This 'n' that

Bill Spight · Post by **Bill Spight** » Thu Jun 24, 2021 1:42 pm

Gérard TAILLE wrote:
Bill Spight wrote:
$$W
$$ -------------------
$$ . . . . . . 1 . . .
$$ . X . X X X O . O .
$$ . . . X O O O . . .
$$ . . . X . . . . . .
$$ . . . . . . . . . .
Click Here To Show Diagram Code
[go]$$W $$ ------------------- $$ . . . . . . 1 . . . $$ . X . X X X O . O . $$ . . . X O O O . . . $$ . . . X . . . . . . $$ . . . . . . . . . .[/go]

What is my conclusion.
In a non-ko environment, the descent is on average as good as the hanetsugi (OC I agree that in certain environment the hanetsugi is better and this is for example obvious if the temperature of the environment is = 0).
In a ko environment however, the descent seems a little better.
For a go player who do not want to analyse in detail the real environment, can we conclude (even if Takagawa did not mention ko threat) that the descent is, on average, a little better than the hanetsugi ?

In a non-ko environment, the hanetsugi dominates the descent, even though they gain the same, on average.

In a ko environment, the descent may be better than the hanetsugi, but we cannot say that it dominates it. Neither dominates the other. As to which is statistically better, my bet goes to the hanetsugi. And I understand komonster analysis.

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Jun 24, 2021 2:28 pm

Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote:
$$W
$$ -------------------
$$ . . . . . . 1 . . .
$$ . X . X X X O . O .
$$ . . . X O O O . . .
$$ . . . X . . . . . .
$$ . . . . . . . . . .
Click Here To Show Diagram Code
[go]$$W $$ ------------------- $$ . . . . . . 1 . . . $$ . X . X X X O . O . $$ . . . X O O O . . . $$ . . . X . . . . . . $$ . . . . . . . . . .[/go]

What is my conclusion.
In a non-ko environment, the descent is on average as good as the hanetsugi (OC I agree that in certain environment the hanetsugi is better and this is for example obvious if the temperature of the environment is = 0).
In a ko environment however, the descent seems a little better.
For a go player who do not want to analyse in detail the real environment, can we conclude (even if Takagawa did not mention ko threat) that the descent is, on average, a little better than the hanetsugi ?
In a non-ko environment, the hanetsugi dominates the descent, even though they gain the same, on average.

In a ko environment, the descent may be better than the hanetsugi, but we cannot say that it dominates it. Neither dominates the other. As to which is statistically better, my bet goes to the hanetsugi. And I understand komonster analysis.

Oops your are not allowed to use the wording "dominate" in a ko environment are you?
Anyway and more generally, seeing you use this term "dominate" twice, it seems you do not accept to say that a move could be "on average" (I mean typically in an ideal environment at temperature t) better than another. In a certain sense "dominate" is the contrary of "average". When you use a difference game basically you look indirectly for very specific environments to prove that a move do not dominate another. You are right OC but why you want to ignore that a move may be "on average" the better than another.

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

It was exactly in this context I said taking the ko with

was not a good move. Surely you can find an environment in which taking the ko is good (you find the subtle {u||||2u|0||-u|||-2u} area to prove that point) but, on average (typically in an ideal environment or in the majority of cases if you prefer) this move is not a good move.

OK Bill I can also understand that you do not want to use the wording "move better than another" if it is not a move that "dominates the other". You are right and for that reason I use the wording "on average better".
BTW it is the same idea for "the average territorial value". this "average" makes sense for me but I know also that for a specific environment the territorial value may be different.

