Black 2.


My point of view is different.
I do not consider the circled stones could be exchanged in either order, and I do not consider a stage ko could take place, at least in a theoritical approach.
My view is the following:
Click Here To Show Diagram Code
[go]$$B
$$ ---------------
$$ | . X 1 X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]
the black move :b1: above is a very small move and this move cannot be played if temperature is greater than 1/3.

Click Here To Show Diagram Code
[go]$$W
$$ ---------------
$$ | 1 X 2 X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]
On the other hand after the white move :w1: above black shoud connect if temperature is less than 7/9.

The conclusion is simple: white waits until temperature drops between 7/9 and 1/3 and white plays the sente exchange :w1: :b2:
In this case the count of the initial position is -2/3

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 Post subject: Re: Engame value of ko
Post #36 Posted: Sat Feb 18, 2023 6:03 am 
Judan

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Yours is a useful strategic advice. However, first we must establish and justify the 7/9.

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 Post subject: Re: Engame value of ko
Post #37 Posted: Sat Feb 18, 2023 7:19 am 
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RobertJasiek wrote:
Yours is a useful strategic advice. However, first we must establish and justify the 7/9.

OC in pracice you don't need to calculate the exact value 7/9. You have just to consider that :w1: is sente as soon as temperature is a little above 1/3.
Anyway how do I calculate the value 7/9 ?

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


white to play
Click Here To Show Diagram Code
[go]$$W :b2: tenuki, :b4: tenuki
$$ ---------------
$$ | O 3 1 X . X .
$$ | . O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]
score : S1 = 2t - 2

Black to play
Click Here To Show Diagram Code
[go]$$B :w2: tenuki
$$ ---------------
$$ | O X 1 X . X .
$$ | . O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]
score : S2 = -t + 1/3

S1 = S2 <=> 2t - 2 = -t + 1/3 <=> t = 7/9

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 Post subject: Re: Engame value of ko
Post #38 Posted: Sat Feb 18, 2023 7:44 am 
Judan

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The white tenuki is essy to justify. The hard part is to justify using the intermediate ko position for evaluating the initial position with two black stones. Apart from these assumptions, your calculation for the intermediate position is correct without komaster.

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 Post subject: Re: Engame value of ko
Post #39 Posted: Sat Feb 18, 2023 8:01 am 
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RobertJasiek wrote:
The white tenuki is essy to justify. The hard part is to justify using the intermediate ko position for evaluating the initial position with two black stones. Apart from these assumptions, your calculation for the intermediate position is correct without komaster.


Yes, basically a ko introduces always a difficulty but for a theoritical point of view using the intermediate poisition to find a sente move is only natural:

Click Here To Show Diagram Code
[go]$$W
$$ ---------------
$$ | 1 X . X . X .
$$ | X O X X X X X
$$ | O O O O . . .
$$ | . O . O . . .[/go]


Click Here To Show Diagram Code
[go]$$W
$$ ---------------
$$ | O 1 . . X . .
$$ | O X . . X . .
$$ | O X X X X . .
$$ | O O O O . . .[/go]


Using the position after white :w1: in order to see that ambiant temperature has increased is common approach to discover a sente move isn't it?

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 Post subject: Re: Engame value of ko
Post #40 Posted: Sat Feb 18, 2023 8:32 am 
Judan

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Ko thermography is not as straightforward as sente because balloon trajectories need not proceed vertically but can have vertical parts.

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