Engame value of ko

[Gérard TAILLE]

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]

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]

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

$$B
$$ -----------
$$ | O O . . O . .
$$ | X X X X O . .
$$ | . . . . . . .

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: Select all

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

and the counts of the leaves are:

Code: Select all

               A
              / \
             /   \
            5     C
                 / \
                /   \
               4     0

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

$$W
$$ -----------
$$ | O O 1 . O . .
$$ | X X X X O . .
$$ | . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ -----------
$$ | O O 1 . O . .
$$ | X X X X O . .
$$ | . . . . . . .[/go]

[RobertJasiek]

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]

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]

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

[Gérard TAILLE]

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]

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]

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]

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.

[Gérard TAILLE]

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.

That's make sense for me but as far as you search a defintion for a move value that means that you have first to define at which node you have to stop the sequence. This last point is not easy to define because now you must avoid to use again "move value" to avoid a loop in the definitions.
Let's take an example

$$B
$$ -----------
$$ | . . . O . .
$$ | X X X O . .
$$ | . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ -----------
$$ | . . . O . .
$$ | X X X O . .
$$ | . . . . . . .[/go]

This is a very simple well known corridor.
The corresponding (pruned) tree is the following

Code: Select all

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

and the counts of the leaves are

Code: Select all

               A
              / \
             /   \
            2     C
                 / \
                /   \
               1     0

We all know the value of a move at A is (b - (d + e)/2) / 2 = (2 - (1 + 0)/2) / 2 = (2 - 1/2) / 2 = 3/4
but the point is not to have the right formula but to have the right defintion of the move value.
Then, starting with the defintion of the move value, the job of the theory will be to show how to calculate this move value.

BTW if you define a move value by using the count of an intermediate node then OC you have first to define this count.
As far as I am concerned my own defintion of a move value does not use the count but that is another issue. First of all I do not want to influence your defintions by my own defintions and secondly, as mentionned earlier, I still need a lot of work to finalise my approach. Without such finalisation I know that my defintions could be of no interest.

Oops, I suspect you prepare a future publication of your work on the subject and maybe you do not wish to give in advance your (complete) defintion of a move value. If it is the case please tell me and OC I will respect your position and I will stop my questions on this specific subject.

[RobertJasiek]

future

Past. See [19].

Hints:

- For long sequences, interatively bottom-up the tree.
- For short sequences (and the ordinary | non-ordinary type of local endgames), the definitions of move value are of the pattern M := m, where m is the tentative move value fitting a condition.
- There is the tentative gote move value m_gote. Black's sequence has its tentative sente move value m_B_sente and White's sequence has its tentative sente move value m_W_sente. The types are given by the possible comparisons m_gote ? m_B_sente, m_W_sente.
- For a player's follow-up move value F and tentative move values and tentative counts c_gote and c_sente, there is equivalence (which Bill mentioned in a clause of a sentence and I have proved; I would be surprised if he had not proved it for himself earlier):

c_sente ? c_gote <=> m_gote ? F <=> m_sente ? F <=> m_sente ? m_gote.

Therefore, even if m_sente ? m_gote comparisons surprise you, they are equivalent to comparisons to a follow-up move value F (and to comparison of the tentative counts).

[Gérard TAILLE]

future

Past. See [19].

Hints:

- For long sequences, interatively bottom-up the tree.
- For short sequences (and the ordinary | non-ordinary type of local endgames), the definitions of move value are of the pattern M := m, where m is the tentative move value fitting a condition.
- There is the tentative gote move value m_gote. Black's sequence has its tentative sente move value m_B_sente and White's sequence has its tentative sente move value m_W_sente. The types are given by the possible comparisons m_gote ? m_B_sente, m_W_sente.
- For a player's follow-up move value F and tentative move values and tentative counts c_gote and c_sente, there is equivalence (which Bill mentioned in a clause of a sentence and I have proved; I would be surprised if he had not proved it for himself earlier):

c_sente ? c_gote <=> m_gote ? F <=> m_sente ? F <=> m_sente ? m_gote.

Therefore, even if m_sente ? m_gote comparisons surprise you, they are equivalent to comparisons to a follow-up move value F (and to comparison of the tentative counts).

As I said before I cannot access to this link [19] so I cannot access to your defintion of a move value.
I understand your way to calculate a move value by propagating the relevant information from the leaves of the tree towards the root and I agree with you.
But it was not my question. For me the move value cannot not be defined by a calculation but by a need of the players. As soon as this defintion has been given then you can show how you can calculate this value.
IOW I agree with your calculation but what is the move value defintion for which you build your calculation?

