I did not reply to your thermography message because I understand too little of the semantics of thermographs to be sure exactly what meaning is conveyed by some definition referring to them.

You continue to talk about common go language, feeling, common go players' understanding WRT double sente but what you suggest as common is not and by asking players you won't find something common (for reference, I asked some strong Koreans what is a ko threat according to their rules and got more different answers than interviewed persons). Besides, I have already said pretty much that can be said about that.

The traditional endgame theory's "points in double sente" as a move value is another aspect that is a) part of common knowledge, b) presumes the flawed concept of local sente for both starting players and c) uses a value that is meaningless as a move value (and slightly more meaningful as a value used for positional judgement). It is not a move value because I) it is not a value per some number of moves and II) it does not inform well enough when to play the move.

Again, you use the word "threat" and I do not understand your intended meaning of this word. Please clarify! In endgame value theory, the word is, unfortunately ambiguous unless used clearly (like in my phrase "threat and its execution" distinguishing first and second moves (or sequences) but you use some different meaning).

There is a purpose of me using "local double sente" for an object (type of a local endgame): The local endgames shall be classified for the purpose of identifying their correct kind of local evaluation, which differs for local gote, Black's local sente and White's local sente (and there are finer differences for such long types). By knowing of the non-existence of local double sente, we know 1) we do not need an evaluation for this type, 2) accurate evaluation is that of one of the other types, 3) roughly how approximative evaluations should behave of local endgames resembling would-be local double sentes. (There can be other terms, such as "global double sente", for other study purposes.)

For your example, the needed term is not "double sente" but "local endgame with global context so that the move value does not always give sufficient information on correct move order and move orders expressed as choices in which local endgames to play differ for different starting players", which you might call by a shorter new term.

{18 | 4 || 0 | -14} itself is not an environment. It is just one combinatorial game.

@ Gérard

Just a couple of questions, not about definitions, not about how go players should use a term, but about your own usage.

1) Given the following combined game with Black to play.
G = {1|0} + {5||1|-1} + {-3|-5} + {6|-1||-5}

What do you call {6|-1||-5}?

2)Black to play.
G = {3|-4} + {4|2||0} + {-4|-5} + {5|0||-2}

What do you call {5|0||-2}?

Thanks.

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It is a combinatorial game. But it could be an environment. Not much of an environment, not a typical environment, but still an environment. I don't know of any practical reason to use it as an environment, however. In real life you want to consider it for its specific properties, not as background. I wouldn't use Beethoven's Fifth Symphony as elevator music, either. You could, but why?

My remaining remarks are not aimed at Robert, but are made to endorse his views.



Well, ko threat is even harder to define than double sente. There are even some people who believe that any move is a ko threat! Which makes the term meaningless. Moi, I say that any move can be a ko threat, depending on circumstances. Robert and I have both done research in which a simple gote can be considered a ko threat.

But yes, Kano's double sente examples show that even 9 dans have different ideas of what a double sente is. (True, I have not asked any 9 dans about them, but they are truly bad. )



Gérard's statistical investigations bear out the fact that it is useless as an indicator of when to play a so-called double sente.



Threat is an informal term. I use it as a synonym for the follower of a game, with the connotation that the opponent may wish to answer it locally. (Local is another term that is not easy to define on a go board.)



One good reason for not bothering to define local double sente is that CGT does not use any term like it. CGT did not, before I defined them thermographically, talk about sente and gote, either, but it did talk about equitable and excitable games, which are synonymous with gote and sente, but not exactly the same. O Meien may talk about double sente moves, but not when calculating evaluations. He doesn't need the term, either, except in certain circumstances.

_________________
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— Winona Adkins

Visualize whirled peas.

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When seeing your question the first thought I had was the following : what percentage of the go players have ever seen such notation?
In this context I will not be surprised to be wrong.
Something looks bizarre in your question: {6|-1||-5} looks like only a pure description of a local game but, just before the question you mentionned it is black to play. That shows my interpretation is certainly not correct and I fear you will have to correct me.
Anyway I will continue without taking into account it is black to play.

