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Post #21 Posted: Fri Jul 26, 2019 3:04 am 
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Hi Bill,

Thanks. So, when we talk about the territorial value of a given local position, what does it mean ?

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Post #22 Posted: Fri Jul 26, 2019 3:15 am 
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Let's try post#15, variation:
Click Here To Show Diagram Code
[go]$$ x
$$ | O O O ? ? ? ?
$$ | . O . O ? ? ?
$$ | O O O O ? ? ?
$$ | . X X ? ? ? ?
$$ | O O X X X X X
$$ | . O X . X . X
$$ +--------------[/go]
Click Here To Show Diagram Code
[go]$$W (a)
$$ | O O O ? ? ? ?
$$ | . O . O ? ? ?
$$ | O O O O ? ? ?
$$ | 1 X X ? ? ? ?
$$ | O O X X X X X
$$ | . O X . X . X
$$ +----------------[/go]
(a) Territorial value = ( :black: local points) - ( :white: local points) = 2 - 3 = -1

Click Here To Show Diagram Code
[go]$$B (b)
$$ | O O O ? ? ? ?
$$ | . O . O ? ? ?
$$ | O O O O ? ? ?
$$ | 1 X X ? ? ? ?
$$ | O O X X X X X
$$ | . O X . X . X
$$ +----------------[/go]
(b) Territorial value = ( :black: local points) - ( :white: local points) = 9 - 2 = 7

swing value = (b) - (a) = 7 - (-1) = 8

The territorial value of the original local position (x) is ( (7 + (-1))/2 ) = 3

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Post #23 Posted: Fri Jul 26, 2019 3:29 am 
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Later, we assume the big groups are OK:
Click Here To Show Diagram Code
[go]$$ x
$$ | ? ? O ? ? ?
$$ | ? ? O ? ? ?
$$ | O O O , ? ?
$$ | . X X X X ?
$$ | O O X ? ? ?
$$ | . O X ? ? ?
$$ +------------[/go]
Click Here To Show Diagram Code
[go]$$W (a)
$$ | ? ? O ? ? ?
$$ | ? ? O ? ? ?
$$ | O O O , ? ?
$$ | 1 X X X X ?
$$ | O O X ? ? ?
$$ | . O X ? ? ?
$$ +------------[/go]
(a) Territorial value = ( :black: local points) - ( :white: local points) = 0 - 1 = -1

Click Here To Show Diagram Code
[go]$$B (b)
$$ | ? ? O ? ? ?
$$ | ? ? O ? ? ?
$$ | O O O , ? ?
$$ | 1 X X X X ?
$$ | O O X ? ? ?
$$ | . O X ? ? ?
$$ +------------[/go]
(b) Territorial value = ( :black: local points) - ( :white: local points) = 7 - 0 = 7

swing value = (b) - (a) = 7 - (-1) = 8

The territorial value of (x) is ( (7 + (-1))/2 ) = 3

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Post #24 Posted: Fri Jul 26, 2019 4:23 am 
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Jika wrote:
I thought the solution would be 7 (the max points for B):
white taking A creates 1 point (A1).
black taking A kills the three stones (3x2=6) plus takes A1 (6+1=7).

All good so far!

If Black moves there he is up by 7 points (locally). If White moves there Black is down by 1 point (locally). So the difference in score depending on who moves there is 8 points.

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Post #25 Posted: Fri Jul 26, 2019 5:02 am 
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EdLee wrote:
Hi Bill,

Thanks. So, when we talk about the territorial value of a given local position, what does it mean ?


Informally, it is an estimate of its eventual local territorial score.

More formally:

1) If the position has a territorial score, that is the territorial value.

2) Otherwise, if the position is a non-ko position, it has a mean territorial value, defined as the average result in the alternating play when Black plays first and when White plays first in 2ⁿ copies of the position, either exactly or in the limit as n approaches infinity.

