If we can project that Black's incursion will be played with sente, then that settles the question of whether to play it instead of capturing the four stones, since, as happened in the actual game, Black can come back and capture the four stones, anyway.

Leela Zero prefers to capture the four stones, and suggests a slightly different incursion. Interestingly, in either case it thinks that Black is ahead, with a komi 2 pts. bigger.

Thank you, John, for sharing this. I'm only sending one like instead of one for each post.

Edit: And for those who like general principles, when the choice between two moves is a close call, in general the move with a substantial follow-up for you will be better.

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LOL. If you expect me to translate informal text, of course, I cannot do it. With the exception below and the general method related to half the move value, the details in the informal text have little relevance, as long as one can infer from the diagrams what O is talking about. If you expect me to provide a complete "translation" and analysis for O's example, I cannot do it because writing more books has very much higher priority.

You had mentioned the "(calling an / certainty of) election" earlier so I asked about its meaning here earlier and somebody said that it would have little meaning in itself. Now you stress this election again. Instead of all the translation, as interesting as it may be and as much as we are grateful for it, I would be more interested in learning about the meaning of "election" or "when to play for certainty" if it adds anything to the calculated values of (half of the) largest move value and error margin (which appears to be a quarter).

(Presumably you have considered copyright issues. Summarising instead of translating several successive pages puts you on the safe side, unless you have rights to translate this particular book anyway.)

Getting the book was easy at least last year: Amazon-Japan. Just the postage may be very high if airmail is your only option. Shipping was fast.

This is the important part and I understood it without translation when reading the book.

"The biggest move on the board is an 8-point gote": difference value = deiri counting gote move value.

"the 'value of the move' is half that, or 4 points": miai counting gote move value of the largest move in the environment, also called the temperature T in modern endgame theory.

"the 'advantage of first move' is half again of that, or 2 points.": playing first in the [ideal] environment is worth half of the miai counting move value of the largest move in the environment, that is, T/2.

"Adding the 'margin of error' of 1 point (half the advantage of first move) [...] to White’s territory": O's error margin is T/4 (a quarter of the temperature aka largest miai move value in the environment).

I am just not exactly sure whether O adds the error margin to the opponent's points or the next moving player's points or somehow else. (In this example, both conditions coincide.)

Allow me to call out the proverbial elephant in the room: the situation in the upper right.

O Meien doesn't discuss whether a White hane there can be cut and Black will win the capturing race, or Black should submit and retract, thereby losing a fair amount of potential territory, presumably in gote. O merely adds a reinforcing Black hane in one of the sequences.

LZ conveniently adds a 24 move sequence to Black's choice to capture the 4 stones in the top middle, proving that he has time to do so and more importantly that move is big enough because there is no threat in the upper right of losing territory in sente.

Putting that aside, it's very comforting for mankind to see that O (and Uberdude) discusses the same moves as LZ. Only LZ prefers the capture of the four stones, presumably seeing that this indeed reduces the temperature at the top, while O wants to deal with the uncertainty of White's moyo (and shifts the focal point one up). In any case, responding to the kosumi is not urgent, because of the reasons O convincingly adds.

So why the elephant? Because life & death remains the key to proper endgame. If you are not capable of calculating what happens to the upper right, you rely on chance to respond to White's hane, or reduce uncertainty while playing there yourself. LZ shows she knows, O presumably knows too. Both then concentrate on the choice between reducing the moyo and capturing the stones. Both dismiss the defence at the bottom. But what can be expected from us, amateurs?

Incidentally, what I don't like about O's diagrams is that he shows how big White's diagonal is, by playing out a sequence as if White had passed. Any analysis should compare the effect of tenuki with the alternative gain. This has always troubled me in professional writing: magnifying the size of a move by having the opponent pass first.

Bears repeating.



Assuming tenuki (not really a pass) is normal for evaluation. It is relevant. But this comment about the left bottom side and your comment about the upper right side indicates that we amateurs could benefit from having more diagrams. I know it's a burden on the writers, but there you are.

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

Visualize whirled peas.

Everything with love. Stay safe.

Local analysis uses pass or tenuki and often need not refer to its value. (Combinatorial game theory goes even further dropping the rule of alternation entirely.) Global analysis might have to consider values of tenuki, depending on the kind of analysis.

For some strange reason O has reverted to deiri counting of the gote at B. After all, the first part of the book is about 一手の価値 (the value of a single play, i.e., miai value). Anyway, all's well that ends well, I guess.

