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 Post subject: Re: Ultimate theory of weiqi rules
Post #21 Posted: Mon May 15, 2023 8:54 am 
Judan

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jann wrote:
Area scoring [...] is known to be inferior to territory scoring in accuracy (masking small endgame mistakes).


1) Whether inferior, of equal value or superior with respect to occurring scores or endgame skill requires a much more detailed discussion and must not be derived only from your false statement.

2) The smallest score increment of territory scoring is 1. The smallest score increment of area scoring is 1. The increments are equal! What differs as to increments is that, for area scoring to have the increment 1, the parity of the number of not scoring intersections ("seki parity") must change and this aspect of strategy typically occurs before the late endgame and, by experience, in only about every 20th game.

3) Even in all those games with ordinary seki parity, their smallest score increment 2 does not mean that small endgame mistakes would be masked but it means that small endgame mistakes with territory scoring move values smaller than 2 typically result in a score difference +-2 rather than +-1. For territory scoring, small endgame mistakes with territory scoring move values smaller than 1 result in a score difference +-1. For area scoring, passing instead of filling the last dame changes the score by 2, passing instead of filling the last basic endgame ko can change the score even by 4 (depending on ko threats and koban), passing instead of taking the shortest corridory as the last available local endgame (without any other dames) changes the score by 2. The endgame mistakes are not masked - quite contrarily, they can incur greater losses under area scoring.

4) Endgame under area scoring is richer than endgame under territory scoring because additional strategies about dame, basic endgame kos and throw-ins creating basic endgame kos arise together with dame ko fights. It is a matter of opinion whether richer endgame is better or worse but you must not fall under the illusion that the more frequent score step 1 during the late endgame under territory scoring would indicate a richer endgame. Instead, the opposite can be justified more easily.

Quote:
Directly giving points for played stones involves a "random" B bias, from his 50% chance to play 1 stone more than W.


If you want statistics, do not forge them! You must take into account that the last move changing the winner requires changing the seki parity, which only occurs in about every 20th game. So divide 50% by 20 and you get 2.5% where 1 stone more matters. For the ordinary case, my following theorem applies:

"
Presuppositions
Assume no handicap stones and single passes. Apply the territory score together with the conditions 'unequivocal', 'without two-sided dame and teire', 'without capturable stones in sekis', 'without asymmetric sekis'. Have no suicide, standard area komi, an odd parity of the number of intersections on the board and a final position with an even seki parity.

Theorem 143 [same winner]
The winner is the same under area and territory scoring.
"
[25]

Note the presupposition of standard area komi, such as 7.5. If you compare area scoring with 7.5 komi to territory scoring with 6.5 komi, then usually it is not the last stone that creates the difference but it is the komi difference that creates the difference.

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Go is the surrounding game, not the filling game.


Opinion. Third opinion: It is the game of greater board control. Fourth opionion: It is the game of more prisoners. Fifth opinion: It is the game of more surrounding and prisoners.


This post by RobertJasiek was liked by: Pio2001
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 Post subject: Re: Ultimate theory of weiqi rules
Post #22 Posted: Mon May 15, 2023 9:38 am 
Gosei
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Anyway the ko or superko rule, suicide, etc. are choices and are not formal consequences of the "axioms" (which are not axioms since they are too imprecise to be qualified as such). Trying to deduce them from the "axioms" looks like trying to deduce Euclid's fifth postulate from the first four.

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 Post subject: Re: Ultimate theory of weiqi rules
Post #23 Posted: Mon May 15, 2023 11:26 am 
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The usual situation used to show that territory scoring is sharper than area scoring is this one :

Click Here To Show Diagram Code
[go]$$ Territory sharper than area \n White to play
$$ -------------
$$ . . X . a O .
$$ . . X X X O .
$$ . . X . b O .
$$ . . X O O O .
$$ . . X O . . .
$$ . . X O . . .[/go]


Under area scoring, it doesn't matter if White plays a or b, while in territory scoring, there is obviously one point in a and none in b.
However, this argument is circular : in this case, territory is sharper only if territory counting is used. The argument also works the other way : area scoring is obviously sharper because dame are worth one point each, while under territory scoring they are worth nothing.

