Approximations are not per se bad and I have not seen your final method so cannot comment on it. I have commented on your analysis of this example. More specifically:
Gérard TAILLE wrote:
- Click Here To Show Diagram Code
[go]. . . . . . .|
$$ . . . . . . .|
$$ . . . . X . .|
$$ . . . . X . .|
$$ . . O O X . .|
$$ . . O X O . .|
$$ . . . . O . .|
$$ . . . O . . .|
$$ . . . . . . .|
$$ . . . . . . .|[/go]
First of all my analyse is based on area scoring (and not territory scoring)
Ok.
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At first sight I was convinced that the best black move as well as the best white move where the hane gote moves showed by dfan in
https://lifein19x19.com/viewtopic.php?p=278108#p278108Quoting dfan:
- Click Here To Show Diagram Code
[go]$$B B+3 (the marked stones are Black's privilege)
$$ . . . . . . .|
$$ . . . . . . .|
$$ . . . . X T T|
$$ . . . . X T T|
$$ . . O O X 3 T|
$$ . . O X O 1 #|
$$ . . . . O 2 #|
$$ . . . O . @ @|
$$ . . . . . T T|
$$ . . . . . . .|
$$[/go]
- Click Here To Show Diagram Code
[go]$$W W+5 (the marked stones are an even split)
$$ . . . . . . .|
$$ . . . . . . .|
$$ . . . . X T T|
$$ . . . . X 2 #|
$$ . . O O X 1 @|
$$ . . O X O 3 T|
$$ . . . . O T T|
$$ . . . O . T T|
$$ . . . . . T T|
$$ . . . . . . .|
$$[/go]
That gives a total swing of 8 points in gote.
The result in area approach is the following:
- Click Here To Show Diagram Code
[go]B . . . . . .|
$$ . . . . . . .|
$$ . . . . X . .|
$$ . . . . X . .|
$$ . . O O X M M|
$$ . . O X O M M|
$$ . . . . O . M|
$$ . . . O . . .|
$$ . . . . . . .|
$$ . . . . . . .|[/go]
The five marked intersections represent the intersections each player can gain by playing first.
How do you derive these intersections from dfan's diagrams and 8 points territory difference?
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On average (I mean the count of the position)
Why may you speak of a count of the [local] position when you consider 5 intersections but ignore the adjacent affected intersections?
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2.5 of these intersections are for black and 2.5 are for white.
Why may you form the average on these intersections in the context of the whole local endgame?
What is the meaning of assigne 2.5 to each player so that the impact is 0 because 2.5 for Black minus 2.5 for White from Black's perspective is 0?
Since you make it 0, why may you call it an average?
Quote:
- Click Here To Show Diagram Code
[go]B . . . . . .|
$$ . . . . . . .|
$$ . . . . X . .|
$$ . . . . X . .|
$$ . . O O X a .|
$$ . . O X O b .|
$$ . . . . O . .|
$$ . . . O . . .|
$$ . . . . . . .|
$$ . . . . . . .|[/go]
What about the black sente move at "a" or the white sente move at "b" ?
Why may / do you mean sente moves at this moment of analysis? (Also "sente point" twice below.)
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If black plays at the sente point "a" and white answers at "b" then, comparing to the previous diagram black takes only two of the five marked intersections
Ok.
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=> count is better for white
Better than what? (I can guess, but it is your analysis and must be clear from it.)
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=> black "a" is wrong
This is an adventurous implication. You presume that a) White must answer, b) if White does answer, necessarily it would be bad for Black to maintain the initiative by playing the exchange in a local sente sequence, c) there cannot be a general condition comparing gote sequence option to sente sequence option sometimes determining one or sometimes the other to be correct. Your implication is premature without these considerations or justifying an approximative method with which they are ignored on purpose.
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On the other hand if white plays at the sente point "b" and black answers at "a" then white takes three of the five marked intersections
Ok.
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=> count is better for white
As before.
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=> white "b" is correct providing it is sente.
Now this is better: you consider the sente as a presupposition and case.
However, you make the statement that, assuming sente, White b was correct. As before, this is a premature implication for analogue reasons.
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Obviously the potential sente ogeima after white "b"
Why is the ogeima sente? By experience (Sensei's Library, Bill Spight, I) with careful endgame value analysis, a monkey into two rows of possible territory along the edge is a local gote move.
Therefore, also your "Obviously" must be wrong.
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proves
Wrong statements prove nothing.
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that white "b" is sente
See above.
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=> white "b" is probably the best move.
Writing lots of implication symbols does not establish a proof by itself.
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=> the position is sente for white
You have made too many mistakes and left too many analysis gaps (more than zero) to make your final "implication".