Thermography

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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote:OK. Let's try again. ;)
Click Here To Show Diagram Code
[go]$$Bc Black first
$$ -----------------
$$ | X 1 . . . W X X 2 |
$$ | X W W W W W X O 3 |
$$ | X X X X X O X 5 O |
$$ | . . . . X O X X X |
$$ | X X X X X X O O O |
$$ | . . . . . . O . . |
$$ | . . . . . . O O . |
$$ | . . . . . . . O . |
$$ | . . . . . . . O . |
$$ -----------------[/go]
:w4:, :w6: elsewhere

Result: 25 - 2t
Click Here To Show Diagram Code
[go]$$Wc White first
$$ -----------------
$$ | X 3 . 5 . W X X 1 |
$$ | X W W W W W X O 2 |
$$ | X X X X X O X 4 O |
$$ | . . . . X O X X X |
$$ | X X X X X X O O O |
$$ | . . . . . . O . . |
$$ | . . . . . . O O . |
$$ | . . . . . . . O . |
$$ | . . . . . . . O . |
$$ -----------------[/go]
:b6: elsewhere

Result: 4 + t

Assuming that these are the sequences of play when t is small enough, we find that t by solving the equation,

25 - 2t = 4 + t

t = 21/3 = 7

And we can verify that when Black plays first, White throws in to make the ko when t ≤ 13¾ , and when White plays first and Black takes the ko, White plays the ko threat when t ≤ 11. So these are the normal sequences of play when t ≤ 7. :)

The mast value of the position is 11.

If I haven't goofed, that is. :lol:
I agree that black will play first if the temperature has droped to 7.
But I do not understand why the mast value of the position is 11 instead of 14⅜.
If for example the temperature is equal to 13 then white should immediatly provoque the ko without waiting for temperature droping to 11 shouldn't he?
BTW how will you eventually draw the thermograph Bill? It looks quite unusual doesn't it?
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Bill Spight
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Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:OK. Let's try again. ;)
Click Here To Show Diagram Code
[go]$$Bc Black first
$$ -----------------
$$ | X 1 . . . W X X 2 |
$$ | X W W W W W X O 3 |
$$ | X X X X X O X 5 O |
$$ | . . . . X O X X X |
$$ | X X X X X X O O O |
$$ | . . . . . . O . . |
$$ | . . . . . . O O . |
$$ | . . . . . . . O . |
$$ | . . . . . . . O . |
$$ -----------------[/go]
:w4:, :w6: elsewhere

Result: 25 - 2t
Click Here To Show Diagram Code
[go]$$Wc White first
$$ -----------------
$$ | X 3 . 5 . W X X 1 |
$$ | X W W W W W X O 2 |
$$ | X X X X X O X 4 O |
$$ | . . . . X O X X X |
$$ | X X X X X X O O O |
$$ | . . . . . . O . . |
$$ | . . . . . . O O . |
$$ | . . . . . . . O . |
$$ | . . . . . . . O . |
$$ -----------------[/go]
:b6: elsewhere

Result: 4 + t

Assuming that these are the sequences of play when t is small enough, we find that t by solving the equation,

25 - 2t = 4 + t

t = 21/3 = 7

And we can verify that when Black plays first, White throws in to make the ko when t ≤ 13¾ , and when White plays first and Black takes the ko, White plays the ko threat when t ≤ 11. So these are the normal sequences of play when t ≤ 7. :)

The mast value of the position is 11.

