Decreasing move values indicate stable followers.

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

Visualize whirled peas.

Everything with love. Stay safe.

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

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?

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.

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:



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?

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

Visualize whirled peas.

Everything with love. Stay safe.

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:

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?

Many years ago, I have become aware that the endgame starts on move 1. My study of endgame theory has greatly improved my assessment of more moves during the opening and middle game fully or partly in terms of the endgame. This often simplifies strategic planning because the complicated remaining part of the middle game shrinks to a few moves, like Lee Changho is said to analyse games.

I agree with you Robert of lot of endgame theory results can be surprisingly applied through all the game and lead to unexpected moves.
BTW I am convinced that a major part of IA strength comes from endgame why? When you build a neural network from nothing you play against yourself a great number of games and try to build your knowledge from the result of the game. In the process the analysis has no choice : it begins by the end of the game going slowing backwards toward the beginning of the game. What does that mean? The IA begins by building a solid knowlelge of endgame technics and all this information is registered in the depth of the neural network. As a consequence IA, in very logical way, will try to apply such technics all over the game before discovering and adding some other technics like attacking a weak group etc.

IA is far more logic that humans. If you try to apply yourself this approach starting with the endgame technics you will really discover a new way of playing Go and you will even be able to understand the background (unfortunetly not the details behind such choice) of strange moves made by IA in the beginning of the game.

Bill: Only a fool rushes in, but I don't mind playing the fool. I do so here because I sympathise. For years I've tried to talk about thickness and nobody seems to listen. In reality they do, I know, but it seems otherwise. And I think that's the case here.

In both cases I believe the root of the problem is that many listeners are not familiar with the foreign language being quoted: Japanese or, here, mathematics.

But English gets in the way, too. You say you and Robert try to 'explain' it. I don't think that's true. What comes over to me is that you try to 'justify' it, or 'prove' it. To a fellow mathematician that may be tantamount to 'explaining' it, but to us non-mathematicians it not only is not an explanation, it actually makes the problems worse. In fact, unless I've missed something, we have not even reached the starting point: we have not even been given an answer to the question "Why?" Why should we care (or not care) about, say, double sentes? Just saying on the one hand you can gain one-sixteenth of a point in every 17.63 games (or whatever: I exaggerate obviously, but essentially that seems to be Robert's approach) or, on the other (your approach), saying that double sentes don't exist but are just ghosts in the machine that have intrinsic and extrinsic forms (i.e. do exist?) is not conducive to a useful auditory experience for most people.

Here are some further examples of English bafflement which make me look like those cartoon characters drawn with two heads pointing in two directions.

You say O Meien did not 'evaluate double sente'. O Meien says, "Black 1 is double sente and must not be overlooked. After that, Black returns to the cut-and-capture with 3 and 5. This hands the turn to move to White." I put it to you that most non-mathematicians would reason that O is telling them play 1 before 3 and 5 because 1 is bigger, i.e. double sentes have a value. Elsewhere he says of a game of his that he could: "play the double sente of 1 and 3, which I felt very smug about" (i.e. double sentes exist).

Now I happen to know that this all has to be qualified by a very important statement by O Meien: "It is impossible to talk about boundary plays in sente, boundary plays in gote and boundary plays in reverse sente if we skirt around the factor of 'value of the move.' The right approach is first to understand 'value of the move' and only then talk about the various kinds of boundary play." But most other people don't know that because they haven't seen his book.

You have, and seem to agree with or approve of most of what he says. Yett I see no reference here to his favoured term "absolute counting", which, to me, given the confusion between deiri and miai counting is 'absolutely' essential. At least, I think it is better to start from scratch with that new term rather than be told (as I think we have here) that absolute counting is just a form of miai counting. Likewise, his concept of 'value of a move' gets not short shrift but zero shrift here. I suspect the reason it doesn't play well here is that Robert is apt to pop up and tell us that there is A-value, B-value, C-scoring, D-scoring, E-counting, F-counting, or whatever. Not wrong, but useless. Trying to define, and so restrict the usage, of ambiguous words that non-mathematical native speakers have learnt and used since toddlerhood is never going to work. O Meien's approach of accepting and living with the ambiguity works fine. At least, I found it useful.

