Because my formula are a little different I think we have to clarify two points: firstly what is the value of a move in a ko threat area and secondly when is the game finished.kvasir wrote:Let's look at this model for an approach ko with explicit ko threats again.
First I want to correct some errors I made.
The game form for the model with corrections marked in red ink:
G = { a | G^R }
G^L = { a │ { a - d_1, G │ … } }
G^R = { { … │ { G^L │ … }, H + d_2 } │ H}
H = { H^L | b }
H^L = { a │ { a - d_3, { … | H^R } │ … } }
H^R = { { … │ { H^L │ … }, b + d_4 } │ b }
Now we play this game to discover its structure:
Left:
G => a-t (1)
Right:
G => G^R+t => G^RL => {G^L-t│…}+t => G^L => G^LR-t => a-d_1 (2)
G => G^R+t => G^RL => {G^L-t│…}+t => G^L => G^LR-t => G …ko continues
G => G^R+t => G^RL => H+d_2+t => H^L+d_2 => t+H^LR+d_2 => a-d_3+d_2 (3)
G => G^R+t => G^RL => H+d_2+t => H^L+d_2 => t+H^LR+d_2 => {…│H^R }+d_2 => t+H^R+d_2 => H^RL+d_2 => t+b+d_4+d_2 (4)
G => G^R+t => G^RL => H+d_2+t => H^L+d_2 => t+H^LR+d_2 => {…│H^R }+d_2 => t+H^R+d_2=> {H^L│…}+d_2 => H^L+d_2 …ko continues
G => G^R+t => G^RL => H+d_2+t => H^L+d_2 => t+H^LR+d_2 => {…│H^R }+d_2 => t+H^R+d_2 => no move => 2t+d_2+b (5)
1)What is the value of a move in a ko threat area?
Let'me take again the following example of ko threat area:
After the white ko treat we reach the following position:
This position is very easy to evaluate. The tree is {2|-4} and the miai value is +3.
Taking your notation is it a good understanding to say here that d = +3 ?
IOW when white plays the ko threat white wins d points and if later white executes the ko threat then white will gain again d other points.
When playing a cooled game is it a good understanding that when white plays a ko threat white gains d-t points?
2)When is the game finished?
In the cooled game you consider, is it a good understanding to say that the game is finished when both players prefer to pass instead of playing locally or instead of playing in a ko threat area?
But this is how it works. 
is t+3d while the value of 
is only t+d. Why? Beause 
to 
is gote for black and black gains only t points (and not K/3). The reason for that is that white gets compensation for losing the ko.
white takes ko to reach G'
is a black ko threat and G' becomes G