Bill Spight · Post by **Bill Spight** » Thu Jun 24, 2021 5:09 pm

Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote:
$$W
$$ -------------------
$$ . . . . . . 1 . . .
$$ . X . X X X O . O .
$$ . . . X O O O . . .
$$ . . . X . . . . . .
$$ . . . . . . . . . .
Click Here To Show Diagram Code
[go]$$W $$ ------------------- $$ . . . . . . 1 . . . $$ . X . X X X O . O . $$ . . . X O O O . . . $$ . . . X . . . . . . $$ . . . . . . . . . .[/go]

What is my conclusion.
In a non-ko environment, the descent is on average as good as the hanetsugi (OC I agree that in certain environment the hanetsugi is better and this is for example obvious if the temperature of the environment is = 0).
In a ko environment however, the descent seems a little better.
For a go player who do not want to analyse in detail the real environment, can we conclude (even if Takagawa did not mention ko threat) that the descent is, on average, a little better than the hanetsugi ?
In a non-ko environment, the hanetsugi dominates the descent, even though they gain the same, on average.

In a ko environment, the descent may be better than the hanetsugi, but we cannot say that it dominates it. Neither dominates the other. As to which is statistically better, my bet goes to the hanetsugi. And I understand komonster analysis.

Gérard TAILLE wrote:Oops your are not allowed to use the wording "dominate" in a ko environment are you?

You are in von Neumann game theory for specific games, but the term has a somewhat different meaning in CGT.

Gérard TAILLE wrote:Anyway and more generally, seeing you use this term "dominate" twice, it seems you do not accept to say that a move could be "on average" (I mean typically in an ideal environment at temperature t) better than another.

Of course it can. That's one point of the heuristic.

Gérard TAILLE wrote:In a certain sense "dominate" is the contrary of "average". When you use a difference game basically you look indirectly for very specific environments to prove that a move do not dominate another. You are right OC but why you want to ignore that a move may be "on average" the better than another.

I am not ignoring that fact, as I have said over and over.

Gérard TAILLE wrote:
$$W
$$ --------------
$$ | X 1 X O X . .
$$ | . X O O X . .
$$ | X . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .
Click Here To Show Diagram Code
[go]$$W $$ -------------- $$ | X 1 X O X . . $$ | . X O O X . . $$ | X . O X X . . $$ | . O O X . . . $$ | . O X X . . . $$ | . X . . . . . $$ | . X . . . . . $$ | X X . . . . . $$ | . . . . . . . $$ | . . . , . . .[/go]
It was exactly in this context I said taking the ko with was not a good move.

It looks like White's best local move.

Gérard TAILLE wrote:Surely you can find an environment in which taking the ko is good (you find the subtle {u||||2u|0||-u|||-2u} area to prove that point) but, on average (typically in an ideal environment or in the majority of cases if you prefer) this move is not a good move.

If you are using on average in the statistical sense instead of the CGT sense, then I agree that if there is a play elsewhere that gains the same, thermographically, as taking the ko, then White should usually play elsewhere.

Gérard TAILLE wrote:OK Bill I can also understand that you do not want to use the wording "move better than another" if it is not a move that "dominates the other". You are right and for that reason I use the wording "on average better".
BTW it is the same idea for "the average territorial value". this "average" makes sense for me but I know also that for a specific environment the territorial value may be different.

For kos, strictly speaking, we have to talk about mast values instead of average values. White means that we cannot talk about the average values of moves, either. in CGT.

We can talk about statistical averages. But, AFAIK, the statistics have not been done for this hanetsugi vs. descent comparison or any other such close comparison, nor is there anyone who wants to spend the time and energy to do so. {shrug}

----

There are two problems with language, here. One is using "dominate" in two senses, one in the sense of CGT, the other in the sense of von Neumann game theory. The other is using "on average" in two senses, one in the sense of CGT, the other in the sense of statistics.

----

Statistically speaking, here is my general belief about a choice between a ko play and a non-ko play. It is based not only upon my own thinking and experience, but also upon what I know about professional preferences. If komonster analysis applies, I lean towards what it says. Otherwise, if one play gains more thermographically, I lean towards it. Otherwise, if the plays gain the same, thermographically, I lean towards the non-ko play.

But as I say, this is guesswork, because nobody has actually done the statistics, AFAIK.

