Thank you Robert.
Sure you will now understand my two questions in my post https://lifein19x19.com/viewtopic.php?p=280542#p280542 and why in Q2 I was interested by white best moves but not black best moves!
Do you know if it already exists theorems allowing to detect such domination of a sente move against a gote one?

Apart from the general tree simplifications, I do not know if some part of CGT implies such. Bill and I have composed a few additional theorems about simplification of specific rather simple trees, of which some can have some sente, due to reversal, see [22]. Then I have proved something related but without sente:

"Suppose a local endgame in which only one player can make territory and the opponent's move creates two separate follow-ups that are simple gotes without follow-ups. A long sequence is not worth playing successively." [14][33]

EDIT:

Of course, there are also my and partly Bill's theorems for choice among several local endgames, which can be local sentes. [22]

In this post the considered tree is quite simple: a depth 2 tree with only four leaves and both players have only one option.

In your famous theorem
Theorem 134 [early endgame, high temperature]
If F < T, it is a good approximation that the starting player starts
- in the environment if T ≥ MGOTE,
- locally if T ≤ MGOTE (the creator chooses the gote option).

The tree is a little more complicated, with five leaves) and looks like the figure here under.
[img][/img]

Let's call a, b, c, ... the count of positions A, B, C, ...
We have c = (e+f)/2 and d = (g+h)/2

Now the situation is not so simple because at the beginning of the analysis you do not know if black AC and white AD are gote or sente.
In this context what do you call MGOTE to try and apply your theorem?
Is it always MGOTE = (b - d)/2 ? (even if it might happen that AD is sente ?)

Even simpler: remove G and H!

I do not understand Robert. If you need to remove G and H in order to apply your theorem then you cannot apply your theorem in the following position:

Click Here To Show Diagram Code

[go]$$B initial position, Black to move
$$ ---------------------------
$$ | O . X X . . . a X . X X .
$$ | O O . O X . O . O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

After white "a" we do not reach a leave because of the remaining ko.
OC you can say that in the position above the white move at a" (move AD in my tree) is gote but in the context of the theory you must prove it is gote and it could not be so easy and it depends also on the environment.

As I have already mentioned, the theory for local endgames with gote and sente options is for single plays or a sente sequence of exactly two plays while all on-board examples have long(er) sequences. This makes application of the related theorems for the late on-board endgame impossible and for the early endgame for also this reason an approximation.

We did not handled the following position.

Click Here To Show Diagram Code

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

How do you prove that black "a" cannot be better than black "b"?

If a local double sente position is a position G without reversible plays, in which MGOTE > MB,SENTE, MW,SENTE, with only one option for each player and only one follow-up (the tree is only a depth-2 tree) then I can agree a local double sente does not exist.

If however, knowing the ambiant temperature is T (not quite high) , a local double sente position is a position G in which white must answer to the initial black move and black must answer to the initial white move then a local double sente position do exist.

With your defintion a local double sente does not exist, but many go players use another defintion and local double sente do exist for them.

BTW do you think the majority of go players knows what reversible play means?

Robert, nobody is wrong. Your are right inside your theory and go players using another defintion are right inside their practice.

BTW, if in position G the players have several options you have not defined what "local double sente" means have you?

What exists is a global double sente (a local endgame in a global position so that either starting player gets a local reply) - do not call this a local double sente and do not excuse all the traditionalists who only discussed local endgames when assessing the difference value as the alleged move value with the alleged justification of having a double sente!

In my previous post I ask the following question:
"if in position G the players have several options you have not defined what "local double sente" means have you"

Could you at least answer the basic simplier following one:
"Assuming in position G both players have SEVERAL options, how do you define a black's local sente position G ?"

Correct. See earlier for an informal approach.



For every choice of one black option and one white option, apply the definition for no options. Yes, this can result in multiple types and values of G. Interpretation may come next and sometimes be "of little use".

