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

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

and the counts of the leaves are

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.

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?

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 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.



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.




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.



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.



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.



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.



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.



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

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



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.

Hehe, now I feel better:)