Bill Spight · Post by **Bill Spight** » Thu Jun 24, 2021 6:04 pm

Let me go over this question again, using komonster analysis, stopping play when the area temperature drops to 0.

Edited for correctness.

Gérard TAILLE wrote:Certainly you can build an environment in which the assumption a reverse black move at "a" is equivalent to the exchange white "a" black "b" is wrong and in which the reverse sente black "a" is better but it is also possible to build an environment in which the ko threat white "a" black "b" makes the descent better:
$$W
$$ -------------------
$$ . . . . . . . . . .
$$ . X . X X X O . O .
$$ . . . . O O O . . .
$$ . . . . . . . . . .
$$ . . . . . . . . . .
$$ . . . . . . . . . .
$$ . . . . . . . . . .
$$ . . X X O O . . . .
$$ . . X O . O . . . .
$$ -------------------
Click Here To Show Diagram Code
[go]$$W $$ ------------------- $$ . . . . . . . . . . $$ . X . X X X O . O . $$ . . . . O O O . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . X X O O . . . . $$ . . X O . O . . . . $$ -------------------[/go]
Assume we are in an area counting context.
In this very simple position with only two small yose points remaining, the descent is best isn't it?

Let's assume that there are no dame, and that there are no ko threats, which is what I think you also mean.

Komonster analysis, stopping when the area temperature is 0.

Click Here To Show Diagram Code: [go]$$W Descent, var. 1 $$ ------------------- $$ . . . . . 2 1 . . . $$ . X . X X X O . O . $$ . . . . O O O . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . X X O O . . . . $$ . . X O 3 O . . . . $$ -------------------[/go]

gains 2 points.

gains 2 points.

White gains net 2 points.

Click Here To Show Diagram Code: [go]$$W Descent, var. 2 $$ ------------------- $$ . . . 6 5 3 1 . . . $$ . X . X X X O . O . $$ . . . . O O O . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . X X O O . . . . $$ . . X O 2 O . . . . $$ -------------------[/go]

fills ko

gains 2 points.

gains 4 points. (2 points on top plus 2 points for lifting the ko ban and changing the bottom from 2 points for Black to 0.)

gains 2 points.

gains 2 points.

White gains net 2 points.

Now, we can call

a ko threat, but

should not answer

.

Click Here To Show Diagram Code: [go]$$W Descent, var. 3 $$ ------------------- $$ . . . . 4 3 1 . . . $$ . X . X X X O . O . $$ . . . . O O O . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . X X O O . . . . $$ . . X O 2 O . . . . $$ -------------------[/go]

takes ko

gains 2 points.

gains 4 points.

gains 2 points.

gains 2 points.

White gains net 4 points. (White need not fill the ko at area temperature 0.)

Click Here To Show Diagram Code: [go]$$W Hanetsugi $$ ------------------- $$ . . . . 2 1 3 . . . $$ . X . X X X O . O . $$ . . . . O O O . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . . . . . . . . . $$ . . X X O O . . . . $$ . . X O 4 O . . . . $$ -------------------[/go]

-

gains 2 points.

gains 2 points. (Again, Black need not fill the ko at area temperature 0.)

Black gains net 2 points.

It looks like, in von Neumann game theory under these conditions, and komonster analysis, the descent is better than the hanetsugi.

After the descent,

descent dominates taking the ko.

Gérard TAILLE · Post by **Gérard TAILLE** » Fri Jun 25, 2021 4:03 am

Bill Spight wrote: There are two problems with language, here. One is using "dominate" in two senses, one in the sense of CGT, the other in the sense of von Neumann game theory. The other is using "on average" in two senses, one in the sense of CGT, the other in the sense of statistics.

I think you have found here the misunderstanding. How could we avoid such misunderstanding in the future?
Because I am far to be as expert as you on such issue I accept all wording you can propose, provided the proposal looks unambiguous.

Can you clarify, for the future, in which meaning you would like to use the words "dominate" or "average"?