And here is another situation where area scoring leads to sharper strategic decisions than territory scoring.

Click Here To Show Diagram Code
[go]$$ Area sharper than territory \n White to play
$$ -------------
$$ . . . . a b -
$$ . . X X X O -
$$ . . X O O . -
$$ . . X O . . -
$$ . . X O . . -
$$ . . X O . . -[/go]


Under area scoring, White needs to carefully think if she wants to challenge Black playing a, risking the two intersections a and b in a ko fight, or safely play b, letting Black having a.
In territory scoring, a is a no-brainer. At worst, it is the same as b (Black looses one point of territory and gains one prisoner), at best, it is one point better (Black looses one point of territory and that's all).

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 Post subject: Re: Ultimate theory of weiqi rules
Post #24 Posted: Mon May 15, 2023 6:35 pm 
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RobertJasiek wrote:
jann wrote:
points for played stones involves a "random" B bias, from his 50% chance to play 1 stone more
the last move changing the winner requires changing the seki parity, which only occurs in about every 20th game.

I haven't talked about changed winner. But with fair area komi of 7, even that can happen easily without seki, since B+6 and B+7 both usually result in B+7 area. You assume unfair komi (7.5 is known to favor W) - hiding a defect with another.

Pio2001 wrote:
this argument is circular : in this case, territory is sharper only if territory counting is used.

This ignores the difference between points earned by skill, and by automatic/direct result of playing one more stone than the opponent. I'm not against area scoring, it does have its advantages, but granularity and score accuracy are not among them.

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 Post subject: Re: Ultimate theory of weiqi rules
Post #25 Posted: Tue May 16, 2023 12:08 am 
Judan

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Calling 7 komi fair and 7.5 komi unfair is your opinion. However, I do not think that integer versus non-integer komi is a matter of fairness. If we knew perfect play and wanted to compensate it exactly, the komi would have to be the integer of the perfect play score. Since we do not know perfect play, komi serves the practical purpose of enabled a game with close to 50% winning chances between roughly equally strong players. For this purpose, komi can be integer or non-integer - neither is fairer than the other.

Granularity and score accuracy are wrong descriptions of your concern. Instead, it is frequency of scores of even or odd parity (of the integer component of the scores in the case of fractional komi).

Quote:
without seki, since B+6 and B+7 both usually result in B+7 area


("With an even number of not scoring intersections" is the more general case of "without seki".)

I think you are trying to say: "Without seki, B+6 and B+7 under territory scoring both usually result in B+7 area scoring." Please try to apply your statement to the following examples:

Click Here To Show Diagram Code
[go]$$B
$$---------------
$$|. . . . . . .|
$$|. . . X . . .|
$$|. . . . . . .|
$$|X X X X X X X|
$$|X X X O O O O|
$$|O O O O O O O|
$$|. . . . . . .|
$$---------------[/go]


Komi 7, territory score 6, area score 6
Komi 6, territory score 7, area score 7

Click Here To Show Diagram Code
[go]$$B
$$---------------
$$|. . . X . . .|
$$|. . . X . . .|
$$|. . . . . . .|
$$|X X X X X X X|
$$|X X X O O O O|
$$|O O O O O O O|
$$|. . . . . . .|
$$---------------[/go]


Komi 7, territory score 5, area score 6
Komi 6, territory score 6, area score 7

Click Here To Show Diagram Code
[go]$$B
$$---------------
$$|. . . . . . .|
$$|. . . X . . .|
$$|. . . . . . .|
$$|X X X X X X X|
$$|O O O O O O O|
$$|. . . O . . .|
$$|. . . . . . .|
$$---------------[/go]


Komi 7, territory score 0, area score 0
Komi 6, territory score 1, area score 1

Click Here To Show Diagram Code
[go]$$B
$$---------------
$$|. . . X . . .|
$$|. . . X . . .|
$$|. . . . . . .|
$$|X X X X X X X|
$$|O O O O O O O|
$$|. . . O . . .|
$$|. . . . . . .|
$$---------------[/go]


Komi 7, territory score -1, area score 0
Komi 6, territory score 0, area score 1

***

I spoke about the last move changing the winner. You have replied that, with area komi 7, the last move changing the winner can occur without seki. Please explain for the examples, how this can occur! An area komi 7 means using area scoring. How does the last move change the winner under area scoring?

