Life In 19x19

Gérard TAILLE 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)."
[...]
Where is your problem?

The problem in your definition is the magic instead of constructing the result! Compare my new definition in my previous message and note that it does construct the result because it relies on earlier CGT definitions effectively prescribing alternate play to a game end position (called "stop" and such in CGT) having some particular result. Therefore, you should be writing your definition more like this:

"The _score_ of a position P is the score of a final position Z reached by min-max alternation abiding by the [non-cyclic] rules."

RobertJasiek wrote:

Gérard TAILLE 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)."
[...]
Where is your problem?

The problem in your definition is the magic instead of constructing the result! Compare my new definition in my previous message and note that it does construct the result because it relies on earlier CGT definitions effectively prescribing alternate play to a game end position (called "stop" and such in CGT) having some particular result. Therefore, you should be writing your definition more like this:

"The _score_ of a position P is the score of a final position Z reached by min-max alternation abiding by the [non-cyclic] rules."

Be serious Robert. I agree that your definition allows to construct this result but it's only a purely theoritical approach without any interest for a fuseki position.

Click Here To Show Diagram Code

[go]$$Bc Start with a one-space high pincer...
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . . . O . . . , . . . . . X . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

What is the result of this position, white to play?
Are you able to give a better result than AI?

I'll try to respond to the OP.

I think this quote quite sufficient to understand temperature.

Mathematical Go: Chilling Gets the Last Point wrote:[...]it is sufficient to think of temperature as a numeric estimate on the value of a move. The units are half the gote-value of a move in Japanese Go literature.

Later the idea, which I doubt is true, was spread around that Go players talked a lot about temperature. I think that is only true when Go players talk about theories such as those presented in the quoted monograph.

Like many concepts it has various realizations, depending on the intention.

For example

Let G be a game G := { L | R }, L and R also games.
Then define an operator, that we call cooling,

cool(G, t) = { cool(L, t) - t | cool(R, t) + t }

unless for some T < t, { cool(L, t) - t | cool(R, t) + t } is a number x (i.e. L - T <= R + T), then

cool(G, t) = x

Now G is said to have temperature T, mean(G) x and to freeze to cool(G, T).

Many other definition that allows for the following properties could be called temperature, even if they are not exactly the same, and I think you could be justified to call something temperature even if these properties are only usually correct. If one wished, then could be very precise about what is meant in each case.

Linearity: cool(G, t) + cool(H, t) = cool(G + H, t)
Order preserving: G >= H implies cool(G, t) >= cool(H, t)
mean(G + H) = mean(G) + mean(H)
temperature(G + H) <= max(temperature(G), temperature(H))

I doubt that these hold if we define

G := { f(L) | f(R) }

where f(x) is katago's score evaluation function, L and R as before. The most obvious violation is that f(x) isn't exact and will violate equalities and inequalities for that simple reason. Another problem is that while statements like G + H may work in form you usually can't actually add two 19x19 game together on a 19x19 board.

But it sure is similar in many ways, especially in form, to be useful.

I like that it is similar on form, I think that can be useful sometimes. If I were to suggest a less problematic definition that doesn't need to be similar in form then that would probably be

mean(G) := (f(L) + f(R)) / 2
temperature(G) := (f(L) - f(R)) / 2

Gérard, you can do either maths or informal opening theory but a combination of both requires research from scratch. My related maths has been as weak as yours so far, except for specific strategic concepts, such as influence stone difference or neutral stone difference. Endgame maths is decades ahead.

In the OP I was trying to explain temperature in layman terms, at least for myself. Now let me apply the concepts to a particular joseki.

Click Here To Show Diagram Code

[go]$$B Joseki
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . b . . . . . , . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . a 9 7 B . . . |
$$ | . . . . . . . . . . . . 0 W 5 2 3 . . |
$$ | . . . . . . . . . . . . . . 8 6 4 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

For the sake of brevity, let's introduce a few abbreviations and functions

S = the score
L = local temperature
T = ambient temperature
P = pass

I'm now evaluating this position, with 7.5 komi, on an otherwise empty board, using KataGo's pointwise evaluation function. This is our substitute for Gerard's function magic(). As Robert has argued sufficiently, it needs many playouts to stabilize at a score which we can rely on. I have not done that.

