Commentary on the Example "Carpenter's Square"
The text evaluates, but does not clearly mention that it evaluates, values of a) the initial position called the Current position, b) the intermediate position after move 10 and c) the intermediate position after move 11 of Black's alternating sequence.
Implicitly, the text presumes, but does not explain, that it might inherit the count of the Current position from the values of the intermediate position after move 10, which is created after a sente sequence. This is a great conceptual mistake because, as my analysis of the carpenter's square sequence shows, this sequence is not worth playing successively.
The text is ambiguous whether it also inherits the move value of the Current position from the values of the intermediate position after move 10. If this is the text's intention, it is a great conceptual mistake for a) the same reason and b) because the move value of the Current position must also be derived from the count of its white follower, which the text does not consider at all.
"Case of black win at ko black"
This text refers to Black wining the ko in the black follower of 'the intermediate position after move 11'.
"x mark 1 point are 4"
This includes 3 empty intersections and 1 white prisoner stone counting for Black. The 1 white prisoner stone was captured on move 11 of the sequence creating the intermediate position after move 11.
"Total 18 + 4 = 22"
This is the count of the black follower of the intermediate position after move 11. It comprises 18 points for Black's 9 captured white stones and 4 points for his empty intersections and the earlier prisoner.
"circle mark 2 points x 4 = 8"
This is White's points of his territory intersections and black prisoner stones removed from them.
"triangle mark black captured white-stone, so -1"
This is the white prisoner stone made on move 11. Since currently the text assesses White's points, this one white prisoner stone contributes as a loss to White's points. Therefore it is subtracted from White's points.
"total 8 - 1 = 7"
This text calculates White's points comprising the previously calculated 8 and -1 points. White's points are the white-count (that is, the count from White's value perspective) of the case White winning the ko in the white follower of the intermediate position after move 11.
"Difference between win at ko and lost at ko is 22 + 7, total is 29"
In this text, "win at ko" refers to the count 22 of the black follower of the intermediate position after move 11. "lost at ko" refers to the white-count 7 of the white follower of the intermediate position after move 11.
For the calculation of the sum 22 + 7 = 29, the text would have to make the implicit assumption that the white-count of the white follower of the intermediate position after move 11 may be added. This operation (addition) abbreviates subtraction of the count -7 of the white follower of the intermediate position after move 11. It is important to understand that the operation addition is only correct together with the white-count of the added value if and only if the white-count is zero or positive, as it is in this example. The value 22 is a count; it is not a white-count. Subtracting a count of the white follower is the generally correct calculation because it allows subtraction of a negative value, as may be necessary in other examples.
However, the text speaks of calculating the difference. As interpretation I, implicitly, the calculation of the sum 22 + 7 = 29 must be understood as a shorthand for the calculation of the difference value 22 - (-7) = 22 + 7 = 29. In this correct calculation of the difference value, (-7) is the negated white-count of the white follower of the intermediate position after move 11, which equals the (black-)count of the white follower of the intermediate position after move 11.
As interpretation II, implicitly, the calculation of the sum 22 + 7 = 29 must be understood as the distance between the count of the black follower of the intermediate position after move 11 from Black's perspective and the white-count of the white follower of the intermediate position after move 11 from White's perspective. From the intermediate position after move 11, the sequence to the black follower has one excess black play (see the diagram with Black 1 as the only move). From the intermediate position, the sequence to the white follower has two excess white plays (see the diagram with White 1 and 3 as the only moves).
"The size per one move is 9 + 2/3"
This is the modern move value. It is a size of a move in the intermediate position after move 11. The text does not explain explicitly how this value is calculated but shows a value diagram, from which calculation is implied: divide the difference value 29 by the tally 3. The tally is the sum of the aforementioned 1 excess black play and 2 excess white plays in the sequences from the intermediate position after move 11 to its followers: 1 + 2 = 3. Hence, the size of a move in the intermediate position after move 11 is 29 / 3 = 9 2/3 = 9 + 2/3. This is the size per one move stated in the text.