This benefit of this looser (and totally normal) use of language is shown in what, for me, was one of the highlight parts of his book. Of one example he says, "This boundary play is only 7 points in sente. Also, it makes Black thick at his back, which gives him a bigger say in the centre (in other words, it will become difficult for White to consolidate his centre moyo), and so it is actually more like 5-point sente." That's a 2-point difference, so understanding and learning from this example is about THIRTY-TWO times more useful than being shown a one-sixteenth infinitesimal, or whatever, and since this type of situation occurs in just about every game and usually several times in each game, it is actually infinitely more useful. It also, incidentally, obliquely answers the fundamental question "Why?"

I strongly believe that what most western go players want - crave, even - when it comes to the endgame is an explanation written like O's. It absence is why people don't appear to listen.

I hope my detailed comments show that some of us DO listen, even though in my case I have close to zero practical interest in the endgame.

Well, I belong to the humanistic school of pedagogy, so that is not a problem in person. When writing for readers with whom you do not interact, it's hard to please everybody.



Well, first, I do not make such a claim. If we are talking about the top, I first talk about how we estimate the territory there. It is not at all difficult to get the interested student to see that we count 2 points for Black and 5 points for White. It is also plain to them that the net estimate is 3 points for White. For the ordinary go player I do not talk about negative points for White.

It is then obvious to her to see that if White plays the hanetsugi at b, the score is 1 point better than the estimate for White, and so we reckon that White has gained 1 point with that play. I do not mention miai counting. What's the point? If she objects that the move is actually worth 2 points, which she has learned elsewhere, I say that that's another way of evaluating moves, but it does not mean the same thing as how much the move gains. I do not talk about averages unless necessary. OC, I have to do so for sticklers, like mathematicians and scientists.



The fact that Black has the possibility of playing a "two point gote" at a or a "one point sente" at b is not a problem for miai counting; it is a problem for deiri counting, which is what most go players still learn, I am afraid. The reconciliation between 2 points and 1 point is not a problem for miai counting, because both of them are 1 point moves.

Edit: When I wrote that I was in the misapprehension that Black b and Black c were equivalent. In fact, Black c is better, because it threaten to kill. That doe not alter the question of whether to play sente or gote.



Well, I don't, do you? I am the guy who came up with the category of ambiguous plays, which this is. And, I may add, that is not difficult to get across to the student. "Black can play sente at c or gote at a. Either one could be correct. So we can't call this position either sente or gote. It's ambiguous."



Wrong about what? About a claim I do not make?

BTW, check back later. I am going to insert the thermograph for the top position later today, maybe tomorrow.

Edit: I'm back!

Here is the promised thermograph.



Small dog, long tail.

Now locally, below temperature 1 Black prefers to gain one point with the gote. Globally, Black might prefer to play the sente. The sente does not show up below temperature 1, but it does above temperature 1. Between temperature 1 and temperature 12 the mast is colored blue. That indicates that Black can play sente between those temperatures without changing the count. Above temperature 12 Black's threat is not big enough, as the black mast indicates.

As I said, the position is ambiguous between sente and gote, and the thermograph indicates that fact.



Well there are principles that apply to both the endgame and other phases of the game, and many lessons scale up. I have written about such things over the years.

Edited 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.

Some endgame decisions can be made informally when obviously some move is more valuable, or moves in a value range but of allegedly different types. Then moves informally known as double sente should be played first. If a player's endgame skill may end at 5 kyu level, then that's it and no value calculations aka mathematics are ever needed. You can use excuses to remain there, such as "no interest in the endgame", "O uses his own terms", "everybody does not want to overcome traditional terms".

When endgame moves have similar values, however, calculations, clear terms and formula (or conditions) become essential.

Most moves of a scored game are endgame moves and most of them must be distinguished by values. Many earlier moves can also be characterised by endgame values to make better decisions. Of all those moves, their values can often only be distinguished by fractions.

Say, there are roughly 100 moves whose values matter. Err on average by 1/8 per move and you lose almost 1 rank. Err 1 point on average and you lose 7 ranks. Making fun of fractions by referring to the 1/16th point disrespects improving some ranks.

That's why the endgame requires values.

