This 'n' that

Bill Spight · **#1021**

Gérard TAILLE wrote:

Bill Spight wrote:

Yes. How silly of me.

I have corrected the above note.

Gérard TAILLE wrote:

Secondly, by applying my formula, why the environment E = {3¾|-3¾} + {1|1} is not ideal for the game G0?

First, it is not hot enough. 3¾ < 5½.
Second, it does not include {2|-2}.
Third, it is not ideal. 3¾ - 1 = 2¾, not 3¾/2 = 1⅞.

OK Bill, it was not clear in your definition that the environment must contain at least a gote point at the temperature of G0 and all its subgames (your first two points).
However I do not understand your third point. Why to calculate the score of the environment at temperature 3¾?

Because that is the temperature of the environment.

Remember, I am adding and subtracting the final score of playing in the environment, which must be ideal, regardless of any other game.

Gérard TAILLE wrote:

I do not see in the defintion where you calculate the score of the environment for a temperature that does not correspond to the temperature of G0 or a subgame of G0.

Because in E = {3¾|-3¾} + {1|1} the gote 5½ and 2 are missing why not to take the simple environment:

E = {5½|-5½} + {3¾|-3¾} + {2|2} + {1|1}

If you ignore the requirement of a constant difference, ∆, between temperatures, that environment will do.

Gérard TAILLE · **#1022**

Bill Spight wrote:

If you ignore the requirement of a constant difference, ∆, between temperatures, that environment will do.

I do not understand Bill.
It is a new requirement isn'it?

Remember your own proposals:

Bill Spight wrote:

The simplest ideal environment that meets all the requirements is this:

{5½|-5½}, {5¼|-5¼}, {5|-5} . . . , {2|-2}, {1¾|-1¾}, {1½|-1½} . . . , {¼|-¼}.

This environment will also work.

{5½|-5½}, {5¼|-5¼}, {4¾|-4¾}, {4¼|-4¼} . . . , {2¼|-2¼}, {2|-2}, {1¾|-1¾}, {1¼|-1¼}, {¾|-¾}, {¼|-¼}.

This requirement is fullfilled in your first example but not in your second example is it?

In addition, for a theoritical point of view, what is the need for such requirement? IOW how this requirement is used inside theory? For proving what?

Bill Spight · **#1023**

Gérard TAILLE wrote:

Bill Spight wrote:

If you ignore the requirement of a constant difference, ∆, between temperatures, that environment will do.

I do not understand Bill.
It is a new requirement isn'it?

No. It was part of the original idea.

Gérard TAILLE wrote:

Remember your own proposals:

Bill Spight wrote:

The simplest ideal environment that meets all the requirements is this:

{5½|-5½}, {5¼|-5¼}, {5|-5} . . . , {2|-2}, {1¾|-1¾}, {1½|-1½} . . . , {¼|-¼}.

This environment will also work.

{5½|-5½}, {5¼|-5¼}, {4¾|-4¾}, {4¼|-4¼} . . . , {2¼|-2¼}, {2|-2}, {1¾|-1¾}, {1¼|-1¼}, {¾|-¾}, {¼|-¼}.

This requirement is fullfilled in your first example but not in your second example is it?

The second example, which is not a proposal, was to accommodate your thinking, that's all.

Gérard TAILLE · **#1024**

Bill Spight wrote:

Gérard TAILLE wrote:

Bill Spight wrote:

If you ignore the requirement of a constant difference, ∆, between temperatures, that environment will do.

I do not understand Bill.
It is a new requirement isn'it?

No. It was part of the original idea.

Gérard TAILLE wrote:

Remember your own proposals:

Bill Spight wrote:

The simplest ideal environment that meets all the requirements is this:

{5½|-5½}, {5¼|-5¼}, {5|-5} . . . , {2|-2}, {1¾|-1¾}, {1½|-1½} . . . , {¼|-¼}.

This environment will also work.

{5½|-5½}, {5¼|-5¼}, {4¾|-4¾}, {4¼|-4¼} . . . , {2¼|-2¼}, {2|-2}, {1¾|-1¾}, {1¼|-1¼}, {¾|-¾}, {¼|-¼}.

This requirement is fullfilled in your first example but not in your second example is it?

The second example, which is not a proposal, was to accommodate your thinking, that's all.