First of all {6|-1||-5} tells me which sequences may happen in this area.
Here I see that white can play first in this game but after his move neither black nor white can play another move.
It is not the case if black plays first. After a black move either Black or white can play another move and after that it does not remain any move.
I deduce this information by only looking at the slashes.
Secondly {6|-1||-5} shows figures (6, -1 and -5) which represent the score (for black point of view) you get for each possible sequence (here only three sequences are identified).
Strictly speaking {6|-1||-5} tells me nothing else.

BTW I see a small difficulty. Seeing a possible follow-up (when it is black to play), surely in the real life black or white may choose other moves which can be better in some (rare?) circumstances (for example a ko-threat which locally will be a loss, or simply a dame move). When seeing {6|-1||-5} I have to understand also that all other moves are considered bad and can be ignored.

Adding something is something else: with this area you can then calculate various average values, you can play a game with a tax assumption or in an ideal environment, you can put some words like gote, sente, threat or whatever but that way you create something else beyong the strict meaning of {6|-1||-5}.

Concerning the second example {5|0||-2} I do not see what I can add Bill.

I am only asking about what you would call these positions.



There is no right or wrong. What you call them is what you call them.



I'm afraid I was not clear. My intention was to show you a whole board position with Black to play. You do this yourself.



Or simply non-existent. And I did not intend there to be other circumstances. I meant that this is it. Sure, I excluded filling in your own territory for no reason, and so on. If you wish, I can include dame. A dame is this simple gote, {0|0}. But my idea is that this is it.



There is no tax, no external plays. This is it.



Well, if it matters that G represents everything on the board, and that changes anything, please say so.

I am a bit surprised that you had nothing more to say, considering that you constructed a whole board that included what you want to call a double sente. If I had asked about, say, {3|-4}, I thought that you would call it a gote, but now I'm not sure.

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Visualize whirled peas.

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Your question is now a little controversal Bill.
It is not only what is my understanding of {6|-1||-5} but it is far beyond it is how I caracterise such area, gote or sente or ...

It is a controversal question because anybody may define gote and sene as she wants. Because it is basically a question of definition it is impossible to say which defintion is the best.
I am completly open to any definition proposed and I can of course discuss with anybody, taking any defintion. In the other hand I expect also that we can discuss taking another defintion.
I understand Robert's defintion of "double sente" and I agree at 100% that with such definition "double sente" does not exist. What can I say more? I agree, I agree, I agree.
Now I proposed for discussion another defintion of "double sente" and the answer is : No, no no, this is not the good defintion, the good defintion is ... and with this definition "double sente" does not exist. How can we discuss?

Yes Bill I see you have open the door and you even use yourself double sente to caracterise certain situations. Fine.

I can try to define such word as gote, sente, reverse sente, double sente but be sure I am completly open to other definitions.

First of all yes Bill I can easily call {3|-4} a gote. In absence of follow-up by defintion it is for me a gote. But do not forget it is only a defintion. We all know that a couple of miai gote may act as ko threat and you may feel such gote point being sente. What is the point? If you say that a gote may be a sente that only means you have not clearly defined these terms. As soon as you propose a definition for sente and gote you have no contradiction providing you do not change the defintion between two sentences.

So let's call gote an area {x|y} with x > y. It is a defintion and nothing else.

Gote points have very important caracteristics: they are comparable, the evaluation (x+y)/2 allows us to tell wich gote is the best one and you can proof that by playing the gote in the order given by this evaluation you are always correct.

What about sente. My definition is : an area {x|y||z} is sente for black if x>y>z and (x+y)/2 > y-z
Here again it is only a defintion and nothing else. In particular I do not claim that white has to answer immediatly to a black move. It may be the case in a lot of practical cases but it is not part of the definition.