If I haven't goofed, that is. :lol:
I agree that black will play first if the temperature has droped to 7.
But I do not understand why the mast value of the position is 11 instead of 14⅜.
The mast value is equal to 4 + 7 or 25 - 2*7. :) 14⅜ is the temperature below which White threatens to win the ko.
Gérard TAILLE wrote:If for example the temperature is equal to 13 then white should immediatly provoque the ko without waiting for temperature droping to 11 shouldn't he?
If White throws in at temperature 13, then:

1) if White lets Black win the ko the result is 26 - 13 = 13, which is worse for White than 11;

2) if White plays the threat then we reach this position with Black to play.
Click Here To Show Diagram Code
[go]$$Wc White first
$$ -----------------
$$ | X W . . . W X X . |
$$ | X W W W W W X O B |
$$ | X X X X X O X . O |
$$ | . . . . X O X X X |
$$ | X X X X X X O O O |
$$ | . . . . . . O . . |
$$ | . . . . . . O O . |
$$ | . . . . . . . O . |
$$ | . . . . . . . O . |
$$ -----------------[/go]
One :wc: prisoner

If :b4: plays elsewhere White can take and win the ko for a result of -18 + 3t (from the original position), which is equal to 39 - 18 = 21. That's even worse for White than above, so Black will play elsewhere and so will White.

What is the mast value of this position? From here White can take and win the ko for a result of -18 + 2t.

If instead Black wins the ko we have this position.
Click Here To Show Diagram Code
[go]$$Wc White first
$$ -----------------
$$ | X W . . . W X X . |
$$ | X W W W W W X . B |
$$ | X X X X X O X B . |
$$ | . . . . X O X X X |
$$ | X X X X X X O O O |
$$ | . . . . . . O . . |
$$ | . . . . . . O O . |
$$ | . . . . . . . O . |
$$ | . . . . . . . O . |
$$ -----------------[/go]
Three :wc: prisoners

If White lives the result is 4. If Black kills the result is 26. The mean value is 15 and at or below temperature 11 White will live.

To find the temperature for this position at or below which the players will play locally, let's first assume that White lives. Then we solve for

-18 + 2t = 4

t = 22/2 = 11

Fine. :) We are done. The mast value of this position is 4.

Assuming that at temperature 13 White makes the ko and then plays the threat, the result will be 4 + 13 = 17 (from the original position), which is worse for White than 11, so White does best to wait until t = 7.
Gérard TAILLE wrote:BTW how will you eventually draw the thermograph Bill? It looks quite unusual doesn't it?
Actually, it looks like a simple ko thermograph. Above temperature 7 the mast rises at a territory value of 11. Below that the right wall is 4 + t and the left wall is 25 - 2t. I'll add the thermograph below, probably tomorrow. :)
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote: If White throws in at temperature 13, then:

1) if White lets Black win the ko the result is 26 - 13 = 13, which is worse for White than 11;
At temperature 13 the result 26 - 13 = 13 looks to me the best result for white. How do you manage to reach the score 11?
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Bill Spight
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Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote: If White throws in at temperature 13, then:

1) if White lets Black win the ko the result is 26 - 13 = 13, which is worse for White than 11;
At temperature 13 the result 26 - 13 = 13 looks to me the best result for white. How do you manage to reach the score 11?
Let m be the mast value.

The scaffolds have been derived above.

Left scaffold up to temperature 7:

25 - 2t

Right scaffold up to temperature 7:

4 + t

4 + t = 25 - 2t

3t = 21

t = 7

m = 4 + 7 = 25 - 14 = 11

Above temperature 7 all White has to do to guarantee the mast value is to play elsewhere.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote: If White throws in at temperature 13, then:

1) if White lets Black win the ko the result is 26 - 13 = 13, which is worse for White than 11;
At temperature 13 the result 26 - 13 = 13 looks to me the best result for white. How do you manage to reach the score 11?
Let m be the mast value.

The scaffolds have been derived above.