Values must be calculated correctly, and that differs for different types of local endgames, whether local gote or local sente. Here, furthermore we must understand how to evaluate alleged double sente. It does not exist as a type of local endgame, so why?

We might evaluate it, as is usually correct in theory, as a local gote. However, doing this precise calculation for an alleged double sente is often very time-consuming. Here, my often much faster approximative evaluation of alleged double sente comes in. So why? To evaluate both reasonably accurate and fast.

I agree with you Robert but this is not my point

Click Here To Show Diagram Code

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

Assume, as white, you have to choose between a move at "a" or a move at "b"
Surely you will choose white "b" because this move dominates clearly move "a".
I know perfectly that thermography do not distinguish these two areas and I know also that the reason is that we suppose the environment being ideal.
That's fine and I agree with you without any doubt. But that is not the point.
The point is the following : if you present a go player your theory and you explain that you are able to valued any local area with a quite accurate value she will be rather upset seeing the theory fails to recognise that the two above areas cannot be equivalent for a go player.
You do not need to try to show me that they are equivalent in an ideal environment. I know that and it is perfectly understandable in the context of the theory. The point is that the theory appears perfect in the majority of situations (I mean with an environment almost ideal) but the theory fails to put a better value to a move dominating another one.
Adding say ε to a move dominating an other one we have 1+ε > 1 that is the point but unfortunatly I see clearly that this adding cannot fit in theory. Maybe it'is life.

As Churchill said (allegedly), "This is gobbledygook up with which I shall not put."

But even if the gobbledygook eventually has a meaning as you go through the labyrinth, it is esoteric and irrelevant.

You wouldn't ask a beginner on the violin to play Paganini. You can hope he might aspire to it, but you'd start him on Twinkle, Twinkle, Little Star, and then work through the grades.

There is no good text, in proper English, that tells ordinary players what comes after our Stage 1 equivalent of TTLS: Ogawa/Davies. And most don't want to know what's at the far end of a fart. They just want Stage 2.

And this Stage 2 material does exist: it just happens to be in Japanese - but in informal, normal, non-mathematical Japanese. So it should be possible to do it in English. I'm not aware of any good Stage 3 material, even in Japanese, yet but I'd guess that's because there's too little demand. You would get severely diminishing returns, and most people would probably get a bigger return on time invested by studying something else, such as tsumego.

Just once, please, please, please, try to see things from the perspective of non-mathematicians.

Yes, it does.



Actually, it does. See thermograph above for the right corner.



Oh, don't cry. See https://senseis.xmp.net/?GoInfinitesimals



Good. Because they are not.



That's because the value is a game, and thermographs show numbers. The combination of these two corners has an average value of -5, but it is greater than -5. How much greater is it than -5? Well, it is greater by itself plus 5. Not much help, I suppose, but it is something.

Here is the thermograph of this combination. It's kind of cute.



Below temperature 1, it looks like a White sente. But it's not a White sente, because above temperature 1 to temperature 12, the mast is blue. So at or above temperature 1 Black can play sente, and at or below temperature 1, no matter what White plays, Black can reply to -5. That is because this combination is greater than -5.

Edit: This combination is ambiguous, too. In case anybody was wondering.

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

Visualize whirled peas.

Everything with love. Stay safe.

As always, John, I appreciate your thoughtful comments and criticism.

BTW, I first became aware of you when I bought your book about shogi at the Jena bookstore in Tokyo. That was before I started playing go, as I recall.

I am going to skip around a bit, and may not reply to everything in one note.

Oh, I am aware that I have an audience, who do listen. I have enjoyed many long and thoughtful discussions with people online about the endgame, kos, thermography, and other go topics. I have no complaints, really.



I have toyed with the idea of writing a short book on difference games. I know it's a niche topic, but it doesn't require any math besides counting up the score. You might think of it as a new kind of tsumego.

Back in 2011, I recruited some readers for an endgame book aimed at kyu players. That turned out to be a bad year for me. A couple of months later I had an operation and two weeks after that my wife's brother died suddenly. Back to the proposed book, though. To my surprise, my readers had little or no trouble with the math. It was the go that gave them problems.