Maybe you do not want to say something about komi only for area scoring but maybe you want to compare territory scoring to area scoring when speaking about komi 7. Komi 7 and the last move changes the winner (or jigo-getting players) from jigo to white win. Komi 6 and the last move changes the winner (or jigo-getting players) from black win to jigo. Under area scoring, 6 or 7 komi keeps the winner the same.

Now, maybe you want to express some opinion on these observations, but which? Since you called the komi 7 fair, does this make the komi 6 any more or less fair?

Quote:
hiding a defect with another.


What defects? Why are they defects?

I think you refer to 1) frequencies of scores of even or odd parity and 2) when some conditions allow, or do not allow, a changed winner. Please explain what of either would be your perceived defect and why you think that it is a defect!

Furthermore, if we compare final positions for which we can compare territory scoring to area scoring, the last move (often even many moves) under territory scoring tends to fill a dame. This last move does not change the winner! Instead, altering the komi changes the winner. (And no, the last move is not played to fill inside one's own territory - the last move is played to fill a dame (or teire).)


EDIT: I deleted a first draft. In this second draft, alternate stone playing is possible in all examples.

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 Post subject: Re: Ultimate theory of weiqi rules
Post #26 Posted: Tue May 16, 2023 7:46 pm 
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RobertJasiek wrote:
Since we do not know perfect play, komi serves the practical purpose of enabled a game with close to 50% winning chances between roughly equally strong players. For this purpose, komi can be integer or non-integer - neither is fairer than the other.

Getting offtopic, but area komi 7.5 is known to be worse on this balancing than area komi 7, or territory 6.5 (esp. at high levels of play). The 2 pt area granularity also doubles the frequency of area ties (B+7), which the half point treats as W wins, for a too large statistical swing.

Quote:
I think you are trying to say: "Without seki, B+6 and B+7 under territory scoring both usually result in B+7 area scoring." Please try to apply your statement to the following examples:

B+6 and B+7 (territory) board result, before komi (last two examples).

OC, either player can also continue a finished game by playing an extra stone into his territory, affecting B+6 or B+7 territory, but this is rare. More common is B playing a bit worse somewhere earlier, resulting in B+6 instead of B+7, but also in getting to play one more move than W (unlike in B+7 case) for an extra area point. Such parity bonus move after B+6 territory, rounding it up to B+7 area (gifting an area tie with komi 7), is worse performance than real B+7 area even in purely area terms, as he needed extra move to achieve the same.

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 Post subject: Re: Ultimate theory of weiqi rules
Post #27 Posted: Tue May 16, 2023 11:17 pm 
Judan

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jann wrote:
area komi 7.5 is known to be worse on this balancing than area komi 7, or territory 6.5 (esp. at high levels of play).


Apparently you are trying to say that emperical statistics for komi, scoring and B or W wins are such. Now, this is a different topic indeed.

Quote:
The 2 pt area granularity


Repetition of false statements do not make them correct. The area granularity is 1.

Quote:
also doubles the frequency of area ties (B+7)


Ties only occur for integer komi. So you cannot say that the frequency of area ties would be doubled. What you seem to want expressing is that, if integer komi are used, area scoring doubles the frequency of ties compared to territory scoring. In this respect, I think you are (approximately) right.

Quote:
for a too large statistical swing.


Too large for what? For your preference of maybe preferring fewer ties under integer komi? Is this only a matter of preference or also an objective advantage or disadvantage for either area or territory scoring?

