Engame value of ko

Gérard TAILLE · **#81**

RobertJasiek wrote:

Compare the stated black and white walls - they are equal!

It is not my method but Berlekamp's method according to Siegel's description. I am just one who currently applies it.

You mention your method but have you stated it somewhere? If alternative methods exist, fine. However, what is it and what is its (proven) scope? Generalised thermography is proven and its scope is simple loopy games (incl. non-ko games).

For intermediate subpositions, move value and count are often needed but you can call them auxiliary move value and count or, in CGT parliance, local temperature and mast value (for ko thermography, mean value would be the wrong term).

Node is a valid term in graph theory or informatics. Siegel uses the term subposition when he studies CGT. CGT explores many games, not just Go, so most CGT terms do not conform to go terms. Left = Black, Right = White etc. Go players use the term follow-up position and (as I have clarified) follower for an unsettled follow-up position. A leaf is a settled position and related to a CGT number. One can assign states to a node aka subposition aka follow-up position.

It is an exaggeration to say that my first post defined terms; rather, I have given some semi-formal descriptions of terms occurring in Siegel's attempted definition. I have not wanted to repeat Siegel's maths annotation but rather tried to explain it briefly for everybody having some thermographic background.

The method I use is not really mine. It is simply a systematic application of tree manipulation you can find under https://senseis.xmp.net/?MiaiValuesList%2FDiscussion
Maybe what is new is the manipulation of a tree in case of a corridor. In this particular case I can reach the result rather quickly. Though it seems to work quite well I have some doubt with your 2-stage ko position.
See https://senseis.xmp.net/?MiaiValuesList%2F000To099#toc2 where you can find the following position

Click Here To Show Diagram Code: [go]$$W $$ ----------- $$ | O a . X . $$ | . O X X X $$ | O O . X . $$ | . O . . . $$ | . O . . .[/go]

It is said that a black move at "a" has a value 1/6 (assuming neither black nor white is komaster).
In my approach a black move at "a" is a weak move and for that the reason I have some doubt on my method.
With your knowledge of this 2-stage ko can you show me how this move can be valued 1/6 ? That way I will know my method is not correct (at least for such kind of positions)

RobertJasiek · **#82**

The 1/6 or 1/9 ko is interesting but I have 30 stage-ko related positions whose evaluation is more urgent because they occur in practice.

The tree manipulation on that webpage

- uses some CGT methods

- was a predecessor mainly by Bill Spight to my method of making a hypothesis

- is somewhat dubios because shorter sequences are checked before longer sequences whether they are worth playing succesdively; making a hypothesis does it the other way round so overriding longer sequences are not overlooked

- is wrong when comparing the tentative initial move value to an alternating sequence's followers' move values; see my counter-example proving that the comparison is not coorect in general; instead, one must compare to the followers' gains, which is more natural anyway and I have proved that one need not compare to the subsequent move value after the traversal sequence to verify its stop

Gérard TAILLE · **#83**

RobertJasiek wrote:

The 1/6 or 1/9 ko is interesting but I have 30 stage-ko related positions whose evaluation is more urgent because they occur in practice.

The tree manipulation on that webpage

- uses some CGT methods

- was a predecessor mainly by Bill Spight to my method of making a hypothesis

- is somewhat dubios because shorter sequences are checked before longer sequences whether they are worth playing succesdively; making a hypothesis does it the other way round so overriding longer sequences are not overlooked

- is wrong when comparing the tentative initial move value to an alternating sequence's followers' move values; see my counter-example proving that the comparison is not coorect in general; instead, one must compare to the followers' gains, which is more natural anyway and I have proved that one need not compare to the subsequent move value after the traversal sequence to verify its stop

Click Here To Show Diagram Code: [go]$$W $$ ----------- $$ | O a . X . $$ | . O X X X $$ | O O . X . $$ | . O . . . $$ | . O . . .[/go]

What'is wrong with my proof that black 1 at "a" is a weak move.
Let's assume the temperature is very small, for example t = 0.01

black to move

Click Here To Show Diagram Code: [go]$$B $$ ----------- $$ | O 1 2 X . $$ | . O X X X $$ | O O . X . $$ | . O . . . $$ | . O . . .[/go]