BTW, does it make sense for you if I use the wording : move "a" is better than move "b" at temperature t ? In such sentence can move "a" be a tenuki (I mean a move in the environment at temperature t)?

Gérard TAILLE · Post by **Gérard TAILLE** » Fri Jun 25, 2021 6:18 am

RobertJasiek wrote:
Gérard TAILLE wrote:for a human, a picture with a left wall and a right wall is far more easier and pleasant to read than equations
I disagree because

- I find equations easier to read than graphs of mappings,

- graphs of mappings rely on equations and we must use the equations anyway to justify correctness of the graphs of mappings,

- after every move, a new graph of mappings occurs,

- when applied while playing a game, calculating equations is simpler than imagining and mentally constructing graphs of mappings.

The thermography approach is quite interesting : we define an ideal environment depending of only one parameter called temperature
This is not thermography. Even my non-thermographic ideal environment has a granularity, such as 2, 1 or 1/2. Thermography also relies on such a second paramater: the arbitrarily small granularity so that a RICH environment is formed.

Yes Robert, RICH environment are very interesting indeed.
I tried to answer the following question: what is the best granularity for modelling the real environment a go player may encounter?
I am not able to answer really this question but at least I have an intuition.
OC we need to have some statistical information about real environment but ... these statistics AFAIK are not available. Let me guess some figures in order to try and start to answer the question.
Assume that 100 moves before the end of the game, the value of a move is 10 points. We may conclude that a rich environment like 0.1, 0.2, 0.3, ... 9.9, 10.0 may be good approximation of a real environment. But we have to take into account that in the real life a lot of yose areas are miai (same value) and thus we have to consider the real enviroment is not made of 100 different values but far less.

I imagine easily that we have maybe only 30 or 50 different values for the last 100 moves and a granularity 0.2 or 0.3 looks quite good. Anyway, as far as I am concerned I like the granularity 0.5 simply because all corresponding gote points are very easy to build!

Surely a granularity 0.01 is far too small and a granularity 2.0 is far to big.
What about the famous "ideal environment" ? This environment looks like the limit of a rich enviroment when the granularity decreases until 0. For a mathematical point of view it is a very good environment because the granularity disappear and the results are thus simplier.

For a go player who is looking for the best model I do not know what is the best choice.
Finally I like to use both the "ideal environment" for its simple results and the rich environment with granularity 0.5 because it is easy to build in practice.

More later

Bill Spight · Post by **Bill Spight** » Fri Jun 25, 2021 8:31 am

Gérard TAILLE wrote:
Bill Spight wrote: There are two problems with language, here. One is using "dominate" in two senses, one in the sense of CGT, the other in the sense of von Neumann game theory. The other is using "on average" in two senses, one in the sense of CGT, the other in the sense of statistics.
I think you have found here the misunderstanding. How could we avoid such misunderstanding in the future?
Because I am far to be as expert as you on such issue I accept all wording you can propose, provided the proposal looks unambiguous.

Can you clarify, for the future, in which meaning you would like to use the words "dominate" or "average"?

BTW, does it make sense for you if I use the wording : move "a" is better than move "b" at temperature t ? In such sentence can move "a" be a tenuki (I mean a move in the environment at temperature t)?

I have been struggling with Safari, and my draft got clobbered.

More later, but let me say this for now.

I would prefer not to base anything on statistics, because nobody has done the relevant statistics, nor does anybody seem inclined to do so. So we are left guessing.

For temperatures greater than 0, I would prefer to avoid talking about domination. Difference games without ko fights occur at temperature 0, and in that limited context, for difference games that compare two plays, it is OK to talk about domination.

RobertJasiek · Post by **RobertJasiek** » Fri Jun 25, 2021 9:57 am

Gérard TAILLE wrote:what is the best granularity for modelling the real environment a go player may encounter?

I am pragmatic and use whichever model environment enables me to prove something.

