The link is broken, BTW. Copying without quoting is probably the reason. It would also work to jump to that page and then copy the URL. Here, again, is the link.
https://www.lifein19x19.com/viewtopic.p ... 35#p194535

The Nihon Kiin position I am absolutely sure was constructed to illustrate the importance of playing double sente. Unfortunately, it did not also illustrate the importance of sometimes not replying locally to double sente. Probably because if you're not supposed to answer it, how can it be double sente?

As for the position in the Nogami-Shimamura book, I strongly suspect that it was originally constructed for the same purpose as the Nihon Kiin position, but the third variation, where the double sente is not answered locally, was inserted before publication. Maybe that variation came from actual play, but I kind of doubt it. It would be interesting if it did. It would also be interesting to see what the bots say about it.

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

Visualize whirled peas.

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Forward values and backward values

Actually, I think I was on to something all those years ago. I was still in the swing value camp, where I took the value of a play in this simple gote, {a|b}, given a > b, as a - b. I also was aware that the best play was not always the largest play as traditionally calculated. I also became aware of the concept of the environment, which, as we know, I modeled as a set of simple gote. I took the value of the largest such gote as my standard for evaluation.

From that perspective, how to evaluate {d|e||f|g}, with d > e > f > g? Well we compare it with a simple gote, {a|b}, given a > b, in an environment of temperature, t, to modernize my thinking slightly. It does not affect the argument. OC, a-b > 2t, but also d-e > 2t and f-g > 2t. Otherwise it is not an environment. And it doesn't hurt to assign a number to a couple of variables. So let's evaluate D = {d|e||0|-g}, given g > 0, with A = {a|0}, with Black to play.

1) Black starts in A. The result is

a + 0 - t/2 = a - t/2.

2) Black starts in D, with sente. The result is

e + a - t/2, which is better for Black than 1), OC. But White does not have to answer in D. Let White play in A.

3) Black starts in D, White answers in A. The result is

d + 0 - t/2 = d - t/2.

So we compare a with d. a is the swing value of A, our standard of comparison. And d is the forward value of D.

OC, if d - e > a, then d > a, so the case of sente is covered. And for the case of gote, the forward value of D is easier to calculate than {d + e + f + g}/4. In fact, we do not have to worry about how to classify D.

In hindsight, we can see that I was actually anticipating the calculation of the sides of the thermograph at different temperatures in terms of the play in an ideal environment. Which is how I redefined thermography in 1998.

----

Whether to answer a double sente, given two of them, of the form {j|k||m|n}.

Let A = {a|0||-b|-c} and D = {d|0||-e|-f}, and let Black play in A to {a|0}. Should White answer?

Well, we already know the answer. We compare a with f, the swing value of Black's threat with the backward value of D (from Black's point of view).

----

OC, I haven't worked anything out in detail, at least not recently, but let's explore Gérard's hypothetical with several such plays where the temperature of the environment is low enough.

First, let's compare threats and find the largest one. Next, compare its swing value with the backward values of each of the others. If it is greater than all of them, it's a good bet that Black should make that threat.

And, as things get more complicated, let's not forget that traditional evaluation arose for a reason. The more double sente there are, the more likely it is that they act as a rich environment for each other, and the traditional evaluation becomes more relevant. And by traditional I do not mean the traditional double sente value, since with even two of them we cannot assume that one of them will be sente against the other, much less double sente.

Edit: Difference games.

Also, as things get more complicated, since difference games allow us to draw conclusions about play in every non-ko environment, they can be useful. OC, working them out on the table can be daunting, but I have done some of the work for us.

Let A = {a|0||-b|-c} and D = {d|0||-e|-f}, and let Black play in A to {a|0}. Should White answer?

Well, when there are only two of them with a sufficiently low ambient temperature, White should answer if a is at least as big as the backward value of D (for Black, that is). But what about non-ko environments? When is answering in A at least as good as playing in D, in every non-ko environment? When a is greater than or equal to both the backward value of D and the forward value of D. Vive la difference game!