Here is the story. The value of a single play is how much one local play gains, on average. If that is indeed, the largest play on the whole board, then that is also the maximum that White gains overall from making that play. OTOH, it is possible (with no ko) that Black will be able to gain that much back (and no more), so that White ends up gaining 0. We may estimate the overall gain at the end of play as the average of the local gain and 0, or half the local gain. We may call that the average profit from playing first. Advantage seems too vague to me.

O realized that, since the average profit is an estimate, it has an associated error, which again, could range from 0 to its value. One half of the average profit is its average error, or its margin of error.

So, recasting that passage, if I may, into more technical language, we get this.



Actually, assuming perfect play, the maximum gain for White at that point was 4 points, which would leave him 6 points behind on the board, assuming the count is correct. With only 5½ komi, that's a sure win for Black.

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

Visualize whirled peas.

Everything with love. Stay safe.

He adds it to the opponent's points. It's an (almost) worst case analysis.

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

Visualize whirled peas.

Everything with love. Stay safe.

It's available as a kindle book from Amazon or a PDF from mycom.

Thanks a lot John!

It certainly makes more sense (to me at least) than the following:

I wish I could read Japanese

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Since O uses an error margin, the questions are: why does he use any; is the used error margin meaningful; what properties has it?

During the early endgame, we can distinguish the "ensemble" of the largest local endgames / hot local endgame regions from its "environment" of smaller, peaceful local endgames. A typical simplifying assumption about, and model of, the environment is that it only consists of simple local gote endgames.

If furthermore their move values drop constantly, we have an "ideal environment". An environment has a largest move value, which is called the "temperature T" (not in O's book though). E.g., the move values of the ideal environment might drop in steps of 1. Then the move values of the ideal environment would be T, T - 1,..., 3, 2, 1. E.g., if the temperature is T = 4, we have the ideal environment 4, 3, 2, 1.

O assumes without proof and I have proven that playing first in an ideal environment is worth half the temperature, that is, T/2. I think that O does not even speak of "ideal environment", but then he assumes this concept implicitly. E.g., in the ideal environment 4, 3, 2, 1, the first playing player gains +4, his opponent lets the player lose -3, the player gains +2 during the sequence, his opponent causes the player to lose -1. In total, we have + 4 - 3 + 2 -1 = 2 as the net profit of the sequence. Since the temperature of this ideal environment is T = 4, half the temperature, or the value of playing first in the ideal environment, is T/2 = 4/2 = 2. This is the player's previously calculated net profit during the sequence of playing out the ideal environment.

If each environment were an ideal environment, in which playing first were worth exactly T/2 (half the temperature, that is, half the value of the largest move value of the environment), we would not need any error margin at all!

However, environments can be non-ideal environments with different drops of move values. If still we assume that an environment only consists of simple gotes, the exact value of playing first in such an environment is at least 0 and at most T. During the early endgame, we do not know what the exact value is even if there should only be simple gotes. Therefore, O in his book and modern endgame theory estimate the value of playing first in the environment. On average, this value is T/2.

Since this is a model value, or estimate, we can just be aware that it can be imprecise or one can also try to estimate an error margin for this value. In his book, O prefers to consider an explicit error margin, which he assumes to be half the value of playing first in the environment. Since T/2 is the value of playing first in the environment, half of it is T/4. In our example of the temperature (largest move value in the environment) 4, we have T/4 = 4/4 = 1.

Error margins can be introduced in different manners. O has the, somewhat arbitrary, preference of taking the player's perspective and a defensive attitude. He calculates a defensive error margin - defensive from the player's perspective. Therefore, O adds the error margin to the opponent's points.

After calculating points, adding T/2 for the value of playing first in the environment and adding the error margin T/4 to the opponent's points, if the player is still ahead, O seems to speak of his "certainty" of winning the game, assuming reasonable play by both players.

Non-ideal environments (maybe also with local sente endgames and other excitements) have an uncertainty in them whether accounting T/2 for the value of playing first in the environment predicts the winner well enough. O's error margin T/4 for half the value of playing first in the environment shall remove most of the uncertainty of whether the player has a guaranteed win. In the translation, O throws in 99% certainty achieved thereby, but this symbolic figure cannot be derived from the error margin he defines.

There are many ways of defining an error margin. E.g., one could also define it as the maximum possible error, T/2, for a non-ideal enviroment of simple gotes. Even then, we would not have 100% certainty because there are also local sentes, kos and other excitements.