I like the granularity 0.5 simply because all corresponding gote points are very easy to build

Right.

For a go player who is looking for the best model I do not know what is the best choice.

A player can a) read the theorems and proofs we mathematicians write, or b) simply believe the results we proclaim as having been established as truths, not use any model environment but simply apply the results. For the early endgame, this means that the results are good (if not the best available) approximations for the ordinary environments of real games. For the late endgame, application might even be perfect play if the environments fulfil the made assumptions.

Gérard TAILLE · Post by **Gérard TAILLE** » Sat Jun 26, 2021 2:04 pm

Though my preference goes to thermography calculation, my mathematical curiosity tells me to look at a theory which will be based on the environment
E_t = {½|-½} + {1|1} + {1½|-1½} + {2|2} + {2½|2½} ... + {t|-t}
Let's try to define the value of a position P in this environment, knowing the only thing at our disposal being the score resulting from a game. My proposal is the following : in order to calculate the value of position P, you choose an environment E_t with t big enough to be higher than the expecting value of a move in P and then you calculate:
Delta = ScoreGame(P + E_t) - ScoreGame(E_t)
one time with black to play and one time with white to play. The average of these two Deltas is, per defintion, the value of position P.

Example 1

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

Let's take the environment E_t with t = 4

Black to play
ScoreGame(E_t) = +2
ScoreGame(P + E_t) = +6
Delta1 = ScoreGame(P + E_t) - ScoreGame(E_t) = 6 - 2 = +4

White to play
ScoreGame(E_t) = -2
ScoreGame(P + E_t) = +1
Delta2 = ScoreGame(P + E_t) - ScoreGame(E_t) = 1 - (-2) = +3

The average (Delta1 + Delta2) / 2 = 3½ is the expected value of P isn't it ?

more later

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Jun 27, 2021 6:42 am

Let's now take a more interesting example

Example 2

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

Let's take the environment E_t with t = 4

Black to play
ScoreGame(E_t) = +2
ScoreGame(P + E_t) = +7
Delta1 = ScoreGame(P + E_t) - ScoreGame(E_t) = 7 - 2 = +5

White to play
ScoreGame(E_t) = -2
ScoreGame(P + E_t) = +3
Delta2 = ScoreGame(P + E_t) - ScoreGame(E_t) = 3 - (-2) = +5

The average (Delta1 + Delta2) / 2 = 5
The expected score of this position was (8 + (3 - 0)/2)/2 = 4¾

How can we explain this difference?

The answer is quite simple : any environment, including the environment
E₄ = {½|-½} + {1|1} + {1½|-1½} + {2|2} + {2½|2½} + {3|3} + {3½|-3½} + {4|4}
has its specificity. If for example you suppress the gote point {½|-½} from E₄ then you have:

Black to play
ScoreGame(E_t - {½|-½}) = +2½
ScoreGame(P + E_t) = +6½
Delta1 = ScoreGame(P + E_t - {½|-½}) - ScoreGame(E_t - {½|-½}) = 6½ - 2½ = +4

White to play
ScoreGame(E_t - {½|-½}) = -2½
ScoreGame(P + E_t - {½|-½}) = +2½
Delta2 = ScoreGame(P + E_t - {½|-½}) - ScoreGame(E_t - {½|-½}) = 2½ - (-2½) = +5

The average (Delta1 + Delta2) / 2 = 4½

How can we eliminate the specificity of the environment E_t?

In theory it is not quite difficult.
Instead of taking only the environment E_t above, you consider all the environment made of the gote points {½|-½}, {1|1}, {1½|-1½}, {2|2}, {2½|2½} ... and you finally make on average on all these environments.
If for example you want to consider the environments at temperature 4. You consider the 8 gote points:
{½|-½}, {1|1}, {1½|-1½}, {2|2}, {2½|2½}, {3|3}, {3½|-3½}, {4|4}
and you form all possible environments made of these gote points. When you eliminate the miai points then it remains 256 possible environments by simply choosing to take or not to take each gote points.

more later

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Jun 27, 2021 10:04 am

Gérard TAILLE wrote:Though my preference goes to thermography calculation, my mathematical curiosity tells me to look at a theory which will be based on the environment
E_t = {½|-½} + {1|1} + {1½|-1½} + {2|2} + {2½|2½} ... + {t|-t}

Why I said I prefer thermography calculation ?