"Namely gyaku-yose size per one move is 9 + 2/3."
By gyaku-yose size per one move, the text means the modern move value.
"This is gote-yose size per one move is 19 + 1/3."
By gote-yose size per one move, the text means the traditional gote move value. The text does not explain but implies its calculation as twice the gyaku-yose size per one move so (9 + 2/3) * 2 = (19 + 1/3). I would write the numbers as 9 2/3 * 2 = 19 1/3.
When assessing the intermediate position after move 11, we have an ordinary ko. The modern ko move value is 9 2/3. Now, the text makes the assumption that every modern move value could be transformed into a traditional gote move value by multiplication by 2. This is a creative invention using exact calculation with modern move values, then maintaining tradition by calibrating everything as if it would be gote moves. In my opinion, this final transformation back to traditional move values calibrated as gote values is unnecessary, superfluous extra calculation work. Furthermore, it disables every other means of modern endgame theory. To start with, it disables gains. So although traditional calibration is correct, it is a bad idea. For non-ordinary kos, more study is necessary.
"Size of black 1 is gote 19 + 1/3. (Case of win at ko) This is same worth of gyaku-yose 9 + 2/3."
This is the first text of the example and is supposed to summarise the conclusion.
The text is ambiguous whether "black 1" refers to a) Black 1 played in the Current position, that is, the first move of the sequence from the initial position to the intermediate positions, b) Black 1 played in the intermediate position after move 10 or c) Black 1 played in the intermediate position after move 11. However, it is of the utmost importance to know which reference is being meant! Proximity of the text to a diagram showing (a) suggests (a). The part "Case of win at ko" of the text suggests (b) or (c). It is unclear what exactly this part of the text means. It might be a general hint that a ko can occur or it might refer to (b) or (c).
If the text refers to (b) or (c), the stated values are correct.
If the text refers to (a), the stated values for Black 1 played in the initial position are wrong, this is an extraordinarily great mistake of the text and correct calculation of the correct values would be missing. Correct calculation of the studied sequence of the carpenter's square, as I have done it in a different thread, would need to I) determine the count of the intermediate positions, II) determine the white-count 8 of the white follower created by White 1 played at the 2-2 point in the initial position, III) derive the modern gote move value of the initial position and IV) calculate the traditional gote move value of the initial position.
As to (I), let us have a look at the aforementioned value diagram for the intermediate position after move 11 again. It also shows this text:
Code:
"
White 1 White territory 7
Current Black territory 2 + 2/3
Black 1 Black territory 11 + 1/3
Black 2 Black territory 22
"
This text contains several mistakes. "11 + 1/3" is a simple calculation mistake for the correct "12 + 1/3" in particular because 12 1/3 + 9 2/3 = 22. We get:
Code:
White 1 White territory 7
Current Black territory 2 + 2/3
Black 1 Black territory 12 + 1/3
Black 2 Black territory 22
Now, the values are 9 2/3 apart. Note that the first value is a white-count. Expressed as a black count and writing "count" instead of the confusing "territory" (confusing because also dead stones and prisoners are accounted so we do not only have territory), writing "count" for "Black count" as done usually in modern endgame theory and omitting the superfluous "+" within each value, we get:
Code:
White 1 count -7
Current count 2 2/3
Black 1 count 12 1/3
Black 2 count 22
Now, you can see -7 + 9 2/3 = 2 2/3 and 2 2/3 + 9 2/3 + 12 1/3 and 12 1/3 + 9 2/3 = 22. The value diagram also denotes the 9 2/3 sizes of the moves.