Left scaffold up to temperature 7:

25 - 2t

Right scaffold up to temperature 7:

4 + t

4 + t = 25 - 2t

3t = 21

t = 7

m = 4 + 7 = 25 - 14 = 11

Above temperature 7 all White has to do to guarantee the mast value is to play elsewhere.
OK BIll, I understand.
Because this result is not the result I expected let me propose a modification
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | X b . . . O X X w |
$$ | X O O O O O X O . |
$$ | X X X X X O X . O |
$$ | . . . . X O X X X |
$$ | X X X X X X O B B |
$$ | . . . . . . O O B |
$$ | . . . . . . O O O |
$$ | . . . . . . O O . |
$$ | . . . . . . O . O |
$$ -----------------[/go]
Why I add the 3 black marked stone?
The only difference is that the figure 14⅜ is now replaced by the figure 16⅜. As a consequence I can consider a white move at temperature 16 and now 26 - t can be less than 11. That is the point I wanted to highlight.
My analyse is then the following:
Above temperature 16⅜ black and white play tenuki
Between temperature 15 and 16⅜ white provoques the ko in the corner to reach the score 26 - t
Between temperature 7 and 15 black and white wait and play tenuki
Under temperature 7 both white and black want to play in the area to reach a score 4 + t or 25 - 2t
Is it correct Bill?
If yes, how do you draw the termograph?
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Bill Spight
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Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:OK BIll, I understand.
Because this result is not the result I expected let me propose a modification
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | X b . . . O X X w |
$$ | X O O O O O X O . |
$$ | X X X X X O X . O |
$$ | . . . . X O X X X |
$$ | X X X X X X O B B |
$$ | . . . . . . O O B |
$$ | . . . . . . O O O |
$$ | . . . . . . O O . |
$$ | . . . . . . O . O |
$$ -----------------[/go]
Why I add the 3 black marked stone?
The only difference is that the figure 14⅜ is now replaced by the figure 16⅜. As a consequence I can consider a white move at temperature 16 and now 26 - t can be less than 11. That is the point I wanted to highlight.
My analyse is then the following:
Above temperature 16⅜ black and white play tenuki
Between temperature 15 and 16⅜ white provoques the ko in the corner to reach the score 26 - t
Between temperature 7 and 15 black and white wait and play tenuki
Under temperature 7 both white and black want to play in the area to reach a score 4 + t or 25 - 2t
Is it correct Bill?
That's what I get, as well. :)

This is a phenomenon that Professor Berlekamp discovered over 30 years ago. I bow to his memory. :bow: :bow: :bow:
Gérard TAILLE wrote:If yes, how do you draw the termograph?
The right scaffold of the thermograph is 4 + t up to t = 11, then it is 26 - t up to t = 16⅜, then it is -6¾ + t upwards from there.

The left scaffold is 25 - 2t up to t = 16¾, then -5½ - t upwards from there.

As already noted, the scaffolds intersect at (m,v) = (11,7). Then a black mast rises at m = 11 up to (11,15), at which point the right scaffold intersects the mast. Then an inclined red mast is v = 26 - t up to (9⅝, 16⅜). Then a black mast rises upwards from there at m = 9⅜. The mast value of the thermograph is 9⅝.

The inclined mast was already known and understood by some players, but, OC, not by that name. :) But I doubt if the zigzag mast and other strange masts were understood or even suspected before Berlekamp's discoveries.

I am having trouble posting a thermograph now. I'll post them when the problem is cleared up.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Here is an example of semeai leading to the studied position:
Click Here To Show Diagram Code
[go]$$W white to play
$$ -----------------
$$ | . . . . . . . . . |
$$ | . . X O O O X . . |
$$ | . . X X . O X . . |
$$ | . . . . X O X X . |
$$ | . . . . X X O O . |
$$ | . . . . . . O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Click Here To Show Diagram Code
[go]$$W white to play
$$ -----------------
$$ | . . . . . 5 6 2 . |
$$ | . . X O O O X 1 . |
$$ | . . X X . O X . 3 |
$$ | . . . . X O X X 4 |
$$ | . . . . X X O O 7 |
$$ | . . . . . . O . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
The handling of such position appears quite difficult.
Assume white is able to use several ko threats (of different values) in the environment then it is not easy to answer the following questions:
When will white provoque the ko?
Should black use one or several moves to destroy some white ko threats at the expense of few points?