Click Here To Show Diagram Code: [go]$$B tenuki $$ ----------- $$ | O 4 O X . $$ | . O X X X $$ | O O . X . $$ | . O . . . $$ | . O . . .[/go]

count c1 = -2 + t

white to play

Click Here To Show Diagram Code: [go]$$W tenuki $$ ----------- $$ | O 1 . X . $$ | . O X X X $$ | O O . X . $$ | . O . . . $$ | . O . . .[/go]

count c2 = -1 + t
c1 < c2 => the move :b1:

in the first diagram is always wrong (assuming no komaster).

RobertJasiek · **#84**

I have not said that the older tree method would always fail. I have just said that one cannot be sure whether it produces the correct values. Maybe it works for this specific example; I have not read its discussion too carefully yet; I have postponed this until I will have studied the more basic corner kos.

Usually, Black a is not the kind of move one plays. However, under special circumstances, such as Black komonster, it can be a good move.

If neither is even komaster or similar circumstances occur, Black a is wrong indeed.

RobertJasiek · **#85**

Gérard TAILLE wrote:

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . . 1 O 2 . . . . | $$ | X X X X O O O O O | $$ | . . . . . . . . . | $$ | . . . . . . . . . |[/go]

The exchange :b1: :w2: is sente for black and for a theoritical point of view this exchange must be played by black when temperature drops between 13/12 and 14/12.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . . . O . . . . . | $$ | X X X X O O O O O | $$ | . . . . . . . . . | $$ | . . . . . . . . . |[/go]

If I have not goofed, the following is the evaluation by the method of making a hypothesis. If the 9x3 board is displayed incorrectly here, download and view in an SGF editor.

count = -2
move value = 1
gain of Black 1 = 1 1/6
gain of White 1 = 1 1/6

Now, please justify your temperature between 13/12 and 14/12 remark!

Gérard TAILLE · **#86**

RobertJasiek wrote:

Gérard TAILLE wrote:

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . . 1 O 2 . . . . | $$ | X X X X O O O O O | $$ | . . . . . . . . . | $$ | . . . . . . . . . |[/go]

The exchange :b1:

is sente for black and for a theoritical point of view this exchange must be played by black when temperature drops between 13/12 and 14/12.

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . . . O . . . . . | $$ | X X X X O O O O O | $$ | . . . . . . . . . | $$ | . . . . . . . . . |[/go]

If I have not goofed, the following is the evaluation by the method of making a hypothesis. If the 9x3 board is displayed incorrectly here, download and view in an SGF editor.

count = -2
move value = 1
gain of Black 1 = 1 1/6
gain of White 1 = 1 1/6

Now, please justify your temperature between 13/12 and 14/12 remark!

I completely agree with your calculation Robert.

Concerning the value 13/12 and 14/12 I mentionned earlier, it is simply the result of a calculation when you take as hypothesis that the first move is gote for black.

Click Here To Show Diagram Code: [go]$$B Black to play => value = -5/6 and M = 7/6 $$ ----------------- $$ | . . 1 O . . . . . | $$ | X X X X O O O O O | $$ | . . . . . . . . . | $$ | . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$W White to play => value = -2 $$ ----------------- $$ | . . 1 O . . . . . | $$ | X X X X O O O O O | $$ | . . . . . . . . . | $$ | . . . . . . . . . |[/go]

IF the first move were gote then the value of temperature would be
t = (-5/6 - (-3)) / 2 = 13/12

Because 13/12 < 7/6 you know that black must play in the initial position if 13/12 < t < 14/12 and you know such black move is sente.
OC it is simply the result of the first phase of analysis and you have to go further in order to have more information.
IOW I gave only the result of the first phase of analyse : it is correct but still incomplete.