OK Bill, finally I understand an ideal environment for a game G0 is a rich environment with granularity ∆ such that:

Bill Spight wrote:

the net score by alternating play for Black playing first for each t(G_i) = t(G_i)/2, and the net score by alternating play for White playing first for each t(G_i) = -t(G_i)/2; and furthermore that there are sufficient gote in the environment at each t(G_i) for all ko and superko fights at that temperature to be resolved at that temperature.

As I mentionned earlier, the problem is that t(G_i) are not known at the beginning of the analysis and in this context it is theoriticaly quite impossible to choose correctly the granularity ∆.

I suspect in practice you use essentially a more general ideal environment (something which looks like the limit of a rich environment when the granularity goes towards 0).
When do you really use a rich environment with granularity ∆ > 0 ?

Bill Spight · **#1025**

Gérard TAILLE wrote:

OK Bill, finally I understand an ideal environment for a game G0 is a rich environment with granularity ∆ such that:

Bill Spight wrote:

the net score by alternating play for Black playing first for each t(G_i) = t(G_i)/2, and the net score by alternating play for White playing first for each t(G_i) = -t(G_i)/2; and furthermore that there are sufficient gote in the environment at each t(G_i) for all ko and superko fights at that temperature to be resolved at that temperature.

As I mentionned earlier, the problem is that t(G_i) are not known at the beginning of the analysis and in this context it is theoriticaly quite impossible to choose correctly the granularity ∆.

Not so. The temperatures of the game and subgames are variables which may be solved for. Once that is done, it is easy to find an acceptable ∆ to construct an ideal environment.

Gérard TAILLE wrote:

I suspect in practice you use essentially a more general ideal environment (something which looks like the limit of a rich environment when the granularity goes towards 0).
When do you really use a rich environment with granularity ∆ > 0 ?

For any given finite combinatorial game, such an ideal environment exists.

Edit: I should qualify that by saying that a game or subgame with temperature 0 does not require an environment.

Gérard TAILLE · **#1026**

Bill Spight wrote:

Gérard TAILLE wrote:

OK Bill, finally I understand an ideal environment for a game G0 is a rich environment with granularity ∆ such that:

Bill Spight wrote:

the net score by alternating play for Black playing first for each t(G_i) = t(G_i)/2, and the net score by alternating play for White playing first for each t(G_i) = -t(G_i)/2; and furthermore that there are sufficient gote in the environment at each t(G_i) for all ko and superko fights at that temperature to be resolved at that temperature.

As I mentionned earlier, the problem is that t(G_i) are not known at the beginning of the analysis and in this context it is theoriticaly quite impossible to choose correctly the granularity ∆.

Not so. The temperatures of the game and subgames are variables which may be solved for. Once that is done, it is easy to find an acceptable ∆ to construct an ideal environment.

Gérard TAILLE wrote:

I suspect in practice you use essentially a more general ideal environment (something which looks like the limit of a rich environment when the granularity goes towards 0).
When do you really use a rich environment with granularity ∆ > 0 ?

For any given finite combinatorial game, such an ideal environment exists.

I see you assume explicitly combinatorial game which means that you exclude kos.
Knowing that a lot of works have been made in termography on kos, do you use also such ideal environment for a position implying a potential ko fight like in the position

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . $$ | a X O O X . . $$ | X . O X X . . $$ | . O O X . . . $$ | . O X X . . . $$ | . X . . . . . $$ | . X . . . . . $$ | X X . . . . . $$ | . . . . . . . $$ | . . . , . . .[/go]

It is easy to find an environment in which "a" is better than "b" and vice versa.
In this context, is it interesting to go further by studying the moves "a" and "b" at various temperatures in an ideal environment or do you consider such analyse cannot be useful.
IOW does it make sense to you to say for example : if t0 < t < t1 then move "a" is better than "b" in an ideal environment.

Though we know there are no ko nor ko threats in an ideal environment I am not sure you accept this wording if t0 < t < t1 then move "a" is better than "b" in an ideal environment because we know also that the local ko is of primary importance.

How do you suggest to continue the analyse to try and reach an interesting conclusion?

Bill Spight · **#1027**

Gérard TAILLE wrote:

I suspect in practice you use essentially a more general ideal environment (something which looks like the limit of a rich environment when the granularity goes towards 0).
When do you really use a rich environment with granularity ∆ > 0 ?

Bill Spight wrote:

For any given finite combinatorial game, such an ideal environment exists.

Gérard TAILLE wrote:

I see you assume explicitly combinatorial game which means that you exclude kos.

My mistake. My redefinition of thermography was in a paper about multiple kos and superkos, so I include them, as well.