Now what about your {6|-1||-5} example. According to my defintion it is neither a gote nor a sente. In fact depending of the circumstances it may have the behaviour of a gote or a sente.
In any case such area do not have the caracteristic of gote area: you can calculate an evaluation like ((6+(-1))/2) + (-5))/2 of course but this time this area can be incomparable to true gote, and you cannot be sure that the calculated evaluation will allow you to play your yose in the best way.

Concerning the area {5|0||-2} it is a sente according to my definition. If, taking my definition, the theory tells me that black will very often (against an ideal environment?) be able to play in this area with an immediat answer by white it is fine. It is a good caracteristic even I know it is only an "average" behaviour.

Now I can propose a definition of a "double sente", oh sorry a "double blabla"
a "double blabla" is an area {a|b||c|d} with a>b>c>d and (a-b)/2 > b-c and (c-d)/2 > b-c
Surely if the theory analyses a "double blabla" it will prove it is a quite hot point with interesting caracteristics etc. etc. and it may even help to choose the correct order for playing them with good chance to find the best one etc.
Here again nobody knows if a play in this area will be answer immediatly by the opponent. It is not in the defintion is it?

I am not sure to have answered completely to your question Bill but it is a difficult one isn'it?

Well, double sente has been controversial for at least 45 years. I don't think that gote and sente are particularly controversial.

One thing is that these terms have been around for a long time, and like words in general, have acquired different senses. For instance, if I have made a play with sente, my opponent has answered it, and we may say that my play was sente. But suppose that he should not have answered it. Then we may say that it was really a gote. It was a sente because he answered it, but it was a gote because he should not have. We also talk about taking sente or taking gote, which use still different senses of the terms. Players pick up these different senses without consulting a dictionary.

But when we talk about estimating the value of a position or of a play, we use the terms, sente and gote, in a technical sense, and they need to be precise and clearly defined. Unfortunately, in the texts that I and many others learned from, these technical terms were not precisely and clearly defined. Instead we were taught that if a position was a double gote, we estimated the territory as the average of the two resulting positions, but if the position was a sente, we estimated the territory as that of the result of the sente sequence. OC, this does not make sense for double sente, since there are two different sente sequences with different results. In any event, no estimate for the territory of a double sente position was ever offered.



Informally, sure. Like Lewis Carroll's Humpty Dumpty: A word means just what I choose it to mean. ;)



That doesn't work for technical terms. They are not a question of definition. If two technical definitions do not produce the same results, then at least one of them is wrong, or they belong to different theories.



I expect that you understand the theory behind his definition.



What is the theory behind your definition?

AFAICT, there is no theory behind the common usage of double sente. Some rather horrible examples exist in textbooks.

I was kibitzing a pro game with Jiang Jujo, 9 dan, several years ago, and one of the players, in the endgame, did not answer one of the textbook examples of a double sente. I nudged Jujo and pointed out, as a joke, that the player did not answer that play, thinking that Jujo knew that I knew that he knew that I knew . . . that the play was not really a sente. Jujo just looked at me like I was crazy.



Nobody I know disputes that there are double sente plays, depending on the global situation. The question is whether there are double sente positions, independent of the rest of the board. The textbooks showed us such positions, independent of the rest of the board, and claimed that they were double sente. Were they right, that's the question. Kano was plainly wrong, dead wrong. O Meien doesn't do that. Yes, as John Fairbairn points out, he mentions double sente in reviewing a game, in the global context of the whole board. No problem. He doesn't isolate the plays and claim that they are double sente.



It has to be local gote because the second player has no local reply.



Sure, but that's a different game, such as {3|-4} + {3|-4}, which is equal to -1. But unlike a simple point of White territory, either player may play in one of the miai pair with sente. Or, in a ko fight, if the opponent ignores the threat, with gote. Because of such possibilities, I classify the miai pair as ambiguous. Technically, you can apply any of the terms, gote, sente, or ambiguous to the situation and get the same result. That's OK. They all fit into the same theory. You can even call the miai pair a double sente. I don't know anyone else but me who does that, however.