More on my method will follow

Gérard TAILLE · **#87**

Code:

My method applies only on "generalized" corridor

               A
              / \
             /   \
            B     C
                 / \
                /   \
               D     E
                    / \
                   /   \
                  F     G
                       / \
                      /   \
                     H     I

Here above is an example of tree corresponding to a corridor.
Nodes A, C, E, G ... are the nodes reached by black when she follows the corridor and white chooses tenuki
Nodes B, D, F, H ... are leaves reached by white when she decides to stop black in the corridor.
I use the word "generalized" corridor because I accept some situation quite similar to common corridor; you will see later what it means really

The most obvious case is the simple gote (I can say a degenerate cooridor ?)

               A
              / \
             /   \
            B     C

let's call "a" the value of node A, "b" the value of node B, etc.
This simple corridor is easy to analyse: because there are two tenuki between B and C, the value of a move from A is (c - b)/2



               A
              / \
             /   \
            B     C
                   \
                    \
                     F

This other simple tree is OC also an acceptable case for me (but not really a common corridor)
You recognize easily a tree corresponding to a ko.
This time we can see three tenuki between B and F, the value of a move from A is (f - b) / 3

With the following trees we have really a corridor:

               A
              / \
             /   \
            B     C
                 / \
                /   \
               D     E

This very important tree will show you the basis of my method:
The point is to know whether of not the temperature increases when the move AC is played. If the temperature increases then the move AC is sente and the move AB is reverse sente. If temperature decreases then AC and AB moves are gote. If temperature does not change then A is ambiguous (you can consider AC as gote or sente but AB is OC always gote).
First step of my method : I assume AC is sente => AB is a reverse sente move => ABvalue = d - b
Second step of my method : between B and E there are three tenuki => an ambiguous situation will occur if 3 * ABvalue = e - b
if 3 * ABvalue < e - b then AC is really sente otherwise the previous assumption is false and I have no other choice than analysing node C.

At this point let's take a (famous) exemple:

Click Here To Show Diagram Code: [go]$$B $$ ----------- $$ | . O X X . $$ | O X X . X $$ | . O X X X $$ | O O O O X $$ | . O . O .[/go]

Code:

The corresponding tree as the following form

               A
              / \
             /   \
            B     C
                 / \
                /   \
               D     E
                      \
                       \
                        G

with the following value for the leaves

               A
              / \
             /   \
           1/3    C
                 / \
                /   \
              2/3    E
                      \
                       \
                        3

1) first step : assuming AC sente then ABvalue = 2/3 - 1/3 = 1/3 in reverse sente
2) second step : between B and G there are 4 tenuki => A is ambiguous if 4 * ABvalue = f -b
Obviously we have 4 * 1/3 < 3 - 1/3 => I know for sure that AC is sente and ABvalue = 1/3 in reverse sente.

If now you want to know exactly when black can play AC in sente then you have to analyse the subtree:

                  C
                 / \
                /   \
              2/3    E
                      \
                       \
                        3

and the value of a move here is obviously (3 - 2/3) / 3 = 7/9

You have the all picture:
AB is a reverse sente move value 1/3
AC is a sente move value 1/3 and you can play this move as soon as temperature drops to 7/9.
in my method this position is clearly part of the simpliest corridors.

RobertJasiek · **#88**

The convention is: Black moves leftwards in trees.

You claim a method for corridor-like trees. What kinds of sequences and local endgame types can exist in them?

Is your method invariant under the order of assumptions of sequences worth playing successively and types?

You characterise an AB move as having the move value 1/3 and the move value 7/9. How do you prefer one value to the other?

In the example, you consider the pruned tree.

Gérard TAILLE · **#89**

To answer in detail to your questions will need dozens of pages and I have no time enough to make such job (its on my to do list but not in a near future).
Anyway its quite clear in mind so please if you have some doubt on the process take an example and I will be able to bring you some more information.

RobertJasiek wrote:

The convention is: Black moves leftwards in trees.

OK it will be easy for me to change that according to the usual convention

RobertJasiek wrote:

You claim a method for corridor-like trees. What kinds of sequences and local endgame types can exist in them?

One important point concerning the type of tree I consider is the following : at each node of the tree I consider that the player to play as only one good move. If it exists another move which I cannot characerize as weak then this tree is out of the scope of my method.