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

Visualize whirled peas.

Everything with love. Stay safe.

It is interesting that n + 0.5b + 0.4w worked best, as that is almost the same as treating the double sente as gote and comparing swing values. The swing value of the gote being n + b/2 + w/2.

Edit: We can accommodate traditional theory this way, can't we?

if w ≥ 2n + b then f = 2n + b ; Black reverse sente or ambiguous
else if b ≥ 2n + w then f = b ; Black sente or ambiguous
else f = n + b/2 + w/2 ; gote

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

Visualize whirled peas.

Everything with love. Stay safe.

Your idea 2n + max(b,w) is interesting but not as good on average than the swing value of the gote:
f(b, n, w) = 2n + max(b,w) => pourcentageOK = 89,68%
f(b, n, w) = n + 0.5b + 0.5w => pourcentageOK = 93,24%

How about traditional theory?

if w ≥ 2n + b then f = 2n + b ; Black reverse sente or ambiguous
else if b ≥ 2n + w then f = b ; Black sente or ambiguous
else f = n + b/2 + w/2 ; gote

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

Visualize whirled peas.

Everything with love. Stay safe.

I begin to understand why you claim double sente doesn't exist.
Let me take an example (it is certainly not the best one example but it is enough to explain the point)

Click Here To Show Diagram Code

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

Let's look at point "a" with different hypothesis.

Click Here To Show Diagram Code

[go]$$B
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . a . . . . . . 1 . . . . . . |
$$ | . . . . X . O . . . . O . X . . . . . |
$$ | X X X X X X O . . . . O X X X X X X X |
$$ | . . . . . . O O O O O O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

After black the white territory is open in the right and as a consequence another black move at "a", though big, would not threaten great damage on white territory and it does not look double sente.

Click Here To Show Diagram Code

[go]$$B
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . a . . . . . 2 1 . . . . . . |
$$ | . . . . X . O . . . . O . X . . . . . |
$$ | X X X X X X O . . . . O X X X X X X X |
$$ | . . . . . . O O O O O O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

After and the context is quite different. The white territory is now closed on the right and a black move at "a" would be a greater threat on white territory and we may call a black move at "a" a double sente move. Here is the point : instead of saying that "a" here is double sente move it may be better to say that white is simply sente, implying black answer at "a" and with this wording a double sente move doesn't exist.
More generally the so called double sente may be only the result of the previous move we can thus consider sente!

Click Here To Show Diagram Code

[go]$$W
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . a . . . . . . 1 . . . . . . |
$$ | . . . . X . O . . . . O . X . . . . . |
$$ | X X X X X X O . . . . O X X X X X X X |
$$ | . . . . . . O O O O O O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

We can see the same phenomenon here
When white plays closing the right side of her territory instead of saying that the point a is double sente we can just say that is sente and black should answers immediately at "a".

In that sense double sente doesn't exist. It is only a part of the flow of the game as an answer to a previous sente move.
I am sure you will able to find more relevant example showing this fact.

Is it your feeling concerning the non existence of double sente or do you have something else in mind?

Practical, accidental double sente certainly exist. and occur quite frequently. They may be illustrated thermographically when both sides of the thermograph are vertical at the same temperature.

However, theoretical, essential double sente do not exist, at least on a finite board. The point is well illustrated by the Nihon Kiin example and the Nogami-Shimamura book. If it is wrong to answer a double sente, how is it a double sente? Your statistical result on estimating the value of double sente moves says that evaluating them as gote moves works very well. (Edit: Rather better than the double sente value.) If so, why consider them to be double sente?

If a play is double sente, it is so only with respect to the rest of the board. It is not intrinsically double sente.

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

Visualize whirled peas.

Everything with love. Stay safe.

Yes Bill I agree with you but how to adapt thermography to this fact?

Click Here To Show Diagram Code

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

at temperature t < 1 the two lines are vertical and the local area is seen double sente ... but local double sente does not exist!