Now I think if I do get a book written, it should be on advanced topics in mathematical go. Everyone else I know of who is capable of writing such a book is dead or has moved on to other things.



Thanks.

I have to say that brings back disappointing memories. Early on in the history of Sensei's Library, I wrote up some material on the endgame on SL, aimed at regular go players. A while later I took a break for several months, to preserve my sanity. When I returned, I found that what I had written had, in the ways of Wikis, been edited to correct it for a mathematical audience, and moved to a new section devoted to math. I never managed to restore it according to my original purpose of explaining things to regular players.

Now if I am discussing some technical topic with another technical type, I have no problem with that kind of writing. If someone wants to kibitz, fine, if not, that's fine, as well. But if my aim is a broader audience, often I have mathematicians, scientists, or computer programmers looking over my shoulder, ready to point out any informal imprecision or inaccuracy. For instance, in explaining the proverb that sente gains nothing, I can't simply say, as I used to, that the local territory after the (normal) sente is the same as before. I have to say that they are equal, on average, or, heaven help us, that they are asymptotically equal or in the limit. I really can't complain, but I miss my audience of regular go players.

Enough bitching. I am really grateful for all of my friends here and on SL and even on rec.games.go, if there are any left there.

Best to all, and stay safe.

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

Visualize whirled peas.

Everything with love. Stay safe.

OK, back to brass tacks.



The only question I have with that statement is that I think that the place to start is with the value of a position, its territorial (or area) count. From that you find the value of a move, and so on. Please note that he does not mention double sente in that sentence.



Having gone over O Meien's calculations of the value of a move, I can say that I talk about his concept all the time. I just call it how much a move gains.

The reason I do not now speak of the value of a move is historical. Too many people have learned ideas about the value of a move that have caused them to be confused. By simply speaking of gain I try to sidestep that confusion.

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

Visualize whirled peas.

Everything with love. Stay safe.

Gerard, some endgame theories are for a) perfection of the last move, b) the late endgame except for the detail (a) or c) the early endgame with tolerating some approximation of assuming certain environments etc. When we teach some theory other than (a), we do not claim the precision of (a). Every player can understand this - it is like solving a local life and death problem correctly only to play a larger move elsewhere during the middle game.

See my reply here: https://www.lifein19x19.com/viewtopic.p ... 96#p260696

I see Bill. I drawed the mast with black colour but, due the ambiguity, you were allowed to use the blue one and my point appears hidden.
Well I have to find a way to avoid ambiguity. Here it is

Click Here To Show Diagram Code

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

Here again you can see that a white move at "b" here dominates a move in a simple 2 points gote area.
But now you cannot paint the mast in blue because a black sente move at "b" looks a loss in an ideal environment. If I am not wrong the thermograph is thus now identical to a simple 2 points gote though we would prefer to see the domination of this area against a simple 2 points gote area.
I do not know if this way I manage to clarify my point. Let's see.
I do not know either if, recognizing such difference, I will gain on average 1 rank or more

Another beautiful example, Gérard.

Black a and Black b are incomparable, but White b dominates, and Black b loses points on average. So the thermograph is not affected by Black b.

Let me see if I understand your point. Here is a possible example based upon my early study of the yose.

Click Here To Show Diagram Code

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

In his book on yose aimed at a kyu level audience, the great Takagawa showed a similar position. He made the point that, although the hanetsugi at a was usual for White, the sagari at b had the same value and was thus playable, and also sometimes preferable. The same holds true for the Black hanetsugi at b and sagari at a.

That was a revelation to me. It was obviously true, but I had never thought of it. Afterwards, I usually played the hanetsugi, but also frequently played the sagari. (Interestingly, today's top bots seem to like the sagari, for reasons I do not know. )

I was therefore surprised, decades later, when David Wolfe pointed out to me that the hanetsugi dominates the sagari. Again, that was easy to explain.

(For our readers, it allows the opponent to also play sagari, for no gain to the original sagari. The difference game is easy to visualize. Imagine two such hanetsugi positions on the board. If your opponent plays hanetsugi in one and then you play sagari in the other, your opponent plays sagari and wins. Conceivably, you could create a ko threat with the sagari, but that is covered by the ko fight caveat. Takagawa did not show such an example.)