Assume A the best local move (can be verified) and B as the most valuable move elsewhere, which is often the 4-4 diagonally opposite the corner played out.

if Black A, S = W+1
if Black P, White A, S = W+11.7
L = |S(A) - S(P, A)| = 10.7

if Black B, as KG recommends, S = 0
if Black P, White B, S = W+13.4
T = |S(B) - S(P, B)| = 13.4
T > L

Since the ambient temperature is higher than the local temperature, this position can be considered finished
or in other words, wasn't sente and Black can/should play elsewhere

We can apply the same reasoning along the whole joseki. I refer to the sgf below for all the computations.

Results:

The marked moves are not sente, neither is
and are all sente
is somewhat ambiguous: L and T are close and with the few playouts done the precision of the evaluation might surpass their difference. Also ...
is sente again, so Black has all reasons to play it

Another observation is that and both increase the local temperature by a lot and also decrease the ambient temperature. I interpret this as the influence the obtained strength after a corner capture has on the whole board.

Edit: I'm now doing the same but on a board where the other corners are occupied by one or two stones.

RobertJasiek wrote: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?

Yes and no. In order to understand the concept of temperature and apply it in practical situations, thermography is very useful. But the definition of "temperature" in CGT is already well established and does not rely on thermography at all. Unfortunately, for most realistic full board positions in go, we have no practical way to calculate the exact temperature. We can only use approximations and heuristics.

By the way, who is Francesco Criado? A google search just sends me back to this site, or else gives false positives for thermal imaging in other sciences.

xela wrote:who is Francesco Criado?

Typo for Francisco Criado, of course. Sorry.

User name Criado here.

Coauthor of 6 proofs of the 149 theorems in [22], in particular, main author of the proof of non-existence of local double sente.

Inventor of a few important counter-examples in [22].

Proofreader of the first half of [22].

Assistant mathematician at Technische Universität Berlin.

kvasir wrote:I'll try to respond to the OP.

I think this quote quite sufficient to understand temperature.

Mathematical Go: Chilling Gets the Last Point wrote:[...]it is sufficient to think of temperature as a numeric estimate on the value of a move. The units are half the gote-value of a move in Japanese Go literature.

Later the idea, which I doubt is true, was spread around that Go players talked a lot about temperature. I think that is only true when Go players talk about theories such as those presented in the quoted monograph.

Like many concepts it has various realizations, depending on the intention.

For example

Let G be a game G := { L | R }, L and R also games.
Then define an operator, that we call cooling,

cool(G, t) = { cool(L, t) - t | cool(R, t) + t }

unless for some T < t, { cool(L, t) - t | cool(R, t) + t } is a number x (i.e. L - T <= R + T), then

cool(G, t) = x

Now G is said to have temperature T, mean(G) x and to freeze to cool(G, T).

Many other definition that allows for the following properties could be called temperature, even if they are not exactly the same, and I think you could be justified to call something temperature even if these properties are only usually correct. If one wished, then could be very precise about what is meant in each case.

Linearity: cool(G, t) + cool(H, t) = cool(G + H, t)
Order preserving: G >= H implies cool(G, t) >= cool(H, t)
mean(G + H) = mean(G) + mean(H)
temperature(G + H) <= max(temperature(G), temperature(H))

I doubt that these hold if we define

G := { f(L) | f(R) }

where f(x) is katago's score evaluation function, L and R as before. The most obvious violation is that f(x) isn't exact and will violate equalities and inequalities for that simple reason. Another problem is that while statements like G + H may work in form you usually can't actually add two 19x19 game together on a 19x19 board.

But it sure is similar in many ways, especially in form, to be useful.

I like that it is similar on form, I think that can be useful sometimes. If I were to suggest a less problematic definition that doesn't need to be similar in form then that would probably be

mean(G) := (f(L) + f(R)) / 2
temperature(G) := (f(L) - f(R)) / 2

I understand the first part of your post but I have difficulties with the second part when you use katago for the f function.

When you write
"Let G be a game G := { L | R }, L and R also games."
that means that the start of the game defined above is a POSITION and not a SITUATION for which we know who is to play first. The issue is the following : because the f function (katago) apply only on SITUATION and not on POSITION what does mean f(L) or f(R)?

For that reason I use in my defintion the PASS move and defined the value of a move by
M = magic(P + M) - magic(P + pass)
and not
M = (magic(P + M) - magic(P + pass)) / 2

IOW when you apply your proposal to the empty board what temperature are you reaching? 7 or 14?