I perfectly understand why thermography says it is double sente at temperature t < 1 but that is not the point.
If we are saying double sente does not exist and they may even be estimate as gote point (value n + b/2 + w/2) we have two problems with thermography:
1) the wording "double sente" in presence of two vertical lines must be clarified
2) two vertical lines does not really exist because eventually any so called double sente have an estimate value of n + b/2 + w/2 which may be far above t but not INFINITY.

OC nobody (including me) wants to change this beautiful thermography theory but how can we be consistant?

Good news Bill.
By changing my model to a far bigger one, the best formula converges towards b + 0.5n + 0.5w
That means that the formula b + 0.5n + 0.4w was only the consequence of a too small model.
Isn't it an interesting result?

No local double sente is not a feeling but a proved theorem. See https://www.lifein19x19.com/viewtopic.p ... 33#p260633 for an example, for which you should calculate move value and follow-up move values. You can hardly get any closer to an alleged double sente, except in doubly ambiguous shapes.

Right. The fact that at some temperatures the two sides of the thermograph does not show that the position is a double sente. For that to be the case, both sides of the thermograph would need to be vertical at all temperatures.

There are two such cases. One occurs with this kind of position, a miai. {a|b||b|c}, a > b > c. The thermograph is vertical at v = b. The other one occurs with this kind of position, a standoff. {a|b||c|d}, b < c, a > b, c > d. The thermograph is vertical at v = median(0,b,c). Nobody, except sometimes me, calls these double sente.



Well, I have been saying this for years. A voice crying in the wilderness.



Don't call a position double sente without qualification. Don't classify a position as double sente, except perhaps in the miai and standoff positions that I have indicated. That's all it takes.

Thermography does not require the term, double sente. However, traditional theory used the term and go players still use it. Thermography can indicate under what circumstances the term might be useful. As we have seen, even at the Nihon Kiin, the belief in intrinsic double sente can be detrimental.

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

Visualize whirled peas.

Everything with love. Stay safe.

If we can explain it, sure.

I take it that your larger model means larger b and w, on average.

How does the traditional theory stack up with your larger model? The traditional model uses b when the position is a theoretical Black sente, which should happen more often, the larger the model.

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

Visualize whirled peas.

Everything with love. Stay safe.

Yes Robert I perfectly understand what you mean but in any case you cannot go too far.
A proven theorem in a given theory is correct only under the hypothesis of the theory and it may happen in real life that the hypothesis were not true.
If in a local situation black can threat to kill a group of 100 white stones and white can also threat to kill a group of 100 black stones the situation is a sure double sente because on a board with 361 points, killing 100 white stones (I assume no ishi-no-shita) wins the game.

What you are saying is consistent with the theory and does not violate any of its assumptions. It says that double sente depends upon the conditions. You just articulated the conditions, that's all.

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

Visualize whirled peas.

Everything with love. Stay safe.

I took the model n ∈ {1, 2, 3, 4, 5, 6, 7, 8} and b,w ∈ {8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
which leads to 1352 possible areas and 789 558 interesting couple of areas.

I am at your disposal if you wish to try another model Bill.

BTW I have to idea how to prove b + 0.5n + 0.5w is the best function!

Here is the traditional model (leaving out the double sente value of n, which we know does not work very well).

if w ≥ 2n + b then f = 2n + b ; Black reverse sente or ambiguous
else if b ≥ 2n + w then f = b ; Black sente or ambiguous
else f = n + b/2 + w/2 ; gote

Edit: Note that b appears in all three comparisons, n appears in two of them, and w appears in only one, and it is w/2 at that. So using traditional theory may well on average disfavor w.

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

Visualize whirled peas.

Everything with love. Stay safe.

The assumption is having any local endgame with simple follow-ups for both players (and no ko), which we are discussing here.

