Approximations for the big endgame?

[Gérard TAILLE]

Basically, for the G = { gote | reverse-sente } case I let

G_L := { 10 + A | 2 }
G_R := { -2 | B - 10 }
G := { G_L | G_R }

I see where is the misunderstanding.
For the reverse sente branch you use
G_R := { -2 | B - 10 }
where I use just
G_R := { - 10 }
The point is the following : in the reverse sente situation you described black cannot allow white to gain B points because B is too big. As a consequence the value B cannot appear in the result.

[RobertJasiek]

how to verify such rules, both based on comparing with exact estimates and based the kinds of errors that are possible.

What is an "exact estimate"? :) How about "exact value"?

Before adding errors, study simple local endgames that do not have any error. (Or make studies boring by introducing all-dominating errors as upper bounds.)

How to verify rules about exact values? Do proper maths! Write down your assumptions and conjecture! Prove it mathematically! (If you can't, try harder or face the possibility that you set bad assumptions or an invalid conjecture.) If you do not want to reinvent the wheel, read my or Bill's theorems.

Once you will have done local, simple endgames correctly, you can then relax some assumptions and study semi-open environments of local endgames. Do proper maths for them. Simplify whenever possible or be prepared to study for years! This is no joke. I did spend years on such.

[kvasir]

Basically, for the G = { gote | reverse-sente } case I let

G_L := { 10 + A | 2 }
G_R := { -2 | B - 10 }
G := { G_L | G_R }

I see where is the misunderstanding.
For the reverse sente branch you use
G_R := { -2 | B - 10 }
where I use just
G_R := { - 10 }
The point is the following : in the reverse sente situation you described black cannot allow white to gain B points because B is too big. As a consequence the value B cannot appear in the result.

First of all G_R := { - 10 } is a set containing the number -10. I have no idea what you mean by that. Do you mean that the value of G_R is -10, i.e. G_R = -10? That could be true for particular cases, that would be same as letting B = 0 in my formulation.

I don't understand what you mean by "described black cannot allow white to gain B points because B is too big". I did point out to you that you appeared to change the meaning of B, can we make sure we are using my B?

[Gérard TAILLE]

First of all G_R := { - 10 } is a set containing the number -10. I have no idea what you mean by that. Do you mean that the value of G_R is -10, i.e. G_R = -10? That could be true for particular cases, that would be same as letting B = 0 in my formulation.

I don't understand what you mean by "described black cannot allow white to gain B points because B is too big". I did point out to you that you appeared to change the meaning of B, can we make sure we are using my B?

Ok let me try my best to unerstand your point.

The position corresponding to G_R is the following

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . . X|
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . . X|
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

From that position is black plays first we reach the position R1:

$$B
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$B
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

with the count -2

If now white plays first we reach the position R2:

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

From this position I understand you continue the analysis considering black playing first and white playing first.

From R2 if black plays first you reach position R3

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . 4 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . 4 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

and you estimate the count to be -10 (OK with you, it does not matter if the estimation is -10 or -9)

From R2 if white plays first you reach position R4

$$W B4 missing
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . O .|
$$ . . . . 4 3 1 . O|
$$ . . . . . 2 5 X .|
$$ . . . . . . X 6 .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W B4 missing
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . O .|
$$ . . . . 4 3 1 . O|
$$ . . . . . 2 5 X .|
$$ . . . . . . X 6 .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

and you estimate the count to be -10 + B (where B is a negative value)

If it is true then my point is the following: assume B being BIG. Starting from R1 the expected sequence becomes only

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . 4 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . 4 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

the black move is mandatory because B is too big to allow a black tenuki.
That means that R1 is a reverse sente position and the count of the position R1 is -10 (the value B cannot appear in this result can it?).

[kvasir]

That means that R1 is a reverse sente position and the count of the position R1 is -10 (the value B cannot appear in this result can it?).

Thank you for the explanation.

I view B as a variable, not a value. The variable will appear even if always B = 0.

I think I need to reiterated that I am talking about a method to estimate various similar positions, not only the exact position shown. This is why there are variables representing values that need to be estimated in each situation. If it was only one position then there would be no need for variables and I this discussion wouldn't make any sense.

Without trying too hard to convince you I still want to point out that even in this exact position there are various ways to play and the correct continuations would change if we were to add or remove stones to create a more realistic position.

You showed this variation but note that white can approach this differently and it could be a problem for black in exactly the kind of open to the center positions shown in the diagrams.

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

Another way for white could be

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . 3 . .|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . 3 . .|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

Which continuation is correct depends on many factors, the player using these formulas would have to choose the continuations.

I hope this clears something up. In the OP I asked some questions but didn't necessarily expect answers.

Anyway, please don't take this too seriously, it is about an idea and having a conversation. For now we appear to talk cross purposes, it is like I want to do one thing here but you want to do another. I think if I were to improve on anything, for example correct mistakes and improve the presentation of the idea, I'd have to understand this confusion. It is possible that I have made some grievous mistake and that is the source of the confusion, I mean I did write "apples" when I meant "applies".

I wanted to reply to Robert's good suggestions just now but that will have to wait another day.

[Gérard TAILLE]

That means that R1 is a reverse sente position and the count of the position R1 is -10 (the value B cannot appear in this result can it?).

Thank you for the explanation.

I view B as a variable, not a value. The variable will appear even if always B = 0.

I think I need to reiterated that I am talking about a method to estimate various similar positions, not only the exact position shown. This is why there are variables representing values that need to be estimated in each situation. If it was only one position then there would be no need for variables and I this discussion wouldn't make any sense.

Without trying too hard to convince you I still want to point out that even in this exact position there are various ways to play and the correct continuations would change if we were to add or remove stones to create a more realistic position.

You showed this variation but note that white can approach this differently and it could be a problem for black in exactly the kind of open to the center positions shown in the diagrams.

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . . . 3|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

Another way for white could be

$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . 3 . .|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . .|
$$ . . . . . . . . .|
$$ . . O . . . . . .|
$$ . . . . O O O O O|
$$ . . . X X X X X O|
$$ . . . . . . . 1 X|
$$ . . . . . . 3 . .|
$$ . . . . . . . 2 .|
$$ . . . . . . X . .|
$$ . . . . . , . . .|
$$ . . . . . . . . .|[/go]

Which continuation is correct depends on many factors, the player using these formulas would have to choose the continuations.

I hope this clears something up. In the OP I asked some questions but didn't necessarily expect answers.

Anyway, please don't take this too seriously, it is about an idea and having a conversation. For now we appear to talk cross purposes, it is like I want to do one thing here but you want to do another. I think if I were to improve on anything, for example correct mistakes and improve the presentation of the idea, I'd have to understand this confusion. It is possible that I have made some grievous mistake and that is the source of the confusion, I mean I did write "apples" when I meant "applies".

I wanted to reply to Robert's good suggestions just now but that will have to wait another day.

I like very much your approach because you try to handle positions in a context where the classical approach (miai calculation) cannot be applied in practice. Maybe (?) I also like very much your approach because I see some similarity with my own method!

The main point that is very satisfactory for me is the top-down approach. You "estimate" the value of the root position and in order to have a better evaluation you try also to "estimate" the value of some follow-up. Though I proceed differently I am convinced that this idea is the best approach in the big endgame phase and I am happy to exchange with you around such idea.