And, as I indicated in my edit, if the game or subgame has temperature 0, it is not necessary to have an ideal environment to play in at temperature 0.

Bill Spight · **#1028**

Gérard TAILLE wrote:

Knowing that a lot of works have been made in termography on kos, do you use also such ideal environment for a position implying a potential ko fight like in the position

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . $$ | a X O O X . . $$ | X . O X X . . $$ | . O O X . . . $$ | . O X X . . . $$ | . X . . . . . $$ | . X . . . . . $$ | X X . . . . . $$ | . . . . . . . $$ | . . . , . . .[/go]

It is easy to find an environment in which "a" is better than "b" and vice versa.

I am not so sure.

Gérard TAILLE wrote:

In this context, is it interesting to go further by studying the moves "a" and "b" at various temperatures in an ideal environment or do you consider such analyse cannot be useful.
IOW does it make sense to you to say for example : if t0 < t < t1 then move "a" is better than "b" in an ideal environment.

Though we know there are no ko nor ko threats in an ideal environment I am not sure you accept this wording if t0 < t < t1 then move "a" is better than "b" in an ideal environment because we know also that the local ko is of primary importance.

How do you suggest to continue the analyse to try and reach an interesting conclusion?

Let me help you out, here.

Although Berlekamp said that thermographs reveal correct play, he did not mean globally correct play for ko or superko fights or potential ko or superko fights, because of the ko caveat. That is why I have suggested using the qualification, "thermographically" for statements about how good a play is at certain temperatures.

So, when you compare move a vs. move b at certain temperatures, which I agree is useful to do, you have to specify the assumptions you are making about the ko situation. Which you have not done. Is either player komaster? Do we assume NTE? Do we assume specific ko threats? Do we assume no ko threats?

Note that you cannot use komonster analysis, because that involves pseudothermography. You can approach that by putting specific temperature drops in the ko ensemble.

Once you have specified the assumptions about the ko situation, we can draw the thermograph. For instance, you might specify no ko threats, and this game, {½|-½}, in the ko ensemble.

Gérard TAILLE · **#1029**

Bill Spight wrote:

Gérard TAILLE wrote:

Knowing that a lot of works have been made in termography on kos, do you use also such ideal environment for a position implying a potential ko fight like in the position

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . $$ | a X O O X . . $$ | X . O X X . . $$ | . O O X . . . $$ | . O X X . . . $$ | . X . . . . . $$ | . X . . . . . $$ | X X . . . . . $$ | . . . . . . . $$ | . . . , . . .[/go]

It is easy to find an environment in which "a" is better than "b" and vice versa.

I am not so sure.

Let's try to convince you.

It seems move "a" is better than move "b" at temperature 0 because white at "b" allows black to try and get a seki.

I believe move "b" is better than move "a" in the following position but I am not completly sure

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

Bill Spight · **#1030**

Gérard TAILLE wrote:

Bill Spight wrote:

Gérard TAILLE wrote:

Knowing that a lot of works have been made in termography on kos, do you use also such ideal environment for a position implying a potential ko fight like in the position

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . $$ | a X O O X . . $$ | X . O X X . . $$ | . O O X . . . $$ | . O X X . . . $$ | . X . . . . . $$ | . X . . . . . $$ | X X . . . . . $$ | . . . . . . . $$ | . . . , . . .[/go]

It is easy to find an environment in which "a" is better than "b" and vice versa.

I am not so sure.

Let's try to convince you.

It seems move "a" is better than move "b" at temperature 0 because white at "b" allows black to try and get a seki.

I believe move "b" is better than move "a" in the following position but I am not completly sure

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

You don't say so, but I think you intend temperature 0 with no ko threats.

Edit: Embarrassing error in SGF file. :oops:

Edit: Life in 19x19 cannot handle a 17x17 board as an SGF file.

Gérard TAILLE · **#1031**

Bill Spight wrote:

Gérard TAILLE wrote:

Let's try to convince you.

It seems move "a" is better than move "b" at temperature 0 because white at "b" allows black to try and get a seki.

I believe move "b" is better than move "a" in the following position but I am not completly sure

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

You don't say so, but I think you intend temperature 0 with no ko threats.

Edit: Life in 19x19 cannot handle a 17x17 board as an SGF file.

Oops a kind of typing error Bill.
I put the position on 19x19 board but I draw it on a 17x17 board. The result is that a gote point is missing in the environment!