As mentioned initially, implicitly, the text presumes, but does not explain, that it might inherit the count of the Current position from the values of the intermediate position after move 10, which is created after a sente sequence. This is a great conceptual mistake because, as my analysis of the carpenter's square sequence shows, this sequence is not worth playing successively. Instead, the text must 1) calculate the count of the intermediate position after move 10 and 2) would have to repeat my long and detailed calculation of the count of the Current position by analysing the counts, gains and move values of every position from the Current position to the intermediate position after move 10 and of the relevant variations. The author of the text is unaware of the necessity for (2). Here, we can at least correct (1):
Code:
White 1 count -7
Intermediate position after move 10 count 2 2/3
Black 1 count 12 1/3
Black 2 count 22
In my interpretation of the text, I have rushed ahead to the conclusion that the count 2 2/3 must belong to the intermediate position after move 10. Let me explain below.
The intermediate position after move 11 is one black play away from its black follower with the count 22 so the count of the intermediate position after move 11 is 22 - 1 * 9 2/3 = 12 1/3 (the 9 2/3 is the modern move value in the intermediate position after move 11, we subtract because undoing a black play loses points from Black's value perspective). Alternatively, the intermediate position after move 11 is two white plays away from its white follower with the count -7 so the count of the intermediate position after move 11 is -7 + 2 * 9 2/3 = -7 + 19 1/3 = 12 1/3 (we add because undoing each white play gains points from Black's value perspective). In conclusion, the count of the intermediate position after move 11 is 12 1/3. Therefore, in the tabular value list, the count 2 2/3 cannot belong to the intermediate position after move 11.
Next suppose, in the tabular value list, the count 2 2/3 belongs to the intermediate position after move 10, that is, where the book's text states "Current". The count of the intermediate position after move 10 is -7 + 1 * 9 2/3 = 2 2/3 because it is one white play away from the position in which White wins the ko. Therefore, the presupposition in this paragraph is correct.
In the intermediate position after move 10, one white play creates the intermediate position's white follower with the count -7. The one white play is called "White 1" in the value diagram. The one white play is, sic, the play White 3 in the diagram showing the plays White 1 and White 3, transforming the intermediate position to its white follower.
Accordingly, in the value diagram, "Black 1" must refer to Black 11 in the diagram showing the sequence from the initial position to the intermediate position after move 11 and, in the value diagram, "Black 2" must refer to, sic, Black 1 in the diagram showing the creation of the black follower of the intermediate position after move 11, that is, the diagram only showing this one move sequence compromising this follow-up play Black 1.
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"The size of the carpenter's square territory"
"This shows that [the marked black territory] is 2 + 2/3. It is a standard of the size calculation at the positional judgement."
With "black territory", the text means the count (from Black's value perspective) in the initial position. If the count were correct, the text would be correct that the count would express the positional judgement (within the implicitly assumed locale as indicated by the mark-up on the board).
We have seen that 2 2/3 is the count of the intermediate position after move 10.
The text is naive and makes the great mistake of deriving the count of the initial position from the count of the intermediate position after move 10.
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As my analysis of the studied sequence of the carpenter's square shows, the correct initial values are the count 4 2/3 and the move value 11 2/3. The book text's values are wrong: count 2 2/3 and move value 9 2/3.
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Conclusion
The author of Yose Size List combines fragments of knowledge with gaps of knowledge on endgame evaluation. As a result, he makes great conceptual mistakes. If the discussed examples are representative, evaluation in the book cannot be trusted, and very much is not explained at all or at least clearly. A low book price is not a mandate for buying. Needless to say, layout and editing are no encouragements, either.
The book repeats mistakes that are frequent in endgame evaluations by various authors of endgame books. In particular, the book makes the naive but wrong assumption that a long alternating sequence would be worth playing successively and calculates wrong values accordingly. It is tempting "for the show" to include sophisticated examples, such as Carpenter's Square, in a book but the author's understanding of endgame evaluation is far from ripe for them. The book is careless with its terminology: instead of using the term 'count', it uses the wrong term 'territory'. It describes some gains but fails to clarify doing so by not giving this concept its name: 'gain'. The book calculates some values without explaining properly how it calculates them.
Remarks
I have not verified yet the just stated values other examples in the book's sample. I do not have a Kindle reader so do not know whether I might buy the book some time out of curiosity.
EDIT: conclusion.
EDIT 2: typos.