Quote:
OC, either player can also continue a finished game by playing an extra stone into his territory, affecting B+6 or B+7 territory, but this is rare. More common is B playing a bit worse somewhere earlier, resulting in B+6 instead of B+7, but also in getting to play one more move than W (unlike in B+7 case) for an extra area point. Such parity bonus move after B+6 territory, rounding it up to B+7 area (gifting an area tie with komi 7), is worse performance than real B+7 area even in purely area terms, as he needed extra move to achieve the same.


I think you try to argue that Black could make 1 point endgame mistake to change the on-board score from B+6 to B+7 while keeping the seki parity constant. How? Every small endgame mistake changes the area score by multiples of 2 points! It is only in territory-scoring-like endgame evaluation / move value theory that we perceive different values, but score-wise it is multiples of 2 points.

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 Post subject: Re: Ultimate theory of weiqi rules
Post #28 Posted: Fri Jul 07, 2023 5:52 am 
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John Fairbairn wrote:

解释:那么能不能还有其他目标呢?公理1围棋组成只有棋盘和棋子,再没有三,因此公理化推论下的必然目标就只有这两个。再设其他目标就是在公理体系以外的人为的加入了。一个公理性的围棋规则体系,如果目标设定在公理体系之外,就很可能会导致体系的不和谐。日本的计空规则,包括死子回填,是一个与公理性无关的人为的设计。不是从公理推导出来的人为设计的规定,很可能会与其他公理冲突,导致自我逻辑悖理。

Discussion: Can there be other goals then? Axiom 1 is that weiqi consists of only the board and the stones, and there is no third element, so that the only two natural goals under axiomatic inference are these. To set other goals would be an artificial addition outside the axiomatic system. An axiomatic system of weiqi rules with goals set outside the axiomatic system is likely to lead to discord in the system. Japanese territory scoring, including backfill of dead stones, is an artificial design that has nothing to do with axiomatics. Artificially designed rules that are not deduced from axioms are likely to conflict with other axioms and lead to self-logical paradoxes.

空的价值意义只有在作为(1)或(2)目标体系中的推理时才成立。使用空这个推理是因为它可以简化(1)或(2)的目标的计算。本质的的公理化的目标只能是(1)或(2)。日本规则的失误就在于被表面所模糊,失落了本质。

The value meaning of the territory only holds when it is used as an inference in the system of goals of (1) or (2). The inference of territory is used because it simplifies calculation of the goal of (1) or (2). The intrinsic axiomatisation of a goal can only be (1) or (2). The failure of Japanese rules is that they are obscured by appearances and so lose their essence.



My question on the above statements: Is there not agreement that the Japanese rules very fundamentally reflect a prevalent (if not exclusive) version of Chinese Weiqi as it was transmitted to Japan (and Korea) at the time? Is it a contention that Japan somehow botched or altered a territory scoring system from China? I know that it seems a bit weird that sekis in Japan should have a seeming the only vestige of the group tax, while live groups do not, but is it really a Japanese innovation, or just reflecting one version of Chinese weiqi practice, that has since been superceded? So is this a "failure" of Japanese rules or of an originally Chinese practice?

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 Post subject: Re: Ultimate theory of weiqi rules
Post #29 Posted: Fri Jul 07, 2023 8:03 am 
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Pio2001 wrote:
The usual situation used to show that territory scoring is sharper than area scoring is this one :

Click Here To Show Diagram Code
[go]$$ Territory sharper than area \n White to play
$$ -------------
$$ . . X . a O .
$$ . . X X X O .
$$ . . X . b O .
$$ . . X O O O .
$$ . . X O . . .
$$ . . X O . . .[/go]


Under area scoring, it doesn't matter if White plays a or b, while in territory scoring, there is obviously one point in a and none in b.
However, this argument is circular : in this case, territory is sharper only if territory counting is used. The argument also works the other way : area scoring is obviously sharper because dame are worth one point each, while under territory scoring they are worth nothing.


What is sharp about playing out dame? It is at best mechanical tedium, if all that is left are truly neutral points, you are just dividing them up, aren't you?

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