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

For the position above I showed you we can reach a good result by an average calculation on 256 environments. It is not easy of course but it is not the most important point.

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

For a position with a ko like the position above I am convinced the average score of the position is 2⅔ but I did not manage to reach this figure by an average calculation on various environments.

As a consequence, though I like an environment like E_t = {½|-½} + {1|1} + {1½|-1½} + {2|2} + {2½|2½} ... + {t|-t}, it is better to use it for practical (or confirmation) reasons but not for try and prove theoritical results.
Anyway we can claim that a result coming from an analysis in such environment is very near the best possible result isn't it?
I suspect I am in alignement with Robert on this point (but I am not quite sure).

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Jun 27, 2021 10:05 am

Gérard TAILLE wrote:
Gérard TAILLE wrote:Though my preference goes to thermography calculation, my mathematical curiosity tells me to look at a theory which will be based on the environment
E_t = {½|-½} + {1|1} + {1½|-1½} + {2|2} + {2½|2½} ... + {t|-t}
Why I said I prefer thermography calculation ?

$$W
$$ ---------------------
$$ | . O . O O . O . . .
$$ | X X X X X X O . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
Click Here To Show Diagram Code
[go]$$W $$ --------------------- $$ | . O . O O . O . . . $$ | X X X X X X O . . . $$ | . . . . . . . . . . $$ | . . . . . . . . . . $$ | . . . . . . . . . .[/go]
For the position above I showed you we can reach a good result by an average calculation on 256 environments. It is not easy of course but it is not the most important point.

$$W
$$ ---------------------
$$ | O O a O O O . X . .
$$ | O X O X X X X X . .
$$ | O X X X . . . . . .
$$ | O O O O . . . . . .
$$ | . . . . . . . . . .
Click Here To Show Diagram Code
[go]$$W $$ --------------------- $$ | O O a O O O . X . . $$ | O X O X X X X X . . $$ | O X X X . . . . . . $$ | O O O O . . . . . . $$ | . . . . . . . . . .[/go]
For a position with a ko like the position above I am convinced the average score of the position is 2⅔ but I did not manage to reach this figure by an average calculation on various environments.

As a consequence, though I like an environment like E_t = {½|-½} + {1|1} + {1½|-1½} + {2|2} + {2½|2½} ... + {t|-t}, it is better to use it for practical (or confirmation) reasons but not for try and prove theoritical results.
Anyway we can claim that a result coming from an analysis in such environment is very near the best possible result isn't it?
I suspect I am in alignement with Robert on this point (but I am not quite sure).

Bill Spight · Post by **Bill Spight** » Sun Jun 27, 2021 10:20 am

Gérard TAILLE wrote:
Bill Spight wrote: There are two problems with language, here. One is using "dominate" in two senses, one in the sense of CGT, the other in the sense of von Neumann game theory. The other is using "on average" in two senses, one in the sense of CGT, the other in the sense of statistics.
I think you have found here the misunderstanding. How could we avoid such misunderstanding in the future?
Because I am far to be as expert as you on such issue I accept all wording you can propose, provided the proposal looks unambiguous.

Can you clarify, for the future, in which meaning you would like to use the words "dominate" or "average"?

Thank you.

Here are my preferences, for your consideration.

As I said above, I would prefer not talking about statistical averages, because, AFAIK, nobody has done the relevant statistics, or is likely to do them anytime soon. So we are lelt with guesswork. Informed guesswork, perhaps, but guesswork, nonetheless.