The difficulty is to find a good compromise between a theory with its model and the real life.
A double sente move exists in the all day real life but what about the theory?
When your are facing a local area with follow-ups as db(15, 3, 17) in a an environment at temperature say 9 it is quite impossible to avoid the wording "double sente" because it is simply common go language.
But here is the point : you must not take the wording "double sente" in a too strictly sense. It is the same with a so called "sente" move : it does not mean that you must answer locally to this sente move (you may answer with another "sente" move on an other area etc.). A sente move simply increases the local temperature but strictly speaking surely "sente" move does not exist.
The problem is not to say that "sente" or "double sente" does not exist, the problem is rather to redefine the words "sente" and "double sente" in order to reach best possible compromise between theory and real life.

What exists in textbooks, except for a few recent ones, is that certain local positions are classified as double sente, without reference to anything else. That is a mistake, but it has deceived many go players over the years.



Where what you say differs from those texts is that they make no reference to that environment, or to any environment at all. This is the problem that Robert, I, and others are running up against.

By contrast, it is possible to classify {18|3||0|-17} as a gote with an average territorial value of 1, where a play by either side gains 9½ points, on average. Furthermore, in an ideal environment with ambient temperature less than 7½, either side will be able to play in this position with sente, given orthodox play. At such a temperature range, you may say that this is a double sente in that range. Strictly speaking, you cannot omit that qualification.



In which case it is simply an informal term. I wish those textbooks had treated it that way.



Actually, it does. Those same textbooks have classified positions as sente and gote for 2 centuries, if not longer. And that's OK. It is quite possible to define sente and gote with no reference to anything besides the position being evaluated. Only double sente is problematic in that regard.

The reason has to do with the evaluation of positions (games in CGT). A gote position is easy to evaluate. All you have to do is take the average value of the stable followers. If they are worth a and b, the gote position is worth (a+b)/2. (I know, I haven't defined stable, yet. But it works, as is obvious with most gote.) A sente position is even easier to evaluate. Just take the result of the sente sequence.

The problem comes with double sente. It has two sente sequences with two different results, say, a when Black plays and White replies and b when White plays and Black replies, with a > b. Which one do you use? Well, neither, obviously. This problem is easier to explain. There is at least one stable follower that you are ignoring. Either there is one when White does not reply to Black, or one when Black does not reply to White, or both. Once you admit that, you can evaluate the position. OC, in that case you no longer consider it a double sente.

By the 1970s go players had recognized that there was a problem with the idea of double sente. Kano tries to introduce the idea of necessity, Ogawa and Davies point out the problem of division by 0. I am the only go player I know of who understood the problem at that time. Conway, Berlekamp, and Guy would have, as well, if they had paid attention to traditional go theory. But they had their own theory, which worked, without anything like double sente.

But what about the fact that a theoretical gote can, in certain circumstances, be played correctly with sente, and vice versa? The theory never claimed anything else. It is a heuristic, such that the theoretical best play is very often correct. The fact that the informally defined double sente can usually be played with sente when it arises does not mean that you can define double sente locally. Double sente always depends upon circumstances.

It is true that in 1998 I redefined thermography in terms of an ideal environment. However, it had existed for more than 20 years without such a definition. An environment is not necessary to define sente and gote thermographically. Conway, Berlekamp, and Guy, who developed CGT, were at that time unaware of any technical meanings of sente and gote, and referred to excitable and equitable positions. I think I was the first one to define sente and gote thermographically, as well as recognizing the ambiguous category. OC, sente and gote retain their informal meanings, as well. As does double sente.



It is not a question of compromise. Most go boards provide nearly ideal environments. Otherwise the original go theory would not have arisen a couple of centuries ago.

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

Visualize whirled peas.

Everything with love. Stay safe.

It can be a global double sente, except that in your example we would be having one player with the turn.

Assessed as a local endgame (possibly covering the whole board except for 2-eye-formations), your example is not a local double sente endgame. Put it on the board and calculate move value and follow-up move values. You are going to find DECREASING move values, as with my linked book counter-example!