Gérard TAILLE wrote:I understand the first part of your post but I have difficulties with the second part when you use katago for the f function.

When you write
"Let G be a game G := { L | R }, L and R also games."
that means that the start of the game defined above is a POSITION and not a SITUATION for which we know who is to play first. The issue is the following : because the f function (katago) apply only on SITUATION and not on POSITION what does mean f(L) or f(R)?

You seem to be asking me to define it completely. Maybe, to be clearer I should have written

G = { { f(x, "White") : x in L } | { f(x, "Black") : x in R } }
meaning that who is to play is specified for the function f, or
G = { f(sup(L), "White") | f(inf(R), "Black") }
where sup(X) and inf(X) are the supremum and infimum of a set X,
or even simply
G = { f(L, "White") | R3 = f(R, "Black") }
which means f operates on the set of possible games, and I think that can be usefully simplified in the way wrote originally as
G = { f(L) | f(R) }
since we do know who is to move and not necessarily need to reflect on that everywhere.

Or I could just have stated instead of "f(x) is katago's score evaluation function" something vague like "f(...) is a suitable score evaluation function". So I think there are various ways to interpret what I wrote, which was the intention

Gérard TAILLE wrote:For that reason I use in my defintion the PASS move and defined the value of a move by
M = magic(P + M) - magic(P + pass)
and not
M = (magic(P + M) - magic(P + pass)) / 2

I gather what you mean by P + x is that the move x is played in situation P (one where we know who is to play). Then I'd assume that the left hand side M is not the same as the right hand side M.

But the main difference to what I wrote is that I was trying to be more general and express that this doesn't in general behave like temperature and it doesn't really make use the notation at all (which I should have mentioned), so you just write (using the preferred interpretation of f(x)) that

mean(G) := (f(L) + f(R)) / 2
temperature(G) := (f(L) - f(R)) / 2

Gérard TAILLE wrote:IOW when you apply your proposal to the empty board what temperature are you reaching? 7 or 14?

The convention for temperature, which I quoted, is to divide by two. That is the start position G ~= 0 and black can makes a move to go to L ~= komi or white could make a move to go to R ~= -komi. I think the desire is that if G = { L | R }, then mean(G) + temperature(G) = mean(L) and mean(G) - temperature(G) = mean(R), rather than mean(G) + temperature(G) / 2 = mean(L) and mean(G) - temperature(G) / 2 = mean(R).

This convention means that when you add and subtract temperatures from mean(A), depending on if you take a left or right edge in a path AB in the game tree, and get mean(B). Right?

kvasir wrote:

Gérard TAILLE wrote:I understand the first part of your post but I have difficulties with the second part when you use katago for the f function.

When you write
"Let G be a game G := { L | R }, L and R also games."
that means that the start of the game defined above is a POSITION and not a SITUATION for which we know who is to play first. The issue is the following : because the f function (katago) apply only on SITUATION and not on POSITION what does mean f(L) or f(R)?

You seem to be asking me to define it completely. Maybe, to be clearer I should have written

G = { { f(x, "White") : x in L } | { f(x, "Black") : x in R } }
meaning that who is to play is specified for the function f, or
G = { f(sup(L), "White") | f(inf(R), "Black") }
where sup(X) and inf(X) are the supremum and infimum of a set X,
or even simply
G = { f(L, "White") | R3 = f(R, "Black") }
which means f operates on the set of possible games, and I think that can be usefully simplified in the way wrote originally as
G = { f(L) | f(R) }
since we do know who is to move and not necessarily need to reflect on that everywhere.

Or I could just have stated instead of "f(x) is katago's score evaluation function" something vague like "f(...) is a suitable score evaluation function". So I think there are various ways to interpret what I wrote, which was the intention

Gérard TAILLE wrote:For that reason I use in my defintion the PASS move and defined the value of a move by
M = magic(P + M) - magic(P + pass)
and not
M = (magic(P + M) - magic(P + pass)) / 2

I gather what you mean by P + x is that the move x is played in situation P (one where we know who is to play). Then I'd assume that the left hand side M is not the same as the right hand side M.