Oh yes I have now a better understanding of one of your previous post


Concerning double sente positions look at this very simple position:

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------
$$ . O X . X a O b . O . O X . .
$$ . O X X . X X O . O O O X . .
$$ . O O X X O O O O X X X X . .
$$ . . O O O X X X X X . . . . .
$$ . . . . . . . . . . . . . .[/go]

Taking your definition, and comparing MGOTE and MSENTE, this position is "only" sente for black.

Being quite convinced that this position is considered double sente by the majority of Go players, I chose to define the notion of sente differently in order to be as near as possible the common understanding of sente positions.
For me black "a" and white "b" are miai and the position is double sente according to my definition.

I still do not understand why you need avoid the existence of double sente positions. To be sure you even added that the position has no revesible play. What really harms Robert?

For the majority of players, the position is settled and double sente is a misnomer. It is also a source of a two-sided ko threat (after which Black has a one-sided ko threat).



Weak players do not have any understanding. Players who have acquired some reasonable understanding know that local positions can be assessed locally or globally. E.g., the most typical endgame evaluation book problem expects a local assessment. E.g., during play, one also needs to take into account the global context.



Please show how you apply your definition to assess this position!



1) This is the consensus of Bill Spight, Francisco Crido and me.

2) It is about local evaluation.

3) More specifically, the understanding of local evaluation of a position as a player's sente is: sente means that the opponent replies locally; in order to reply locally, it must be more (or ambiguous: equally) valuable for the opponent to reply than it is valuable for the player to start local play; hence, the ("player's") follow-up move value must be larger than the initial local move value. For local assessment as a local double sente, this means that it must be so for both starting players. This gives the pair of value conditions that would characterise a local endgame as a local double sente (if it exists / existed).

4) First, we did not see a necessity for excluding local double sente. However, careful study revealed that it might not exist. Therefore, we have tried to and then proved the non-existence (for the basic case).

My own definition of the status of a position is indeed surprisingly very simple and very general because it works whatever the number of options for black and white:

What is the statuus of a position P?
Assume P is put into a rich environment at a high temperature (any local move in P would be a mistake at this temperature).
If you can play a game without mistakes, in which the first move in P leads to a local gote sequence, then the position P is called a gote position.
If you can play a game without mistakes, in which the first move in P is a black (resp. white) move leading to a sente sequence, then the position P is called a black (resp. white) sente position.
A position which is both gote and sente is called ambiguous.
A position which is both black sente and white sente is called double sente.

Applied to the very simple position I proposed in my previous post you will find easily it is a double sente position instead of a simple black sente position with your definition.

I am able to show you far more interested positions but such positions have several options and you explained that you might not be able to find the status of such position.

Your definitions of types have the potential to mostly make sense. Currently, you need to remove equivocalities:

- "you" -> "Black" / "White" / "either starting player".

- Define "mistake" or use a different concept.

- There must also be a type ("terminal" ?) when neither player has a legal local play.

- You mix the meanings of the type of one player's move sequence(s) and the type of the position considering either starting player. Distinguish and possibly define them!

- Since conceptually you define a kind of global double sente, call it "global double sente"!

(I have not checked whether parity of the of moves in the environment before the first local move has an impact.)

When you will have corrected / clarified your definition, you should actually apply it to your example by annotating and calculating with the rich environment!

I am not very satisfied with all the definitions I gave in my previous post: basically my goal was only to define what a sente position is. I added the definition of gote position and ambiguous position in order to try and imitate your approach but it is not a good idea because my notion of sente is different from yours.

So please note the following update (without the definition of an ambiguous position) :

What is the status of a position P?
Assume P is put into a rich environment at a high temperature (any local move in P would be a mistake at this temperature).
If you can play a game without mistakes, in which the first move in P is a black (resp. white) move leading to a sente sequence, then the position P is called a black (resp. white) sente position.
A position which is both a black sente position and a white sente position is called a double sente position.
If a position is neither a sente position nor a leaf position then this position a gote position

It seems understandable for me and I am sure you understand what I mean.

A move made by a player is a mistake if she cannot reach the best result after this move.