Well, it can't be sente by itself. I.e., it cannot be intrinsically sente. It may be played with sente in certain situations, but that's different. That's accidental, in a philosophical sense.



You can also prove it as Nogami/Shimamura did by showing that {x|y} + {x|y} = x + y, when x > y.



BTW, I think that you mean (x-y)/2 > y-z. It's a definition that fits the theory. (And, FWIW, it is the same one that I derived way back when. Some friends thought that I should publish it, but I thought that it was fairly obvious. In retrospect, maybe I should have tried.) For kos, there are different theories, any of which may or may not apply to any particular situation. But for these types of plays and positions CGT evaluates non-ko positions in line with traditional go theory up to and including O Meien's approach, if in some cases more precisely. Traditional go theory did not evaluate double sente positions, and CGT does not need the term.



Nor is it a part of traditional go theory or CGT. I remember as a shodan explaining to people why a certain play was sente. I pointed out that the threat of the sente was larger than the reverse sente, so that if there were other plays on the board that were smaller than the threat and greater than the reverse sente then the player whose sente it was would be able to play the sente before the other player could play the reverse sente. (I was aware that there were exceptions. ) That is why, I continued, we assume, as a rule, that the sente will be played. Traditional go theory calls that phenomenon the privilege of a sente. In thermographic terms, the privilege is indicated by a colored mast.



Right. Your definitions are too narrow. The theory encompasses more general definitions. In terms of them the average value of this position, m = (6 - 1 - 2*5)/4 if and only if -1 ≥ m ≥ -5. m = -1¼, so that condition is met. Inequality holds, so that also means that the position is technically, intrinsically gote. However, given the other positions on the board, correct play is for Black to play in this position with sente. We may say that it is globally, accidentally, sente. Even better, perhaps, is to say that the position is gote, but on this board the move is sente.



Accidentally.



Sure it has gote characteristics. It does not raise the local temperature when played with gote. In fact, it lowers it. That is an essential characteristic of gote, in the theory. Furthermore, {6|-1||-5} + {6|-1||-5} + {6|-1||-5} + {6|-1||-5} = -5. Only gote and some ambiguous positions have the characteristic that a finite number of them equals a number.



Because this is a technical, intrinsic sente, four of them will not equal 0, which is its mean value. If Black plays first in the foursome, the correct result will indeed be 0. But if White plays first the correct result will be -2. The average value, m, will satisfy 0 ≥ m ≥ -2/4 = -½. This result if White plays first approaches m in the limit as the number of instances goes to infinity. That is so for all intrinsic, local sente. (I used to think that that characteristic defined sente, but it doesn't.)



It appears that you are making a definition based upon analogy with your definition of sente for {x|y||z} as (x-y)/2 > (y-z)/1. (I supplied the divisor of 1.) Is there a theory behind that definition? In The Endgame by Ogawa/Davies, Davies points out that (according to traditional go theory) the divisor comes from the net number of plays between the two results. Between x and y there are two net plays, and between y and z there is one net play. However, for {a|b||c|d} the net number of plays between b and c is 0. Davies points out that the divisor for (b-c) should therefore be 0.

Edit: This is a long note. Let me highlight a major point.



It's not you.

It's the old textbooks.

I repeat, adding emphasis:

Nobody I know disputes that there are double sente plays, depending on the global situation. The question is whether there are double sente positions, independent of the rest of the board. The textbooks showed us such positions, independent of the rest of the board, and claimed that they were double sente. Were they right, that's the question. Kano was plainly wrong, dead wrong. O Meien doesn't do that. . . . He doesn't isolate plays and claim that they are double sente {in themselves}.

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What prevented that characteristic from defining sente?

First, there are ambiguous positions that are similar to sente, but do not raise the local temperature, so that there is no privilege. Example: {4|0||-2}.