But the main difference to what I wrote is that I was trying to be more general and express that this doesn't in general behave like temperature and it doesn't really make use the notation at all (which I should have mentioned), so you just write (using the preferred interpretation of f(x)) that

mean(G) := (f(L) + f(R)) / 2
temperature(G) := (f(L) - f(R)) / 2

Gérard TAILLE wrote:IOW when you apply your proposal to the empty board what temperature are you reaching? 7 or 14?

The convention for temperature, which I quoted, is to divide by two. That is the start position G ~= 0 and black can makes a move to go to L ~= komi or white could make a move to go to R ~= -komi. I think the desire is that if G = { L | R }, then mean(G) + temperature(G) = mean(L) and mean(G) - temperature(G) = mean(R), rather than mean(G) + temperature(G) / 2 = mean(L) and mean(G) - temperature(G) / 2 = mean(R).

This convention means that when you add and subtract temperatures from mean(A), depending on if you take a left or right edge in a path AB in the game tree, and get mean(B). Right?

Let me propose an example as a support for the discussion.
Let's suppose the board is made of 14 independant gote areas with the miai values 14, 13, 12, ... 2, 1 or if you prefer with swing values 28, 26, 24, ... 4, 2.

What is the final score if it is black to play?
f(L) = 14 -13 + 12 - 11 ... + 2 - 1 = +7
if is white to play then
f(R) = -14 + 13 - 12 + 11 ... -2 + 1 = -7
Note that if you choose komi = +7 this game G is even for the players.

I agree with you that mean(G) = (f(L) + f(R)) / 2 = 0
but I have still difficulties to say that this game with miai values 14, 13, 12, ... 2, 1 or swing values 28, 26, 24, ... 4, 2 is at temperature +7. I understand you prefer to divide the temperature by 2 but for me it is far more natural to say that temperature = 14. For the time being I do not see really your goal but maybe I have to think about it a litttle more.

Gérard TAILLE wrote: Let me propose an example as a support for the discussion.
Let's suppose the board is made of 14 independant gote areas with the miai values 14, 13, 12, ... 2, 1 [...]

What is the final score if it is black to play?
f(L) = 14 -13 + 12 - 11 ... + 2 - 1 = +7
if is white to play then
f(R) = -14 + 13 - 12 + 11 ... -2 + 1 = -7

Let me propose another example showing the limits of yours:

Let's suppose 27 local gotes without follow-ups with the miai values

14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1.

The final score with Black to play is f(L) = 14.
The final score with White to play is f(R) = -14.

Tedomari matters.

RobertJasiek wrote:

Gérard TAILLE wrote: Let me propose an example as a support for the discussion.
Let's suppose the board is made of 14 independant gote areas with the miai values 14, 13, 12, ... 2, 1 [...]

What is the final score if it is black to play?
f(L) = 14 -13 + 12 - 11 ... + 2 - 1 = +7
if is white to play then
f(R) = -14 + 13 - 12 + 11 ... -2 + 1 = -7

Let me propose another example showing the limits of yours:

Let's suppose 27 local gotes without follow-ups with the miai values

14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1.

The final score with Black to play is f(L) = 14.
The final score with White to play is f(R) = -14.

Tedomari matters.

Your point is valid Robert and it conforts my approach.
In your example we have f(L)- f(R) = 28

But know you can also take the counter example with 28 gotes without follow-ups with the miai values
14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1.
The final score with Black to play is f(L) = 0.
The final score with White to play is f(R) = 0
and f(L)- f(R) = 0
Miai matters also

Taking gotes without follow-ups with the miai values 14, 13, 12, ... 2, 1 acts as a kind of average of all games. Isn't it the approach commonly used in endgame theory?

I applied the earlier reasoning on another joseki. This time I put 4-4 stones in every other corner, reducing the ambient temperature (I think). Again, the number of playouts is not very large, only a couple of thousand. Mostly I stopped the KG analysis when the score was stable for more than 10 seconds.

Repeating the idea: a move is sente if the local temperature is higher than ambient temperature. Local/ambient temperature means the value of a move/locally elsewhere, computed as (half) the difference between Black or White playing the best move locally/elsewhere. The measure is KataGo's score estimator.

Since I haven't done sufficient playouts, I'm taking 1 point as an error margin. If the difference between Local and Ambient is smaller than that, I'm calling the position ambiguous.