I do not see any interest to define such position. Defining a leaf position would be more interesting. For me a leaf node is simply a node in which neither white nor black have an interest to play, even when the ambiant temperature is T = 0.

Done. After each "sente" word I added either "position" or "sequence"

No a double sente position is not a global notion but a local one.

Leaf (position) has a specific term in informatics, CGT, graph theory etc.: there is no child. Children are given due to moves to them. Therefore, there is no child if there is no legal move.

Your conceptual idea is not what is called a leaf. What you want is closer to settled position or CGT-like stop position.



Since you want to define "double sente position" via some environment and perfect whole-board/token-set play, it is global, regardless of your desire for local!

A double sente position is simply a position which is both a black sente position and a white sente position.
If you say that my double sente position notion is a global notion that means that you think my sente position notion is also a global notion.

I know you do not use a rich environment and it is not surprising you do not understand clearly the meaning of such environment.

Click Here To Show Diagram Code

[go]$$W
$$ -----------------------
$$ . . X a . X X X . O . .
$$ . . X O O O O O O O . .
$$ . . X X . . . . . . . .
$$ . . . . . . . . . . . .
$$ . . . . . . . . . . . .[/go]

In the position above, with my definition (and also yours OC) black position is sente. What does that mean for a go player?
Firstly it does not mean that black can play immediately at "a" expecting a local white answer. Many other areas on the board could be far more interesting and must be played before. As you see it is not an immediat global sente position
Secondly it does not mean either that in the future black will be really able to play at "a" with an immediat answer by white: depending of the real environment it may well happen that white will be able to play first in the local position by a reverse sente move. It may also happen that white would prefer to not answer to black move at "a" by proposing a furikawari.
Saying that the position is a black sente position means only that black as good chances to be able to play later in the game at "a" in sente, based on the experience of go players concerning the type of environment you can encounter in practice. That is the meaning of a rich environment : a kind of approximation of the real environment we can encounter in practice.
Puting P in a rich enviroment instead of the real environment is a proof that the result of the analysis will depend only on the position itself and not the real environment. Using a rich environment is a guarantee that the analysis is local to the position P and not global depending of a real environment.

"In the position above, with my definition [...] black position is sente"

Prove it by applying your definition to your example! So far, you only claim it.

"Puting P in a rich enviroment instead of the real environment is a proof that the result of the analysis will depend only on the position itself and not the real environment."

Prove it! So far, you only claim it.

"Using a rich environment is a guarantee that the analysis is local to the position P and not global depending of a real environment"

As before.

Oops I expected it was obvious for you Robert!
Let's take a rich environement at a high temperature T (for exemple you can take T = 100) and assume for example it is black to play.
If black is able to play in P in sente then the final score of the game will be
S1 = -7 + T/2
Now let's assume white plays in P when the temperature of the environment reach the temperature t. The score of the game will be
S2 = -8 + T/2 + t
S2 < S1 => -8 + T/2 + t < -7 + T/2 => t < 1
That means that white will be able to play first in P only if black is unable to play in sente in P before the temperature of the environment reach the value t = 1. Because the value of the threat after black "a" is equal to 3.5 it is clear that black will be able to play in P in sente before white can play herself in P.
That proves position P is sente according to my definition.


I already explained that for me a rich environmemnt is simply a good approximation of any real environment. In order to analyse any position P, I always put this position in a rich environment. All local positions being handled in the same manner, in the same environment, that means that all results obtains are specific to the local position P analysed. By defintion I say that these results are local to the position P.

Let me remind you the main point behind this choice.
When I find a position P is a black sente position that means that, within a rich enviroment, black may be able to play first in P with a sente local sequence. Because a rich environment is expected to be a good approximation of any real environment a go player may conclude that, within the existing real environment, black can really expect to play first in sente in P (following OC a good timing based on the decressing temperature of this real environment).

Let's now take your defintion (MSENTE < MGOTE and so on). I agree your defintion is a local one but how do you prove that black in the example can expect to play first in P in a real game?