Temperature

[Knotwilg]

There's SL's definition by Bill, closely related to CGT: https://senseis.xmp.net/?Temperature
I have added my own understanding: https://senseis.xmp.net/?Dieter%2FTemperature

[RobertJasiek]

I prefer move value and only use [ambient] temperature as "largest move value on the rest of the board". I speak of move value (and - different concept - gain) instead of local temperature and - CGT concept - incentive. I speak of the largest move value on the board instead of the global temperature. Simple! No need to follow CGT when one does not use CGT.

[Gérard TAILLE]

There's SL's definition by Bill, closely related to CGT: https://senseis.xmp.net/?Temperature
I have added my own understanding: https://senseis.xmp.net/?Dieter%2FTemperature

In your article you have written under late endgame:
"The global temperature is still more complicated, as we need to compare two sequences of endgame moves, with either player going first. That's why we estimate the global temperature in the endgame to be half of the biggest local temperature."
Two comments :
1) for me the global temperature is in general equal (very near) to the biggest local temperature and not half of this local temperature.
2) In your sentence it is difficult to see what means each occurence of the word "tenmperature". Is it the "new" temperature calculated by the difference between position after the good move and after the pass, or is it the temperature defined in CGT?

[Gérard TAILLE]

define the value of a move M in a position P by: value of move M = magic(P + M) - magic(P + pass)

I know you do not like mistakes. (Nor do I;) ) However, Katago's magic does make mistakes so your magic move value or temperatures can become negative:)

No my magic function cannot lead to a negative value but if you use katago instead of the magic function, then yes in very rare situations I can imagine you might get a negative value.
BTW do you have a better defintion of temperature when you are not in the endgame phase?

[RobertJasiek]

A minority occurrence but not rare!

Definition of global temperature: If you want to do it CGT style, ko thermography must be taken into account and this is far beyond of what I have completely understood of CGT. So, no, I cannot provide an even more thorough definition. As Francesco Criado points out, ko thermography is incomplete. So before creating somthing better, one should consider first completing CGT definitions... Will my ko definition be needed?

[Gérard TAILLE]

A minority occurrence but not rare!

Interesting. In order to avoid any misunderstanding can you show us at least one example?

[RobertJasiek]

I do not have an example at hand because such AI mistakes I quickly discard / avoid / dissolve by deeper or follow-up position search. Typically, the occurrences are of ordinay kind when choice between close competitors depend on a) tactics of medium complexity or b) conquering vast empty space when dozens of candidates make finding the best hard but eventually understanding emerges that one candidate is significantly better and the reasons are only revealed by search of at least medium depth. Similar to what humans can experience in their games when good follow-up sequences are found early enough in the game sequence to outplay the opponent.

Typical choices are between 0.1% or 0.1 points off candidates. Above cases, however, can change about 2% or 0.3 to 2 points.

[Gérard TAILLE]

I do not have an example at hand because such AI mistakes I quickly discard / avoid / dissolve by deeper or follow-up position search. Typically, the occurrences are of ordinay kind when choice between close competitors depend on a) tactics of medium complexity or b) conquering vast empty space when dozens of candidates make finding the best hard but eventually understanding emerges that one candidate is significantly better and the reasons are only revealed by search of at least medium depth. Similar to what humans can experience in their games when good follow-up sequences are found early enough in the game sequence to outplay the opponent.

Typical choices are between 0.1% or 0.1 points off candidates. Above cases, however, can change about 2% or 0.3 to 2 points.

Maybe there is a misunderstanding Robert.
I perfectly understand that katago can prefer a move that is not the best one and, as a consequence I understand that evaluating the result of the real best move may lead to some contraction but this point has nothing to do with my defintion of move value.
For me the move value is defined by comparing the local move to the PASS move (which in general is not a close competitor!). I do not compare the local move to the best move on the board.

[RobertJasiek]

Remove the magic and AI reference and create perfect play. This avoid misunderstandings.