Do somebody know if such position already appeared in pro game?
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Here is an example of position we encounter very often in practice and not that easy to analyse
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . . . . . . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
What is your analyse of the yose in the upper part of the board?

My view is the following.
Let's suppose white to play with a temperature between 1 and 3. In that case white can play the sequence
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . . . 3 2 4 . . . |
$$ | . . 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
This sequence seems better that playing :w1: at :b2: to gain 1 point but in gote.
:w1: at :b4: may be possible if white has enough ko threats

Now let's suppose black to play. Black being able to play in sente as soon as temperature drops to 4 I conclude that in practice black will play first in the area when temperature is between 3 and 4.
What black will play?
The first idea is the hane
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . b . 1 . . . . |
$$ | . . a O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and white can answer with a or b.
If the temperature is greater then 3 the more logical move is :w2: at "a" expected following later with :w4: and :b5:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . 4 1 5 . . . |
$$ | . . 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
The point is the following : in this hypothesis the result is exactly the same if black plays first or if white plays first and, as a consequence the miai value looks like 0.

Does that mean that black cannot gain something by playing first?

Black may choose to play:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . 4 . 3 . . . . |
$$ | . 2 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
next we can expected the following exchange
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . a O 6 X 7 . . . |
$$ | . O . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and here we can see a small gain for black : a ko threat at "a".

Depending of the environment, black may also expect to follow with
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . 4 3 B 5 . . . |
$$ | . . W O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
But in such situation white can change his first move to:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . 2 . 1 . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and after the following expected exchange
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . b W 4 B 5 . . . |
$$ | . . a O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
you can see that black is happy to get 2 ko threats instead of one.

To summarize my analyse :
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . . b . . . . |
$$ | . . a O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
It seems to me that black must play at "a" or "b" when temperature is between 3 and 4. Such move will gain nothing in points but only in terms of ko threats. In addition the choice between a move at "a" or "b" seems quite difficult.

What is your view concerning this quite common situation?
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Bill Spight
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Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:Here is an example of position we encounter very often in practice and not that easy to analyse
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . . . . . . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
What is your analyse of the yose in the upper part of the board?

My view is the following.
Let's suppose white to play with a temperature between 1 and 3. In that case white can play the sequence
Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . . . 3 2 4 . . . |
$$ | . . 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
This sequence seems better that playing :w1: at :b2: to gain 1 point but in gote.
:w1: at :b4: may be possible if white has enough ko threats

Now let's suppose black to play. Black being able to play in sente as soon as temperature drops to 4 I conclude that in practice black will play first in the area when temperature is between 3 and 4.
What black will play?
The first idea is the hane
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . b . 1 . . . . |
$$ | . . a O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and white can answer with a or b.
If the temperature is greater then 3 the more logical move is :w2: at "a" expected following later with :w4: and :b5:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . 4 1 5 . . . |
$$ | . . 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
The point is the following : in this hypothesis the result is exactly the same if black plays first or if white plays first and, as a consequence the miai value looks like 0.

Does that mean that black cannot gain something by playing first?

Black may choose to play:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . 4 . 3 . . . . |
$$ | . 2 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
next we can expected the following exchange
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . a O 6 X 7 . . . |
$$ | . O . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and here we can see a small gain for black : a ko threat at "a".

Depending of the environment, black may also expect to follow with
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . 4 3 B 5 . . . |
$$ | . . W O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
But in such situation white can change his first move to:
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . 2 . 1 . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and after the following expected exchange
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . b W 4 B 5 . . . |
$$ | . . a O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
you can see that black is happy to get 2 ko threats instead of one.

To summarize my analyse :
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . . . b . . . . |
$$ | . . a O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
It seems to me that black must play at "a" or "b" when temperature is between 3 and 4. Such move will gain nothing in points but only in terms of ko threats. In addition the choice between a move at "a" or "b" seems quite difficult.