RobertJasiek wrote:

Is your method invariant under the order of assumptions of sequences worth playing successively and types?

Take an example because the question is really very large indeed.

RobertJasiek wrote:

You characterise an AB move as having the move value 1/3 and the move value 7/9. How do you prefer one value to the other?

Yes, in the process, the AB value (as well as the AC value) could be 1/3 or 7/9 but later in the process, when I found that AC is sente, then it remains only the value 1/3 for AB. For AC it is a sente move (value 1/3) that can be played as soon as temperature drops to 7/9.

RobertJasiek wrote:

In the example, you consider the pruned tree.

Yes you can see two pruning situations:
1) I eliminate sure weak moves
2) when a simple ko with value 1/3 is reached I prune systematically the subtree of ko, taking the standard count (for a larger ko, I mean a value greater than 1/3 the pruning is not allowed).

RobertJasiek · **#90**

Gérard TAILLE wrote:

the AB value (as well as the AC value) could be 1/3 or 7/9 but later in the process, when I found that AC is sente, then it remains only the value 1/3 for AB. For AC it is a sente move (value 1/3) that can be played as soon as temperature drops to 7/9.

(So far) your method does not consider ambient temperature so, in terms of your theory, you cannot make a statement like "can be played as soon as temperature drops to 7/9".

However, your analysis generates 7/9 as move value of C, gain of AC, gain of CD, gain of CE and gain of EG. Therefore, you can say that White can play AB with the move value 1/3 and gain 1/3 while Black can play AC with the move value 1/3 and gain 7/9. Not considering preserving ko threats, this is a neat internal characterisation at least for this particular initial position with its pruned tree.

Gérard TAILLE · **#91**

RobertJasiek wrote:

Gérard TAILLE wrote:

the AB value (as well as the AC value) could be 1/3 or 7/9 but later in the process, when I found that AC is sente, then it remains only the value 1/3 for AB. For AC it is a sente move (value 1/3) that can be played as soon as temperature drops to 7/9.

(So far) your method does not consider ambient temperature so, in terms of your theory, you cannot make a statement like "can be played as soon as temperature drops to 7/9".

However, your analysis generates 7/9 as move value of C, gain of AC, gain of CD, gain of CE and gain of EG. Therefore, you can say that White can play AB with the move value 1/3 and gain 1/3 while Black can play AC with the move value 1/3 and gain 7/9. Not considering preserving ko threats, this is a neat internal characterisation at least for this particular initial position with its pruned tree.

Good Robert. Seeing you are able to correct my (poor) wording shows that you understand what is behind my method.
I did not know the wording : "AC has a move value 1/3 but gains 7/9". It looks a little strange and I suspect many player will not understand the meaning of this statement. Though this wording is quite acceptable for me it seems less ambiguous for a go player to say "AC gains 1/3 in sente and AC can be played as soon as temperature drops uneder 7/9.
Any view from another reader?

RobertJasiek · **#92**

The move value compares the resulting counts of Black's and White's sequences. The gain of a player's move compares its change in his favour to the counts of the position before and after it. One must not study endgame while overlooking either concept of move evaluation nor the concept (the count) of positional evaluation!

Gérard TAILLE · **#93**

RobertJasiek wrote:

The move value compares the resulting counts of Black's and White's sequences. The gain of a player's move compares its change in his favour to the counts of the position before and after it. One must not study endgame while overlooking either concept of move evaluation nor the concept (the count) of positional evaluation!

Obviously you are a theorician and as such you look for a strict application of unambiguous definitions. That's fine for me and quite often I also like to have a theorician's approach. If I like such approach I know for sure that it is often quite difficult to build such unambiguous defintions. In addition I would also say that a defintion should also be as clear and simple as possible.
Ok let's try this job by taking a basic example to help the discussion

Click Here To Show Diagram Code: [go]$$B $$ ----------- $$ | O O . . O . . $$ | X X X X O . . $$ | . . . . . . .[/go]

We all know it is the simpliest form of a sente situation for white and of a reverse sente situation for black
The tree starting with this position is the following

Code:

and the counts of the leaves are:

Code:

Now begins the problem. How handle the nodes A and C ?
IOW how do you define a move value and a count for a node, and how do you define a gain for a move?