Average territorial or area values for combinatorial games (go positions without ko fights in the game tree) do not rely upon statistics, and are fine in that context. Average gains of plays or sequences of play which are the differences between the average territorial or area values of the final positions and average values of the starting positions are also fine.

As for domination, it is possible, for instance, to say that a play by Black that moves to a final net score of Black 4 dominates a play that moves to a final net score of Black 3, but that occurs at temperature 0 or below. It is not in general possible to say that a Black play that moves to an average value of 4 dominates a Black play that moves to an average value of 3. Von Neumann game theory requires final scores to assert domination, unless one can prove otherwise. CGT domination can be proven with difference games, which, perforce occur at temperature 0. Now, there are cases where we may feel confident that one play dominates another, even if we haven't proven that, but in general I would prefer not to talk about domination except at temperature 0 or with difference games.

Gérard TAILLE wrote:BTW, does it make sense for you if I use the wording : move "a" is better than move "b" at temperature t ?

My preference would be to restrict that to cases where the miai value of move a is greater than the miai value of move b. Otherwise, we are talking about statistics, which requires guesswork.

Edit: If the statement is based upon unstated information about subsequent plays, IMO, that information should be stated. If not, then my preference is as I said.

Gérard TAILLE wrote:In such sentence can move "a" be a tenuki (I mean a move in the environment at temperature t)?

Well, a move in the environment at temperature t, gains t. So that would mean that move b gains less that t.

Gérard TAILLE · Post by **Gérard TAILLE** » Sun Jun 27, 2021 11:09 am

Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote: There are two problems with language, here. One is using "dominate" in two senses, one in the sense of CGT, the other in the sense of von Neumann game theory. The other is using "on average" in two senses, one in the sense of CGT, the other in the sense of statistics.
I think you have found here the misunderstanding. How could we avoid such misunderstanding in the future?
Because I am far to be as expert as you on such issue I accept all wording you can propose, provided the proposal looks unambiguous.

Can you clarify, for the future, in which meaning you would like to use the words "dominate" or "average"?
Thank you. Here are my preferences, for your consideration.

As I said above, I would prefer not talking about statistical averages, because, AFAIK, nobody has done the relevant statistics, or is likely to do them anytime soon. So we are lelt with guesswork. Informed guesswork, perhaps, but guesswork, nonetheless.

Average territorial or area values for combinatorial games (go positions without ko fights in the game tree) do not rely upon statistics, and are fine in that context. Average gains of plays or sequences of play which are the differences between the average territorial or area values of the final positions and average values of the starting positions are also fine.

As for domination, it is possible, for instance, to say that a play by Black that moves to a final net score of Black 4 dominates a play that moves to a final net score of Black 3, but that occurs at temperature 0 or below. It is not in general possible to say that a Black play that moves to an average value of 4 dominates a Black play that moves to an average value of 3. Von Neumann game theory requires final scores to assert domination, unless one can prove otherwise. CGT domination can be proven with difference games, which, perforce occur at temperature 0. Now, there are cases where we may feel confident that one play dominates another, even if we haven't proven that, but in general I would prefer not to talk about domination except at temperature 0 or with difference games.

Gérard TAILLE wrote:BTW, does it make sense for you if I use the wording : move "a" is better than move "b" at temperature t ?
My preference would be to restrict that to cases where the miai value of move a is greater than the miai value of move b. Otherwise, we are talking about statistics, which requires guesswork.

Edit: If the statement is based upon unstated information about subsequent plays, IMO, that information should be stated. If not, then my preference is as I said.

Gérard TAILLE wrote:In such sentence can move "a" be a tenuki (I mean a move in the environment at temperature t)?
Well, a move in the environment at temperature t, gains t. So that would mean that move b gains less that t.