What is your view concerning this quite common situation?
If White is not komaster, this is a so-called 1 pt. sente, where the reverse sente gains 1 pt.
Click Here To Show Diagram Code
[go]$$B Black sente
$$ -----------------
$$ | . . 2 . 1 . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Local score = +4

As you have pointed out, Black has two net ko threats.
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . . . . 1 2 . . . |
$$ | . . 3 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Score = +3

The mast is colored. (Sorry, I still can't post thermographs. :() Up to temperature 3 White can play with sente, and the mast is purple.
Click Here To Show Diagram Code
[go]$$W White sente
$$ -----------------
$$ | . . . 3 2 4 . . . |
$$ | . . 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Score = +4
:b2: - :b4: gains 3 pts.

From temperature 3 up to 4¼ the mast is blue. Black can play with sente.
Click Here To Show Diagram Code
[go]$$B Black sente
$$ -----------------
$$ | . . 4 . 3 . . . . |
$$ | . 2 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
If Black plays sente above temperature 1 this looks like the best sequence, as Black gets 1 net ko threat.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote: As you have pointed out, Black has two net ko threats.
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . . . . 1 2 . . . |
$$ | . . 3 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Score = +3
Because in the position proposed the key point is the number of ko threats I think you obviously answered here a little too quickly. The move :b2: in the above diagram is not correct. You have to play:
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . 5 4 7 1 6 . . . |
$$ | . 3 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
or
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . 5 3 . 1 6 . . . |
$$ | 7 4 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and in any case black gets a good ko threat
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Here is an example where all possibilties have to be carefully analysed
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . . . . . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . . O O X X X X X |
$$ | O . O X . X . X X |
$$ | . O O X . X O X . |
$$ | O O O O X X . X . |
$$ | O O X X X O O O O |
$$ | O X . X X O . O . |
$$ -----------------[/go]
It seems white can get a draw in two ways:
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . . 3 2 4 . . . |
$$ | . . 1 O O X . . . |
$$ | O O O X X X . . . |
$$ | . . O O X X X X X |
$$ | O . O X . X . X X |
$$ | . O O X . X O X . |
$$ | O O O O X X 5 X 6 |
$$ | O O X X X O O O O |
$$ | O X 7 X X O . O . |
$$ -----------------[/go]
and white wins the ko
or
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . 5 7 4 8 . . . |
$$ | . 3 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . . O O X X X X X |
$$ | O . O X . X . X X |
$$ | . O O X . X O X . |
$$ | O O O O X X 1 X 6 |
$$ | O O X X X O O O O |
$$ | O X 9 X X O . O . |
$$ -----------------[/go]
and again white wins the ko (one ko threat for black and one ko threat white)

but the second sequence is not correct. Black must play
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . . . 2 . . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . . O O X X X X X |
$$ | O . O X . X . X X |
$$ | . O O X . X O X . |
$$ | O O O O X X 1 X . |
$$ | O O X X X O O O O |
$$ | O X . X X O . O . |
$$ -----------------[/go]
and now black wins by one point by
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . 5 4 B 6 . . . |
$$ | . . 3 O O X . . . |
$$ | O O O X X X . . . |
$$ | . . O O X X X X X |
$$ | O . O X . X . X X |
$$ | . O O X . X O X . |
$$ | O O O O X X W X 7 |
$$ | O O X X X O O O O |
$$ | O X 8 X X O . O . |
$$ -----------------[/go]
or
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . 3 5 B 6 . . . |
$$ | . . . O O X . . . |
$$ | O O O X X X . . . |
$$ | . . O O X X X X X |
$$ | O . O X . X . X X |
$$ | . O O X . X O X . |
$$ | O O O O X X W X 4 |
$$ | O O X X X O O O O |
$$ | O X 7 X X O . O . |
$$ -----------------[/go]
and now black wins the the ko because black has two ko threats against only one for white.