[Gérard TAILLE]

Remove the magic and AI reference and create perfect play. This avoid misunderstandings.

Ok let's remove the magic and AI reference. What remains on the table? The defintion of "the value move" disappears and and the definition of the "temperature" disappears also. Your are not very constructive Robert.

[Gérard TAILLE]

No my magic function cannot lead to a negative value but if you use katago instead of the magic function, then yes in very rare situations I can imagine you might get a negative value.

Oops its a wrong to say that "the magic function cannot lead to a negative value".
Let'me clarify this point:
1) the magic function magic(P) is the result of the game starting from position P. The result can be of course any number, for example +7 or -7
2) the value of move M = magic(P + M) - magic(P + pass) can also be a negative value: if the move M is a terrible mistake (like playing in its own eye) then the pass can lead to a better result than a move M.
3) concerning the temperature of a local area (defined as the max value of all possible moves in this area) this temperature cannot be negative because a pass move is always a part of all possible moves in this area.

[RobertJasiek]

I do not do all your work:) Hint: you might do what others did in the past - imagine the perfect play automaton. Katago assumed to play perfectly so to say or brute force playing perfectly instantly by assumption. We do not know how it decides but we assume it does play perfectly instantly.

[RobertJasiek]

Oops its a wrong to say that "the magic function cannot lead to a negative value".
Let'me clarify this point:
1) the magic function magic(P) is the result of the game starting from position P. The result can be of course any number, for example +7 or -7
2) the value of move M = magic(P + M) - magic(P + pass) can also be a negative value: if the move M is a terrible mistake (like playing in its own eye) then the pass can lead to a better result than a move M.
3) concerning the temperature of a local area (defined as the max value of all possible moves in this area) this temperature cannot be negative because a pass move is always a part of all possible moves in this area.

You begin to understand. Now, if you did not remove AI, it could also pass incorrectly.

[Gérard TAILLE]

Oops its a wrong to say that "the magic function cannot lead to a negative value".
Let'me clarify this point:
1) the magic function magic(P) is the result of the game starting from position P. The result can be of course any number, for example +7 or -7
2) the value of move M = magic(P + M) - magic(P + pass) can also be a negative value: if the move M is a terrible mistake (like playing in its own eye) then the pass can lead to a better result than a move M.
3) concerning the temperature of a local area (defined as the max value of all possible moves in this area) this temperature cannot be negative because a pass move is always a part of all possible moves in this area.

You begin to understand. Now, if you did not remove AI, it could also pass incorrectly.

Obviously you did not understand my point Robert and I have to explain again.
in my post https://lifein19x19.com/viewtopic.php?p=280075#p280075 I wrote:
"Assume you have a magic fonction (katago?) which gives you the result of a game starting from a given position P : result = magic(P)."
In this sentence the magic function looks like a God function. The parenthesis suggests only to take katago as a good estimation of this function. As you see, stricly speaking the magic function has nothing to do with AI.
This being, AI appears to me to be good tool to give a good estimation of the magic function. OC katago may be not accurate to evaluate magic(P) or magic(P+M) or magic(P+pass) and it will never be perfect. I said magic(P) can be positive or negative, I said also that the value of move M = magic(P + M) - magic(P + pass) can be positive or negative (in this case the pass is better that the move M) and finally I said that the temperature of an area cannot be negative.
Where is your problem?

[RobertJasiek]

Actually, it is very much simpler than automatons, magic or AI! We apply my Definition 2 in [22], which repeats this kind of CGT definition:

"Definitions 2 [score of a position]
If Black or White starts, B(P) or W(P) is the resulting score of P, respectively.

Remarks

The resulting score occurs by applying the presuppositions, that is, letting the players alternate to a settled position while Black maximises and White minimises. Combinatorial game theory assumes a game G, the players Left and Right, and calls L(G) or R(G) the left or right stop, respectively, which reveals either score. Compare [31]"

Now, I think what you want is for either player to move. Therefore, let me define while generalising:

S(P) is the resulting score of P with its player having the turn.

References:

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