How evaluate double sente moves ?

[Bill Spight]

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. 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.

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

$$B
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O . . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------

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!

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.

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

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

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?

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.

[Bill Spight]

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?

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?

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.

[Gérard TAILLE]

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.

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.

[Bill Spight]

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.

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.

[Gérard TAILLE]

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?

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?

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.

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!

[Bill Spight]

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?

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.

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.

[RobertJasiek]

it may happen in real life that the hypothesis were not true.

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

[Gérard TAILLE]

it may happen in real life that the hypothesis were not true.

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.

[Bill Spight]

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?

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.

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.

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.

But here is the point : you must not take the wording "double sente" in a too strictly sense.

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

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.

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.

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.

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.

[RobertJasiek]

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. ;-)

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!

[Bill Spight]

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!

Decreasing move values indicate stable followers.

[Gérard TAILLE]

For me the major (awesome) contribution of thermography is the fact that the status of a local area depends of the environment temperature.

$$B
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O . . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------

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]

When temperature is > 4 we may say that the local position is sente, between 4 and 2 we may claim for reverse sente position, between 2 and 1 we can see a gote position and under 1 a double sente position. It was really an amazing revelation for me and I immediately adhere to this idea.

When you (Bill or Robert) are talking about essential or intrinsic double sente it seems to refer to an area analysed by default in an environment at very high temperature. Yes OC I agree with you at 100%; in this context double sente does not exist.

Anyway we have to be careful to what the reader will keep in mind when reading such discussion.

For a go player the wordings gote, sente, reverse sente and double sente makes sense even if she has no clear (mathematical?) definition for these terms.
If you put in front of such go player a theory saying double sente does not exist this player have good chance to not adhere immediately to the theory because it hurts her go language.
On contrary if you explain that all these term makes sense thanks to the existence of an environment with a temperature t, surely she will be far more interested and both go players and theoricians will be happy won't they?

[RobertJasiek]

Players using the phrase double sente informally may have learned the difference value, which alone says nothing about when to play locally. They should better learn from Bill and me because we give advice of timing and move order. Yes, this requires becoming familiar with formal terms.

[Bill Spight]

For me the major (awesome) contribution of thermography is the fact that the status of a local area depends of the environment temperature.

$$B
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O . . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------

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]

When temperature is > 4 we may say that the local position is sente, between 4 and 2 we may claim for reverse sente position, between 2 and 1 we can see a gote position and under 1 a double sente position. It was really an amazing revelation for me and I immediately adhere to this idea.

When you (Bill or Robert) are talking about essential or intrinsic double sente it seems to refer to an area analysed by default in an environment at very high temperature. Yes OC I agree with you at 100%; in this context double sente does not exist.

Anyway we have to be careful to what the reader will keep in mind when reading such discussion.

For a go player the wordings gote, sente, reverse sente and double sente makes sense even if she has no clear (mathematical?) definition for these terms.
If you put in front of such go player a theory saying double sente does not exist this player have good chance to not adhere immediately to the theory because it hurts her go language.
On contrary if you explain that all these term makes sense thanks to the existence of an environment with a temperature t, surely she will be far more interested and both go players and theoricians will be happy won't they?

What do you think I have been doing all these years?

In 2000 I presented a paper about the first environmental go game between Jiang Jujo and Rui Naiwei, in the introduction to which I described how to read a thermograph and described sente, gote, and double sente in thermographic terms. OK, that was at the Mathematical Sciences Research Institute in Berkeley, CA. But in 2002 I created the page, Double Sente is Relative on Sensei's Library ( https://senseis.xmp.net/?DoubleSenteIsRelative ), in which I clearly state:

Double sente is relative. It depends on what else is on the board. Every Go position can be categorized as sente, gote, or ambiguous. Any play, whether a sente or gote in the abstract, can be a double sente if the reply when either player makes the first play is larger than anything else on the board. Usually, double sente are played as soon as they arise.

I have also explained double sente on rec.games.go and here as well as on Sensei's Library.