Here is the position I had in mind

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

The idea is the following

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

Click Here To Show Diagram Code: [go]$$Wm7 White to play $$ -------------- $$ | X 1 X O X . . . . . . . $$ | 3 X O O X . . . . . . . $$ | X 5 O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | X O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O 6 O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O 4 O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O 2 O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O O O . . . . . $$ |------------------------[/go]

you see that :w1:

is not very attractive because black is able to take three of the four gote points in the environment.
I hope it works well.

Very sorry for this error Bill.

Bill Spight · **#1032**

Thanks.

It looks like the throw-in beats the sagari.

Edited for correctness.

Gérard TAILLE · **#1033**

[quote="Bill Spight"]Thanks.

It looks like the throw-in beats the sagari.

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | 2 O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

after

why did you not play :b2:

as I suggested?

Bill Spight · **#1034**

Gérard TAILLE wrote:

Bill Spight wrote:

Thanks.

It looks like the throw-in beats the sagari.

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | 2 O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

after

why did you not play :b2:

as I suggested?

I did, in the diagram with 3 4 point gote. But I played too quickly in the intended diagram.

You are right, that works to let Black get 3 of the 4 4 point gote.

Gérard TAILLE · **#1035**

Bill Spight wrote:

Gérard TAILLE wrote:

Bill Spight wrote:

Thanks.

It looks like the throw-in beats the sagari.

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | 2 O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

after

why did you not play :b2:

as I suggested?

I did, in the diagram with 3 4 point gote. In the intended diagram with 4 4 point gote, the 2 miai pairs act as defensive ko threats for White if Black takes the ko. Besides, the hane sets up the sente to hold White to ½ point less than if Black does not play the hane.

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | a O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | b O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

In your sequences, on :w1:

I see only the answer black hane at "b" but not my suggestion black takes at "a".
What is your answer if black takes at "a"?

Gérard TAILLE · **#1036**

Gérard TAILLE wrote:

Bill Spight wrote:

I did, in the diagram with 3 4 point gote. In the intended diagram with 4 4 point gote, the 2 miai pairs act as defensive ko threats for White if Black takes the ko. Besides, the hane sets up the sente to hold White to ½ point less than if Black does not play the hane.

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | a O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | b O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

In your sequences, on :w1:

I see only the answer black hane at "b" but not my suggestion black takes at "a".
What is your answer if black takes at "a"?

edit : four gote points in the environment instead of three

Bill Spight · **#1037**

Gérard TAILLE wrote:

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | a O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | b O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

In your sequences, on :w1:

I see only the answer black hane at "b" but not my suggestion black takes at "a".
What is your answer if black takes at "a"?

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | 2 O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | 3 O X X . . . . . . . . $$ | 4 X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | 2 O . . X . . . . . . . $$ | 1 X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | 4 O X X . . . . . . . . $$ | 3 X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

Both of these sequences lose 2 points to the initial sagari, I believe.

Gérard TAILLE · **#1038**

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

In the position above, are you now convinced that the sagari is the best move or are you still analysing the different variants?

Bill Spight · **#1039**

Gérard TAILLE wrote:

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ | X X X X X X O . . . . . $$ | X O O O O . O . . . . . $$ |------------------------[/go]

In the position above, are you now convinced that the sagari is the best move or are you still analysing the different variants?

Yesterday, as a favor to you, I did a fairly exhaustive analysis of the ko ensemble with 3 simple gote, because you had expressed some doubts. Later I was in a rush on the 4 simple gote ko ensemble and now believe that the initial sagari is better in that case.

Gérard TAILLE · **#1040**

Bill Spight wrote:

Yesterday, as a favor to you, I did a fairly exhaustive analysis of the ko ensemble with 3 simple gote, because you had expressed some doubts. Later I was in a rush on the 4 simple gote ko ensemble and now believe that the initial sagari is better in that case.

With this last answer I have no more doubt on the fact that it exists environment implying sagari is the best move. I appreciate your help Bill, thank you very much for all the time you use for that.

Click Here To Show Diagram Code: [go]$$W White to play $$ -------------- $$ | . O . b X . . . . . . . $$ | a X O O X . . . . . . . $$ | X . O X X . . . . . . . $$ | . O O X . . . . . . . . $$ | . O X X . . . . . . . . $$ | . X . . . . . . . . . . $$ | . X . . . . . . . . . . $$ | X X . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . . $$ | . . . . . . . . . . . .[/go]

My goal is to try to draw the thermograph of the position above but it is not easy !

OC I will first try to draw the thermograph of the position:

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

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