Not so easy is it?
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Gérard TAILLE wrote:
Bill Spight wrote: As you have pointed out, Black has two net ko threats.
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . . . . 1 2 . . . |
$$ | . . 3 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Score = +3
Because in the position proposed the key point is the number of ko threats I think you obviously answered here a little too quickly. The move :b2: in the above diagram is not correct. You have to play:
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . 5 4 7 1 6 . . . |
$$ | . 3 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
or
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . 5 3 . 1 6 . . . |
$$ | 7 4 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
and in any case black gets a good ko threat
OC the best sequence for white is
Click Here To Show Diagram Code
[go]$$W White reverse sente
$$ -----------------
$$ | . 5 4 7 1 6 . . . |
$$ | . 3 2 O O X . . . |
$$ | O O O X X X . . . |
$$ | . O . . . X X X X |
$$ | O O . . . . . X . |
$$ | . O . . . . . X X |
$$ | O O . . . . . X . |
$$ | . . . . . . . X X |
$$ | . . . . . . . . . |
$$ -----------------[/go]
because the black threat is smaller
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Let me propose the following small yose problem:
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . . . . . O . . |
$$ | . . . . X O O . . |
$$ | . X X X X O . . . |
$$ | O X O O O O . . . |
$$ | . O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
As we all know you usely cannot get the best yose move without knowing the exact environment.
Here I assume area counting, I assume black is komaster and I assume temperature equal to zero.

Note : I hope the white sequence is unique against the best black defense!
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Bill Spight
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Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:Let me propose the following small yose problem:
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . . . . . . O . . |
$$ | . . . . X O O . . |
$$ | . X X X X O . . . |
$$ | O X O O O O . . . |
$$ | . O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
As we all know you usely cannot get the best yose move without knowing the exact environment.
Here I assume area counting, I assume black is komaster and I assume temperature equal to zero.

Note : I hope the white sequence is unique against the best black defense!
A couple of thoughts. No guarantees. ;)
Click Here To Show Diagram Code
[go]$$Wc Variation 1
$$ -----------------
$$ | . 7 . 2 1 0 O . . |
$$ | 6 4 3 . X O O . . |
$$ | 5 X X X X O . . . |
$$ | W X O O O O . . . |
$$ | 8 O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
:w9: takes back at :wc:
Click Here To Show Diagram Code
[go]$$Wcm11 Variation 1, continued
$$ -----------------
$$ | . O 1 X 2 X O . . |
$$ | X X O . X O O . . |
$$ | . X X X X O . . . |
$$ | O X O O O O . . . |
$$ | . O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Seki. Black gets the last play.
Click Here To Show Diagram Code
[go]$$Wc Variation 2
$$ -----------------
$$ | . 5 9 1 2 . O . . |
$$ | 4 . 8 . X O O . . |
$$ | 3 X X X X O . . . |
$$ | W X O O O O . . . |
$$ | 6 O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
:w7: takes back at :wc:

Seki. White gets the last play.

Better for White.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: Thermography

Post by Gérard TAILLE »

Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | d d b a b d O . . |
$$ | d c b d X O O . . |
$$ | b X X X X O . . . |
$$ | O X O O O O . . . |
$$ | d O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Very good Bill.

If I am not wrong the result (area counting) for each move are the following:
move at "a" point : score -7
move at "b" points : score -5
move at "c" points : score -3
move at "d" points : score -1
tenuki : score +1

For me, the correct move at "a" looked quite difficult to find.

Let me mentionned another tricky variation:
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------
$$ | . 7 1 2 . . O . . |
$$ | 6 4 3 . X O O . . |
$$ | 5 X X X X O . . . |
$$ | O X O O O O . . . |
$$ | 8 O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Click Here To Show Diagram Code
[go]$$Wcm9 White to play
$$ -----------------
$$ | . O O X . 2 O . . |
$$ | X X O . X O O . . |
$$ | . X X X X O . . . |
$$ | 1 X O O O O . . . |
$$ | X O O . . . . . . |
$$ | O O . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -----------------[/go]
Because black is komaster :b10: is possible and white cannot reach the score -7 with this variation.
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