Second, I have discovered some actual gote that exhibit the same property. One player always gets an advantage from playing first.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

You won't hide that gote, will you?:)

Oops I am not aware of these 45 years of controversial discussion.
Maybe there is some misunderstandig on this point. Taking a real game with several subgames, my view is that subgames like the one I called "double blabla" may add some uncertainty on the result of the game. Because of that calculating acurate values for gote subgames might look irrelevant. To avoid that I would have liked to extract such positions from the set of gote but I see you do not like the idea. Considering all these positions as gote I fear that it will be more difficult for the theory to give reliable results.

Let's concentrate essentially on gote.

Can you make the same exercice and define without any ambiguity what is gote, sente or maybe unknown position as I did.

I said:


and you even add {x|y} + {x|y} = x + y which is nice result

What caracteristics remains with your gote defintion? Or, if you prefer, how do you reformulate such caracteristics with you gote definition?

Surely, without an unambiguous gote definition the discussion could not be very usefull.

I know my definion of gote is quite narrow but be sure I am I advance ready to take yours providing it is unambiguous Bill.

Kano's Yose Jiten came out in 1974. Kano defines double sente as a place where whoever plays first, Black or White, can play with sente. In the discussion of his very first example, he recognizes that one player may be much more likely to not reply than the other. Instead of admitting that in that case the position is really a sente for the other player, he introduces a new term, hitsuzensei, meaning certainty or necessity. See previous discussion here: https://www.lifein19x19.com/viewtopic.p ... 67#p178067

The Endgame by Ogawa and Davies came out in 1976. Davies' observation about dividing the so-called double sente value by 0 tolled the mathematical death-knell for double sente, but few go pros are mathematicians.



Remember that a gote position may be played with sente, given the global situation. Which number is more likely to get the average non-mathematical player's attention, a "2 point double sente" or a "20 point gote"?



Here is a prototypical gote thermograph. (BTW, humans reason pretty well with prototypes. )



The left and right walls are each inclined, which indicates a play or sequence of plays made with gote for each player playing first. Where they meet the black mast rises vertically, indicating that neither player will play in that game above that temperature (tax). This is how a gote thermograph looks where the left and right walls meet, whatever it may look like below that temperature.

Some thermographs for kos look similar, but the angles of the walls are different. As you know, ko thermographs can look strange.

Here is a prototypical sente thermograph.



The left wall of the thermograph is vertical, which indicates a sequence of plays with an even number of plays by each player, starting in this case with a Black play and ending with a White play. I.e., Black played with sente. The right wall is inclined, indicating that White played with gote. Above where the walls meet the left wall rises vertically as the mast before the mast becomes black. The blue mast indicates the privilege of Black to play first with sente in that temperature range. This is how a Black sente thermograph looks where the walls meet, no matter how it looks below that temperature. A White sente thermograph, OC, has a vertical right wall and an inclined left wall.

The thermograph of a gote has a black mast, below which each wall is inclined.

The thermograph of a sente has a blue or red mast where the walls meet, depending upon whose sente it is, below which the wall of that color descends vertically while the other wall is inclined.

There are non-ko positions that are ambiguous between sente and gote, with different thermographs. We have already seen one where the mast is blue where the walls meet, but the blue wall is inclined below that while the red wall is vertical!

_________________
The Adkins Principle:
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— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

OK Bill, in order to know if a area is gote I only have to look where right and left wall meets. If they meet with two inclined line it a a gote. Fine and let's proceed.

Now consider G1, G2, G3 ... gote areas with mean values (I mean the temperature where left and right wall meet) g1 >= g2 >= g3 ...
What theory tell us to help finding the best move to play?
Is it correct to say: the best play is probably a play in game G1 but, unfortunetly, be aware it is not sure at 100%.