For miai value I already mentionned the following attempt of definition:
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.
This defintion is a good starting point but for a theoritical point of view this defintion is not quite satifactory for two reasons:
1) the need of the player is not clear
2) the defintion is quite ambiguous because we don't know what exactly means "on average".

BTW where do you put the miai value in your approach where you use move value and gains. Is it a third concept?

[RobertJasiek]

As I said before I cannot access to this link [19] so I cannot access to your defintion of a move value.

My references to text sources point to the message in
thread = Book References in Other Threads
author = RobertJasiek
date = Jul 21, 2013
In that message, you find the reference [19]. You can find the message using the forum's Search function.

the move value cannot not be defined by a calculation

The move value is a value. Since it is a value, it is determined by a calculation. Since there are several types of move values having different kinds of calculations, my definition contains both a) the algebraic conditions for determining the correct type and b) the algebraic calculation.

what is the move value defintion for which you build your calculation?

I have given you the hints for this.

For short sequences: all you need is to replace the parameter ? by suitable relations <, <=, >, >=, =. If you can't figure it out, study the sources!


Example type local gote:

local gote :<=> m_gote < m_B_sente, m_W_sente.

If this pair of conditions is fulfilled, then move value M := m_gote.


For long sequences: method of making a hypothesis.

For miai value

Miai value is an alternative phrase for the term move value of modern endgame theory, which calibrates a move value as a value per move, whereas deire value of traditional endgame theory calibrates a move value of a) sente as a value per move, b) gote as a value per two moves and c) does not know well how to handle ko move values.

I already mentionned the following attempt of definition:
A local position can be given a count. This represents what the final score of the position will be on average.

What average? In one local sente, you do not form an average. Conway formed averages (mean values) by forming the limit to infinity in playing correctly in arbitrarily multiple copies together. Which average do you mean?

Mean value is a CGT term, which I do not use in my definitions of count and move value. I just need tentative counts and move values to define counts and move values.

the difference between the two counts represents by how much the play increased the final score in the local position.

No. This difference is the gain or the negated gain. The score of the / a final position remains the same. What is different is the COUNT before the move and the COUNT after the move.

This is the essence of what the miai value is – how much a move gains on average.

No. This is the move's gain.

The miai value is the modern move value.

The miai value has an average, for which you can say that it is how much a move gains on average: the limit for arbitrarily many copies of the local endgames played together correctly.

1) the need of the player is not clear

What is "the need of the player" conceptually? Strategic advice for him? If so, indeed, the move value alone is insufficient information for strategic advice, in general.

2) the defintion is quite ambiguous because we don't know what exactly means "on average".

You don't. Conway does, see above and [20] in

https://www.lifein19x19.com/viewtopic.p ... 45#p143245

BTW where do you put the miai value in your approach where you use move value and gains. Is it a third concept?

Miai value is (the Japanese name of modern) move value. Do you mean 'mean value'? My approach to defining move value is so elegant that I do not need mean value.

BTW, thermography is also elegant when it writes things like L_t(G) = l_t(G), that is, the Left score is the (value of the) Left wall (at temperature t of the game G).

[Gérard TAILLE]

What average? In one local sente, you do not form an average. Conway formed averages (mean values) by forming the limit to infinity in playing correctly in arbitrarily multiple copies together. Which average do you mean?

Mean value is a CGT term, which I do not use in my definitions of count and move value. I just need tentative counts and move values to define counts and move values.

the difference between the two counts represents by how much the play increased the final score in the local position.

No. This difference is the gain or the negated gain. The score of the / a final position remains the same. What is different is the COUNT before the move and the COUNT after the move.

This is the essence of what the miai value is – how much a move gains on average.

No. This is the move's gain.

The miai value is the modern move value.

The miai value has an average, for which you can say that it is how much a move gains on average: the limit for arbitrarily many copies of the local endgames played together correctly.

1) the need of the player is not clear

What is "the need of the player" conceptually? Strategic advice for him? If so, indeed, the move value alone is insufficient information for strategic advice, in general.

2) the defintion is quite ambiguous because we don't know what exactly means "on average".

You don't. Conway does, see above and [20] in

https://www.lifein19x19.com/viewtopic.p ... 45#p143245

BTW where do you put the miai value in your approach where you use move value and gains. Is it a third concept?

Miai value is (the Japanese name of modern) move value. Do you mean 'mean value'? My approach to defining move value is so elegant that I do not need mean value.

BTW, thermography is also elegant when it writes things like L_t(G) = l_t(G), that is, the Left score is the (value of the) Left wall (at temperature t of the game G).

Oops, the text
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.
is not mine. It is what is written on the link https://senseis.xmp.net/?MiaiCountingMa ... Discussion and I do not like very much this text though the idea behind may be good.