In his yose book in 2004, O Meien, rightly did not try to evaluate double sente. In fact, he did not evaluate sente, but only reverse sente. In doing so he promoted understanding while avoiding controversy. (Edit: Nothing about how the 2 point double sente really isn't.) We do not need the idea of double sente for evaluation. Thermography can replace the old notion of absolute double sente for the useful idea of relative double sente, but Go professionals do not pay much attention to western amateurs. It is going to take some time for the new understanding to take hold.

Edit: BTW, my paper was published in More Games of No Chance (Cambridge University Press, 2002) and may still be online on the MSRI site. The thermograph I use in it to illustrate double sente does not require a high temperature. The double sente temperature range is from 1½ to 2½. One of the positions that you constructed to be double sente had a double sente temperature range of 3 - 4½.

Readers of O Meien's book are going to be in awe of him and simply accept the fact that he does not evaluate double sente, and they won't, either, even if they don't know why not. Western amateurs who interact with Robert and me are going to bring up the question of double sente. So we try to explain it. But who listens?

[Gérard TAILLE]

What do you think I have been doing all these years?

In 2000 I presented a paper about the first environmental go game between Jiang Jujo and Rui Naiwei, in the introduction to which I described how to read a thermograph and described sente, gote, and double sente in thermographic terms. OK, that was at the Mathematical Sciences Research Institute in Berkeley, CA. But in 2002 I created the page, Double Sente is Relative on Sensei's Library ( https://senseis.xmp.net/?DoubleSenteIsRelative ), in which I clearly state:

Double sente is relative. It depends on what else is on the board. Every Go position can be categorized as sente, gote, or ambiguous. Any play, whether a sente or gote in the abstract, can be a double sente if the reply when either player makes the first play is larger than anything else on the board. Usually, double sente are played as soon as they arise.

I have also explained double sente on rec.games.go and here as well as on Sensei's Library.

In his yose book in 2004, O Meien, rightly did not try to evaluate double sente. In fact, he did not evaluate sente, but only reverse sente. In doing so he promoted understanding while avoiding controversy. (Edit: Nothing about how the 2 point double sente really isn't.) We do not need the idea of double sente for evaluation. Thermography can replace the old notion of absolute double sente for the useful idea of relative double sente, but Go professionals do not pay much attention to western amateurs. It is going to take some time for the new understanding to take hold.

Edit: BTW, my paper was published in More Games of No Chance (Cambridge University Press, 2002) and may still be online on the MSRI site. The thermograph I use in it to illustrate double sente does not require a high temperature. The double sente temperature range is from 1½ to 2½. One of the positions that you constructed to be double sente had a double sente temperature range of 3 - 4½.

Readers of O Meien's book are going to be in awe of him and simply accept the fact that he does not evaluate double sente, and they won't, either, even if they don't know why not. Western amateurs who interact with Robert and me are going to bring up the question of double sente. So we try to explain it. But who listens?

Oh I see Bill. It'is really a pity.
With my scientific formation I am very fond of theory like thermography may be because I am used to study first the assumption of the theory and I am used to appreciate the various theorems we can prove starting from these only assumptions. That's fine for me Bill.
For a non-scientific person the problem is completly different. If she notes that a theorem seems not true, you will probably explain that it is because the environment is non conform to the assumption. But that does not change anything : the feeling will be that the theory seems not so interesting.

Let's take a very simple example:

$$B
$$ -----------------
$$ | . . b a . . . |
$$ | X X X O . O O |
$$ | . . X O . O X |
$$ | . X X X O O X |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ | . . . . . . . |
$$ -----------------

Click Here To Show Diagram Code

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

if you claim a go player that the position above has a miai value = 1 she will have some difficulty with the credibility of the theory. Why?
Simply because instead of "a" she will clearly see the possibility black "b" which could very interesting if the environment looks like a tedomari situation with only one remaining 2 gote points (all 1 gote points being miai).
How can you ignore the adding value of such possibility when, for other situations, you estimate a value with a precision of 1/16 if not still better? She is not wrong is she?
By discussing with you on this forum I expect to motivate some readers to study such theory but I confess I have no miracle idea to help you valorising the work done.

BTW Bill, did you try to explain how work on endgame (CGT) may change your view of the game in all phases of the game, including fuseki?