Tax all the positions with the same amount and find the minimax results of play at that temperature. If the local temperature of G1 is greater than that of G2, then we know for a certainty that between temperatures G2 and G1 orthodox play (best play) is in G1. We can figure out the thermograph of the combined play. We are looking for best play at temperature 0, I assume.

Heuristically, OC, initial play in G1 is likely to be correct. That's why go players developed traditional go theory centuries ago. And that's why we usually start reading with the largest play. We also know that if all the gote are simple gote, best play is in G1. Other heuristics and theorems exist. For instance, in example 1) above, it was obvious that Black could make the first play with sente.

Edit: One heuristic, of which I know you are aware, is that of getting the last play before a significant temperature drop.

BTW, the go theory term for the temperature at which the walls meet is miai value, which is how much the gote move or reverse sente move indicated by the wall there gains.

_________________
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One of those theorems is whether Black should prefer to play in

G = {g|0} or in D = {b|n||0|-w}, where b > n > 0, w > 0, and g > 0 and b, g, n, and w are all numbers.

Black should prefer to play in D
if b-n ≥ g or (b ≥ g and n+w ≥ g),
and Black should prefer to play in G
if g ≥ n+w and g ≥ b,
with the ko fight caveat.

Note that the "double sente value", n, is not relevant.

Edit for correctness.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Let's take G1 = {8|5||0} and G2 = {6|0}
G1 et G2 are incomparable and g1=3¼ g2=3
I assume each G3,G4,.. not too complex (I mean only of the forms {x|y} or {x|y||z} or {x||y|z} and the majority of them of the form {x|y})

Without having any knowledge of CGT theory I have to read all the game (not so easy is it?) in order to find the best move (in G1 or G2 if not in G3 or ...).

Now the question is : how CGT knowledge can help me?

I assume I have to consider temperature between 3 and 3¼ ?

What doaes that mean? If I have to read all the game G1 + G2 + G3 ... to find the result of the game, I fear I will gain nothing in the process.

I already calculated the miai values 3 and 3¼ for G1 and G2. What do you suggest here?

Obviously I must have missed something because, for the time being, I don't see clearly what CGT knowledge brings me in the process to find the best move.

Since you are vague about G3 and other positions, let us take them as the environment for G1 and G2. All we need to know now is the miai value or estimated miai value of G3. Let's call it t, with t < 1½, since we know {8|5} and assume that it is relevant, and we also let the mean value of the environment be 0, for convenience. If {8|5} is not relevant, then we can replace it with its mean value, 6½.

At temperature t < 1½ the left wall of the thermograph is max(0+8-t,6-0) = 8-t. And the right wall is min(0+6,0+5+t) = min(6,5+t). When t < 1 it is 5+t, when 1 ≤ t < 1½ it is 6.

So, given what we know, when t < 1½ Black plays in G1. When 1 ≤ t < 1½ White also plays in G1, but when t < 1 White plays in G2.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Two points Bill
1) I was assuming the miai values g1 ≥ g2 ≥ g3 were droping not too fast => g3 should be say between 2 and 3
2) My question concerns the best move. I know that an heuristic choice is quite perfect with CGT theory but I do not know if CGT theory can help me finding the real best move (OC assuming you know all the environment). If in the process you assume somewhere an ideal environment then you will only have en heuristic choice won't you?

If you don't want to be vague, let t = 0. But anyway, heuristics can help guide reading.

If you want 2 ≤ t < 3, then replace {8|5} with 6½ and play G1. If you are not more specific, what can be said about best play?

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

OK Bill let's simplify the problem and formulate it in a different way.

Let's take G1 = {8|5||0} and G2 = {6|0}
and let's assume G3,G4,.. only of the forms {x|y} (I mean only simple gote) with g1 ≥ g2 ≥ g3 ≥ g4 ...
In addition let's suppose the game black to play G1 + G2 + G3 + G4 + ... is quite close and let's suppose that the god play allows black to win the game.
Question : what is the best way to proceed in order to be sure at 100% to choose as a first black move a winning move?