Is it a good understanding to say that if a reference to ko exist then you do not want to use the term "better than" ?
Isn'it a pity in certain position like:

Click Here To Show Diagram Code: [go]$$B Black to play $$ --------------------- $$ | . . . . . O b . . | $$ | . . c a O O X X X | $$ | O O O O X X X . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]

Though it is common sense for me to say black "a" is "better" than black "b", obviously I agree that the miai value of black "a" is not greater than black "b".
BTW black "a" is more sente than black "b" because after black a and a white tenuki, black may follow by black c.

Bill Spight · Post by **Bill Spight** » Sun Jun 27, 2021 11:45 am

Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote: There are two problems with language, here. One is using "dominate" in two senses, one in the sense of CGT, the other in the sense of von Neumann game theory. The other is using "on average" in two senses, one in the sense of CGT, the other in the sense of statistics.

Gérard TAILLE wrote:I think you have found here the misunderstanding. How could we avoid such misunderstanding in the future?
Because I am far to be as expert as you on such issue I accept all wording you can propose, provided the proposal looks unambiguous.

Can you clarify, for the future, in which meaning you would like to use the words "dominate" or "average"?
Thank you. Here are my preferences, for your consideration.

As I said above, I would prefer not talking about statistical averages, because, AFAIK, nobody has done the relevant statistics, or is likely to do them anytime soon. So we are lelt with guesswork. Informed guesswork, perhaps, but guesswork, nonetheless.

Average territorial or area values for combinatorial games (go positions without ko fights in the game tree) do not rely upon statistics, and are fine in that context. Average gains of plays or sequences of play which are the differences between the average territorial or area values of the final positions and average values of the starting positions are also fine.

As for domination, it is possible, for instance, to say that a play by Black that moves to a final net score of Black 4 dominates a play that moves to a final net score of Black 3, but that occurs at temperature 0 or below. It is not in general possible to say that a Black play that moves to an average value of 4 dominates a Black play that moves to an average value of 3. Von Neumann game theory requires final scores to assert domination, unless one can prove otherwise. CGT domination can be proven with difference games, which, perforce occur at temperature 0. Now, there are cases where we may feel confident that one play dominates another, even if we haven't proven that, but in general I would prefer not to talk about domination except at temperature 0 or with difference games.

Gérard TAILLE wrote:BTW, does it make sense for you if I use the wording : move "a" is better than move "b" at temperature t ?
My preference would be to restrict that to cases where the miai value of move a is greater than the miai value of move b. Otherwise, we are talking about statistics, which requires guesswork.

Edit: If the statement is based upon unstated information about subsequent plays, IMO, that information should be stated. If not, then my preference is as I said.

Gérard TAILLE wrote:In such sentence can move "a" be a tenuki (I mean a move in the environment at temperature t)?
Well, a move in the environment at temperature t, gains t. So that would mean that move b gains less that t.
Is it a good understanding to say that if a reference to ko exist then you do not want to use the term "better than" ?
Isn'it a pity in certain position like:

$$B Black to play
$$ ---------------------
$$ | . . . . . O b . . |
$$ | . . c a O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------
Click Here To Show Diagram Code
[go]$$B Black to play $$ --------------------- $$ | . . . . . O b . . | $$ | . . c a O O X X X | $$ | O O O O X X X . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]
Though it is common sense for me to say black "a" is "better" than black "b", obviously I agree that the miai value of black "a" is not greater than black "b".
BTW black "a" is more sente than black "b" because after black a and a white tenuki, black may follow by black c.

That falls under the reliance upon subsequent play, which will be different after a and after b. My objection was to the bald statement without reference to subsequent play, which was why I made my edit.

If you say that Black a is better than Black b because it threatens Black c, fine.

Or even because it produces ko threats, that is fine as well, because it implies a possible ko fight.

But you need to spell these things out, to keep misunderstandings to a minimum.

Edit: In this case:

Click Here To Show Diagram Code: [go]$$B Black to play $$ --------------------- $$ | . . 4 3 6 O 5 . . | $$ | . . 2 1 O O X X X | $$ | O O O O X X X . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]

This sequence is better than

-

at temperature 1, because it yields a possible ko threat for Black.

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