A simpler model would not use any error margin at all. We might simply consider T/2 for the value of playing first in the environment. John likes to claim that my theory would be an overkill, but we can ask whether O's use of his error margin at all is an overkill. I am not convinced that we need such an error margin. Not using it is simpler. Then we also need not worry how good or bad the specific error margin is.

To start with, why should it be more meaningful to add the error margin to the opponent's points instead of using it as a plus-minus tolerance of the next moving player's points?

Well, you claimed to have understood O's theory perfectly, so you tell us.

In fact you have omitted an important question: When to use O's "trick". See the heading of Chapter 4.

Furthermore, by projecting your own approach onto O you are misrepresenting him. That is not good science. He says




Mathematical elegance and mathematical proofs do not necessarily equate with simplicity. For most practical purposes humans want something that is easy too understand and useful in practice. That's what O's book gives. That's why it's good and other books are not.

You use many words to avoid admitting that O does not justify his use of an error margin well.

His experience is weak justification. A study of possible simple environments is good justification because of the extreme values 0 and T, the symmetry and therefore the average T/2.



Again, why have an error margin at all? It is not easy to understand, it is unclear why it is more useful in practice than not using any.



Rather WRT to early endgame it is good because it is still the only book considering the value of first playing in the environment by a value with good theoretical justification.

However, go players know that one simple value does not explain everything. The literature on life+death, opening, josekis etc. goes into details despite our wish for easy and useful in practice. Endgame evaluation is no different. There are further aspects that do require details and profit from more detailed theory. Not only books that stop at the easy basics can be good. Recall your praise of certain life+death books studying lots of detailed aspects.

Of course.

Regardless of this insight and therefore my preference to separate teaching from presentation of proofs, mathematics affects two aspects of the current discussion.

How reliable is half the largest move value in the environment, aka half the temperature, or T/2? With O's opinion alone, it was as reliable as postulating atoms more than 2000 years ago. My mathematical proof transforms opinion into confirmation, like physical evidence of atoms confirmed the old conjecture. The proof is not necessary for applying the simple concept of the value T/2, but it is good to know that the simplicity is supported by the mathematical theorem.

O's error margin has much weaker mathematical support because there can be different kinds of error margins. Every player is aware of maybe the best error margin for score certainty: being ahead / behind by a number of points is the better / worse the larger the number. This is a dynamic error margin and so can be interpreted flexibly depending on how flexible and open to uncertainty a studied position is. There is no need for artificially replacing this dynamic, and therefore more powerful, error margin by O's static one.

AFAIK, O Meien's book is the first endgame book by a pro even to deal with the question of temperature (the value of having sente, or the value of the move, or the value of the advantage of first move). I remember when I first read Sakata's book on endgame evaluation aimed at dan players, I was disappointed to discover than he did not address the value of the move, he just made a static evaluation. So it is quite refreshing to see O Meien tackle the question.

O does not consider an ideal environment, or even (explicitly) a rich environment with many plays of similar value. Let us assume that all we know about the board is that it contains a move that gains T pts., which is the maximum gain of any play, and that it does not contain any ko position that messes up our calculations. Then what is the value of having sente? The minimum with correct play is 0. For instance, we may make a move that gains T pts., and then the opponent replies with a move that gains T pts., and that move is the last play, and so the value of having sente is 0. The maximum is T pts. For instance, that play may be the last play. (OC, that is not so if the move is a regular ko, in which case the maximum value is 2T.) So the value of having sente lies between T and 0, based upon our assumptions. How do we estimate that value? One way is to minimize the maximum error of our estimate, which we can do with an estimate of T/2. Our maximum error is then T/2. (I doubt if O made his estimate this way. There are a number of ways of coming up with it.)

O carries this one step further. He wants to know his chances of winning, at least as well as the newsroom projections of elections. We can do the same thing again. We know that the maximum error of the value of having sente is T/2. The minimum error is 0. So we can estimate the error as T/4, with the maximum error of that estimate as T/4. Again, I don't know how O came up with his figure, which he calls the margin of error, but in his experience in actual play it was hardly ever violated.

In practice this is an improvement over Sakata. Sakata could be sure of winning if he is already ahead and has sente. O is almost certain of winning if he is less than T/4 pts. behind and has sente. To be sure, he will probably win if he is less than T/2 pts. behind, but he may still feel the need to take some chances. If he is less than T/4 pts. behind he can play more conservatively.

O's use of temperature is a definite improvement over the old ways.

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

Visualize whirled peas.

Everything with love. Stay safe.