Gérard TAILLE wrote:
white plays first : white "c" : count = ((-34.33) + (-23.33)) / 2 = -57.66/2 = -28.83
White starts in reverse sente: the local count is R := -23 1/3.
White starts locally and Black replies in the environment taking T: the count of the settled regions is -23 1/3.
White starts with two successive moves, one local, one in the environment taking T: the count of the settled regions is -34 1/3.
You treat the position after White's local start as one in which to calculate the gote count of the largest region in the environment and ignore the remaining the environment, wherefore you calculate accordingly getting -28 5/6.
This is not what the theory uses.
The theorem is:
"If F < T, usually start
- in the environment if MGOTE ≤ T,
- locally if MGOTE ≥ T (the creator chooses the gote option)."
To apply the theorem, we need to determine F, T and MGOTE.
The temperature T is determined by analysing only the T region locally as a local gote and calculating its gote move value T = (11 - 0 ) / 2 = 5 1/2 or by counting 5 stones (contributing 5) and 1 inside intersection (contributing 1/2) to the move value. You have failed to determine T at all.
You have failed to calculate F. To determine the sente option's follow-up move value F, you need to consider the suitable intermediate local follow-up position after the start of the sente sequence:
- Click Here To Show Diagram Code
[go]$$B start of the sente sequence
$$ ---------------------------
$$ | O . X X . . 1 3 X . X X .
$$ | O O . O X . O 2 O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]
- Click Here To Show Diagram Code
[go]$$B intermediate follow-up position
$$ ---------------------------
$$ | O . X X . . X X X . X X .
$$ | O O . O X . O O O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]
- Click Here To Show Diagram Code
[go]$$B Black continues locally
$$ ---------------------------
$$ | O . X X . 1 X X X . X X .
$$ | O O . O X . O O O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]
- Click Here To Show Diagram Code
[go]$$W White continues locally
$$ ---------------------------
$$ | O . X X . 1 X X X 2 X X .
$$ | O O . O X 3 O O O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]
Now, calculate F.
Quote:
black plays first :
1)black "a", gote option : count = (-12 + -23)/2 = -17.5
Black starts locally taking the gote option: the local count is H := -12.
You have failed to identify the meaning of this value as such.
In more careful annotation, you would have calculated a gote count = (-12 + (-23))/2 = -17.5 for the combination of the gote option after Black taking it and the T region but we do not need such a value.
Quote:
2)black "b", sente option : count = -23.33
MGOTE = ((-17.5) - (-28.83)) / 2 = 11.33/2 = 5.66
MSENTE = (-23.33) - (-28.83) = 5.5
Black starts locally taking the sente option: the local count is S := -19.
The gote option's gote move value is
MGOTE = (H - R) / 2 = (-12 - (-23 1/3)) / 2 = 5 2/3.
You have calculated the gote move value wrongly.
The sente option's sente move value is
MSENTE = S - R = -19 - (-23 1/3) = 4 1/3.
You have calculated the sente move value wrongly.
Although the theorem does not explicitly refer to H, S and MSENTE, a careful use before its application verifies these additional conditions:
H ≥ S > R <=> -12 ≥ -19 > -23 1/3 (so that the gote and sente options are meaningful).
F > MSENTE (so that the sente option is such indeed).
The theorem requires the other assumption of having a high temperature explicitly: F < T.
You can verify the latter two relations after you will have calculated F.
Quote:
MGOTE > MSENTE => in this position your theorem does not apply;
This relation is irrelevant for using the theorem. Both as implicit presupposition or as explicit condition in the theorem.
Quote:
you know that the sente option is not a good option without looking at T or F.
If you cannot find a position in which your theorem can be applied can you simply give us a tree showing the idea behind your (strange?) theorem?
Correct your mistakes, complete your missing parts and then judge about my example again!
3 EDITs: calculations related to F > MSENTE and MGOTE > MSENTE.