Click Here To Show Diagram Code

[go]$$B Joseki $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 6 . O . . . | $$ | . . . O . . . . . , . . . . c b 4 . . | $$ | . . . . . . . . . . . . d . . 1 2 . . | $$ | . . . . . . . . . . . . . . . 5 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . a . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . 7 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . X . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

In this "ambiance"
is sente (13.2 > 11.9)
is sente (14.9 > 12.0)
is sente (18.6 > 10.4)
is sente (13.8 > 11.9)
is ambiguous, might be sente (12.1 ~ 11.6)
is ambiguous, might not be sente (11.7 ~ 12.5)
is not sente (10.3 < 12.0)

Hence we can consider the sequence one whole joseki up until included.
White's best local move after is A, which we can consider a "follow-up" of the joseki.
Black's follow-up is not so clear: B and C are more like forcing moves. D is the candidate I selected for the evaluation.

As for the overall temperature of the game, it starts out at 13.2, heats up considerably at B3 (18.6), then cools down again to (slightly above) 12.

Comments welcome.

Knotwilg wrote:I applied the earlier reasoning on another joseki. This time I put 4-4 stones in every other corner, reducing the ambient temperature (I think). Again, the number of playouts is not very large, only a couple of thousand. Mostly I stopped the KG analysis when the score was stable for more than 10 seconds.

Repeating the idea: a move is sente if the local temperature is higher than ambient temperature. Local/ambient temperature means the value of a move/locally elsewhere, computed as (half) the difference between Black or White playing the best move locally/elsewhere. The measure is KataGo's score estimator.

Since I haven't done sufficient playouts, I'm taking 1 point as an error margin. If the difference between Local and Ambient is smaller than that, I'm calling the position ambiguous.

$$B Joseki $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 6 . O . . . | $$ | . . . O . . . . . , . . . . c b 4 . . | $$ | . . . . . . . . . . . . d . . 1 2 . . | $$ | . . . . . . . . . . . . . . . 5 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . a . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . 7 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . X . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$B Joseki $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 6 . O . . . | $$ | . . . O . . . . . , . . . . c b 4 . . | $$ | . . . . . . . . . . . . d . . 1 2 . . | $$ | . . . . . . . . . . . . . . . 5 3 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . a . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . 7 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . X . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

In this "ambiance"
is sente (13.2 > 11.9)
is sente (14.9 > 12.0)
is sente (18.6 > 10.4)
is sente (13.8 > 11.9)
is ambiguous, might be sente (12.1 ~ 11.6)
is ambiguous, might not be sente (11.7 ~ 12.5)
is not sente (10.3 < 12.0)

Hence we can consider the sequence one whole joseki up until included.
White's best local move after is A, which we can consider a "follow-up" of the joseki.
Black's follow-up is not so clear: B and C are more like forcing moves. D is the candidate I selected for the evaluation.

As for the overall temperature of the game, it starts out at 13.2, heats up considerably at B3 (18.6), then cools down again to (slightly above) 12.

Comments welcome.

Interesting analysis Knotwilg.
I understand the main point of your post is to have some criteria for the start and the end of a joseki and I agree with you on this point.
I note also a secondary point in your post. In the fuseki the temperature between two joseki is more probably equal to 12 rather than equal to 14. Maybe someone can confirm this point with more playouts.

Gérard TAILLE wrote:I note also a secondary point in your post. In the fuseki the temperature between two joseki is more probably equal to 12 rather than equal to 14. Maybe someone can confirm this point with more playouts.

I did an analysis of how KataGo evaluates handicap stones to komi. It is something I might share. I found that if h is the handicap then 13.5 * (h - 0.5) - 0.25 is a function for the komi that KataGo evaluates as fair after substantial playouts. This function was designed to give whole or half komi A robust estimator found 13.33 and if we are only interested in small handicaps then 13.2 was the average for the first 3 handicap stones.

I actually wanted to make more analysis on it before mentioning it here. One question I have is if this komi actually give equal winning chances in games. I know it is not that far off for 9 stones, black wins some and white wins some.

Basically, I can confirm 13.2 in the early game with open corners.

Btw the range was [12, 15.5] for handicap stones. I have seen it down to about 10 in actual games during the opening, maybe even less.

==Edit
I meant to write 13.5 * (h - 0.5) - 0.25 when I wrote 13.5 * (h - 0.5) + 0.25, so I corrected this.