To my knowledge this problem is not outside Bill'theory in a pure theoritical approach. In practice I think it is again far too difficult.
Why do you say that each player has two options on the first move?

Click Here To Show Diagram Code

[go]$$ simplified
$$ . . X X . X X|
$$ . . X X X X M|
$$ . . X . X M M|
$$ . . X X X M M|
$$ O O O O X M M|
$$ O . O . O M M|
$$ O O O O O M M|
$$ O X X O M M M|
$$ O X X M M M M|
$$ O X X X X X X|[/go]

For a theoritical point of view each player has 18 options. In practice OC I know each player can prune a lot of options but it is always the same problem: you yourself often claimed (see for example https://lifein19x19.com/viewtopic.php?p=278141#p278141) that if you do not PROVE that a given pruning is justified then you cannot be sure of your result.

For your own method I am very surprised you can think that this position may be outside your theory.
I am far more optimist. I am sure this position is not outside your theory.
Theory is not practice.

Right, after ignoring all the obviously inferior move candidates.

Maybe your preference of a rich end of Black's region results in a theoretically more interesting position more likely testing my theory.

Why do you think it would fit Bill's theory rather than mine? As far as I recall, his was the partial draft of mine. Maybe you have some other of his theories in mind, which I do not recall right now?

I hope we will not need thermography on two pairs of options; this would be hard to extract from the theory books and apply.

It is not my preference. It YOUR suggestion to simply the position and to avoid ambiguity


Conerning Bill's theory I remember Bill mentionned options at each node of the tree including the root => I guess Bill's theory takes really all options including at root but I am not an expert on such theory.
For your theory I have only available the information you gave on this forum. If you have doubts about the handling of options at the root in your theory then, though it appears quite surprising, I have to have also doubts.

In any case I you claim that the position considered is out the scope of the known theory I trust you but you do non seem to be so sure, are you?

Not his theory, but sometimes his good practice. He knew the basics of CGT, which always considers all options:)



I suspect it might be but I have to look at it more carefully.

flashcard 39

Click Here To Show Diagram Code

[go]. . . . . . .|
$$ . . . . . . . .|
$$ . . . . . O . .|
$$ . . O . O . . .|
$$ . . . . . . . .|
$$ . . . . . . . .|
$$ . . O O O O a .|
$$ . . X O X X b .|
$$ . . X X . . . .|
$$ . . . . . . . .|
$$----------------|[/go]

The diagram of the flashcard suggests a black move at "a".
My feeling is that black "b" is better. What is your view?

Assuming one gote and one sente option, the choice between both also depends on the global environment. A local analysis predicts the more likely choice. Another interesting question is whether it is White's local sente but the position is ambiguous with respect to the lower side.

Let's try to answer concerning the two options for white:

I guess with white sente you mean white sagari but after

Click Here To Show Diagram Code

[go]$$W diag 1
$$ . . . . . . . .|
$$ . . . . . . . .|
$$ . . . . . O . .|
$$ . . O . O . . .|
$$ . . . . . . . .|
$$ . . . . . . . .|
$$ . . O O O O 1 5|
$$ . . X O X X 2 3|
$$ . . X X . . . 4|
$$ . . . . . . . .|
$$----------------|[/go]

black plays tenuki => white is gote

In now you play white hane instead of white sagari then it follows

Click Here To Show Diagram Code

[go]$$W diag 2
$$ . . . . . . . .|
$$ . . . . . . . .|
$$ . . . . . O . .|
$$ . . O . O . . .|
$$ . . . . . . . .|
$$ . . . . . . . .|
$$ . . O O O O 7 .|
$$ . . X O X X 1 .|
$$ . . X X 4 3 2 5|
$$ . . . . . . 6 .|
$$----------------|[/go]

Compararing diag 1 and diag 2, it appreas that diag2 is better for white => as first move white hane is better than white sagari

Why move 7 instead of tenuki?

You are right Robert white move 7 tenuki is very interesting but it was not the point in my previous post.
My purpose was ONLY to show white hane is better than white sagari. The white 7 connect move is enough to show that white hane is better => white sagari is a bad option.

What about the following position for which each player has only one option (move at "a") on the first move:

Click Here To Show Diagram Code

[go]$$B
$$------------------------
$$ . . . . . . . a . O . .
$$ . . . . . . . X O O . .
$$ . . X . . . . . X O . .
$$ . . . . X . X X X O . .
$$ . . . . . . . . . .
$$ . . . . . . . . . .[/go]

How do you calculate the move value in your theory?
Robert, could this position be out the scope of your theory?

Edit: after a deeper analysis, the position above has not all the properties I expected. Here after is a position corresponding to what I had in mind.

Click Here To Show Diagram Code

[go]$$B
$$----------------------------
$$ . . . . . . . a . O O . . .
$$ . . . . . . . X O . . O . .
$$ . . X . . . . . X O O O . .
$$ . . . . X . X X X . . . . .
$$ . . . . . . . . . . . . . .
$$ . . . . . . . . . . . . . .[/go]

What is the definition of the move value? With this definition how do you calculate the move value of this position?

If we ignore intermediate ko options, my theory should apply. With them, I would need to check carefully if it applies, Currently, people try to load tasks for 300% of my time on me; you cannot show more and more positions and expect solutions when I do not even have time for the first.