OC, the thermograph does not show the dominated sagaris.

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

Visualize whirled peas.

Everything with love. Stay safe.

Because the textbooks we learned from led us, and many others, astray. How so?

First let me say what they got right. From time to time, and quite often, positions arise on the go board such that, given the rest of the board, either player can play locally with sente. Everybody calls these positions double sente. In addition, we are told to hasten to play in those positions. (Some translations say to play them "early", which is problematic. It implies leaving them on the board for some time, albeit short.) If we leave them on the board, we could lose points with zero compensation, offering a free lunch to our opponent.

What they get wrong — and let me say again that the Nogami-Shimamura book is a shining example of not doing so — is identifying certain positions as double sente without regard for the rest of the board. Two common examples are the double hanetsugi on the first line, each with a large follow-up, and the double kosumi on the second line, said to be worth 2 points and 6 points respectively. Each of these can arise fairly early in the game and remain on the board for some time.

As you know, the beginning of wisdom for me about double sente came when I was 4 or 5 kyu and observed the formation of a double kosumi position in the game record of a pro game. After a while one player played the kosumi and his opponent did not answer it. Tilt! How can that be double sente when it is not even sente! I thought.

It gets worse. Kano, 9 dan, in his Yose Dictionary (in Japanese) in the 1970s, knew that there was something wrong with the idea of double sente and struggled with the concept. Nonetheless, he put the following two examples in the book. You have seen both of them, but I repeat them for our readers.

Click Here To Show Diagram Code

[go]$$ Double sente???
$$ --------------------
$$ | . . . . . . . O X .
$$ | . . . X O . . O X .
$$ | X X . X O . O O X .
$$ | . X . X X O . O X ,
$$ | X X X X O O O O X .
$$ | O O O O X X X X X .
$$ | . . . O O O . . . .
$$ | . . . . . . . . . .[/go]

Kano presents this as an example of the double hanetsugi 2 point double sente. In fact, it is easy to show that it is a 7 point Black sente. (O Meien would not have made that mistake.)

He gives the following as an example of the double kosumi. To be fair, he does not claim that this is worth 6 points, only 2.

Click Here To Show Diagram Code

[go]$$B Two point double sente???
$$ -----------------------
$$ | . . . . . . . . . O .
$$ | . . . . . . . . . O .
$$ | X X X X X . O O O O .
$$ | . . . , . . . . . , .[/go]

Really? You've got to be kidding. This is fairly obviously a gote position. I calculated it as gaining 3⅔ points for the first player, but it is possible that I made a small error.

OC, we can blame Kano's amateur ghost writer, but Kano signed off on these examples. I cannot imagine O Meien making a similar mistake.

I have already linked in this discussion to the infamous Nihon Kiin whole board double sente example, which came out, not in the 1970s, when writers were beginning to question double sente, but in 2000! I am sure that it led many readers astray.

These are not examples of beautiful flowers that sprout on the go board and are quickly plucked. They are weeds that entangle the mind.



Well, he doesn't. Take a look at the evaluation section. No double sente there. O Meien doesn't even focus on the sente, but on how much the reverse sente gains. Perhaps because prior teachings about sente gave many readers the impression that a sente sequence, which includes the reply, gains points. It is the reverse sente that gains points and that value usually determines when to play the sente or reverese sente. Perhaps there was an excess of caution on his part regarding sente, but if so, it was well motivated, I am sure.

Edit: One example of how talking about the value of sente might not be a good idea. A so-called 3 point sente is a position, not where the sente play or sequence gains 3 points, but where the reverse sente gains 3 points. Calling it a 3 point sente is asking for trouble.



I don't know the position, but that sounds quite right. Don't give your opponent a free lunch.



Well, they do. But as gote or sente, or maybe ambiguous plays, on occasion. Not as double sente. The threats are probably big enough not to require computation.



This I feel less confident about. If he feels smug about the play, perhaps it is because his opponent failed to see it, or it was not so obvious. In such a case, maybe it was not really a global double sente.

But even if O Meien made a mistake in his commentary, he has not led his readers astray as so many earlier authors did.

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

Visualize whirled peas.

Everything with love. Stay safe.