Let's begin with the move value definition
You say "The move value compares the resulting counts of Black's and White's sequences" but what does that mean exactly?
With node C I have to compare the counts of the sequence CD and CE. Well I have to compare "4" and "0" and what else? Nothing tells me to use a calculation like ((e - d) / 2 or another formula.
With node A it is far more difficult because you can see three sequences.
In order to apply the good formula I fear that before defining what a "move value" is you have first to define what an "ideal" environment is and this is not an easy defintion is it?

In addition I am sure you also noticed that the tree I showed above is already a pruned tree.
What about the various sequences beginning by

Click Here To Show Diagram Code: [go]$$W $$ ----------- $$ | O O 1 . O . . $$ | X X X X O . . $$ | . . . . . . .[/go]

RobertJasiek · **#94**

There are different approaches to definitions. Thermography is one of them but overkill. Mine is tentative values, checking conditions defining the types of local endgames and keeping the values fitting the conditions. You know this as you also apply this. For the formal definitions and proofs, see reference [19] at https://www.lifein19x19.com/viewtopic.p ... 45#p143245

Gérard TAILLE · **#95**

RobertJasiek wrote:

There are different approaches to definitions. Thermography is one of them but overkill. Mine is tentative values, checking conditions defining the types of local endgames and keeping the values fitting the conditions. You know this as you also apply this. For the formal definitions and proofs, see reference [19] at https://www.lifein19x19.com/viewtopic.p ... 45#p143245

That's look quite interesting Robert.
the reference [19] at https://www.lifein19x19.com/viewtopic.p ... 45#p143245 seems to be https://www.lifein19x19.com/viewtopic.p ... 40#p276840
but this link does not seem to be on the server.

RobertJasiek · **#96**

It's just a back and forth referencing and works here.

Gérard TAILLE · **#97**

RobertJasiek wrote:

It's just a back and forth referencing and works here.

on the link https://senseis.xmp.net/?MiaiCountingMa ... Discussion you can find not a formal defintion but at least the idea behind the count and the miai value:

A local position can be given a count. This represents what the final score of the position will be on average. If a play is made in a local position, the resulting position could then also be given a count, representing what the final score would then be on average. Therefore, the difference between the two counts represents by how much the play increased the final score in the local position. This is the essence of what the miai value is – how much a move gains on average.

Seeing this defintion it appears to me that the miai value seems identical to what you call gain of a player's move i.e. the difference between the count of initial position and the count of the folllowing position. Is it true?
You introduced also the move value notion but, as I said in a previous post, it is not clear to me for the moment.

RobertJasiek · **#98**

Black move gain = B - A

White move gain = A - W

Notice the sign reversion! A gain expresses what a player gains from his perspective (unless he makes a mistake).

***

Move value gote (x-y)/2

Move value sente x-y

Move value ordinary ko (x-y)/3

etc.

Gérard TAILLE · **#99**

RobertJasiek wrote:

Black move gain = B - A

White move gain = A - W

Notice the sign reversion! A gain expresses what a player gains from his perspective (unless he makes a mistake).

***

Move value gote (x-y)/2

Move value sente x-y

Move value ordinary ko (x-y)/3

etc.

For the move value you did not give a defintion but at least you said:
"The move value compares the resulting counts of Black's and White's sequences".
This sentence help a little to understand what the move value is but it still remains unclear.
First of all what is a sequence? Is the end of a sequence a leaf of the tree? Secondly when you mentionned Black's and White's sequences do you consider all possible black and white sequences or only best sequences? Knowing that the best sequences do depend on the ambiant temperature do you take into account this ambiant temperature to define the move value? More generally have you to define an environment (ideal? rich? other?) before defining what a move value is?

RobertJasiek · **#100**

Alternating sequences.

For simple local endgames with short sequences (1 or 2 moves), the definitions are what you expect (and more). For local endgames with long sequences, first determine for how long Black' and White's alternating sequences are worth playing successively.

Engame value of ko

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