3) If the position is a ko (or superko) position, its value depends upon theory, and there is no single theory for ko values. Professor Berlekamp, Martin Mueller, Kim Yonghoan, Nakamura Teigo, Bill Fraser, and I have extended thermography to evaluate kos, superkos, and multiple kos and superkos. :)

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Post #26 Posted: Fri Jul 26, 2019 5:38 am 
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Jika wrote:
I managed to solve 3 exercises on this basis, but now I'm stuck with another one (sigh):

Attachment:
Bildschirmfoto vom 2019-07-26 06-48-22.png


I thought the solution would be 7 (the max points for B):


There is a game theoretic value of a position which depends upon who plays first, namely, the result of perfect play, In this position, when Black plays first that value is 7. When White plays first that value is -1 (i.e., 1 pt. for White). In go we do not evaluate positions that way, because typically we do not know who will play first in any given local position.

Quote:
white taking A creates 1 point (A1).
black taking A kills the three stones (3x2=6) plus takes A1 (6+1=7).
They can't have the same territorial value both at the same time, so 7-1 does not work either?!


You are on the right track. Since it is gote, and Black gets 7 pts. in one play and White gets 1 pt. in one play. the value of the position is (7-1)/2 = 3 pts. (for Black).

Quote:
Or maybe it is 3?!


That is the value of the local position. Well done!

Quote:
So, why 8?


For historical reasons, go players have traditionally used swing values to compare plays (not positions). The swing value for a gote play is the difference in the position after Black makes a play and in the position after White makes a play. (Note that we are actually talking about two different plays, one by Black and one by White. ;)) In this case the swing value is 7 - (-1) = 8.

Some people get confused because of the way swing values are often taught. Informally, people say that the value of a play in the corner is 8 pts,, when actually it is the value of two different plays taken together, one play by White and one by Black. Each play actually gains 4 pts., and together they gain 4 + 4 = 8 pts. Swing values are fine for comparisons, but people make mistakes when they use them to figure gains and losses.

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Post #27 Posted: Fri Jul 26, 2019 7:19 am 
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Bill Spight wrote:
Swing values are fine for comparisons, but people make mistakes when they use them to figure gains and losses.


Indeed. In the last game I played in the US Open (I haven't gotten to it yet in my journal thread), I played a peculiar sequence, which lost me several points. I know that the moves were bad, but more than that, I have been contemplating for the last few days about the *reason* I played that sequence: it was weird, and seems obviously bad in review. So what state was I in during the game, which made me think to play those moves?

The answer I've come up with, albeit maybe incomplete, is that I don't feel comfortable having a small lead in a tournament game. I only get comfortable when I feel that I have a large lead. Otherwise, my poor endgame could screw up the result of the game.

While this may be true, I believe that I overcompensate for that feeling, because I overestimate what I can lose in the endgame, due to swing values. When people talk about a 15 or 20 point swing value, to me, I feel that missing a single one of these could change a 10 point lead to a loss. And so, I don't feel comfortable with such a small lead. But in reality, when people are talking about a 15 point swing value, the actual gain is probably around half of that. Add that to the fact that I'll probably play *some* move that's kind of decent, so while I'll lose points by missing these big endgame areas, the loss isn't as extreme as it seems when I think about the swing value. If the swing value I miss is 15 points, and I play one with swing of 10 points instead, that's a loss of 5 swing value points, but with both players, I guess it'd just be a few points?

To be clear, I don't advocate ignoring the endgame, and these few points could very well cost the game (I lost a game by 0.5 last week). But thinking in terms of the swing value, I think I've added more fear than necessary, and it sometimes leads me to feel inclined to make weird moves (i.e. invade in weird ways when I don't need to, adding more risk to the game, and potentially costing me points).

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Post #28 Posted: Fri Jul 26, 2019 11:03 am 
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@jlt: Well, this actually occurred to me.

But my confused question remains (as I said with "7-1 is not possible", because Bill's and Ed's discussion seemed to be about subtracted values) how can both values count at the same time?
So, the territorial value is the possible points B and W could make each, added??

The other exercises there are much, much, much more simple.

Like, oh, I see, black can close a gap, so the territory is closed, and look, in this territory there are two empty intersections plus two white stones on the other 2 intersections, oh, I'll say "6" - right!"
321go explain things patiently with exercises that get more difficult.
Here, I feel like I've skipped a class or something.

PS: How do you quote (multiple) posts, or parts of posts, in one reply? Copy-paste-quoteTag, or something else?

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Post #29 Posted: Fri Jul 26, 2019 12:00 pm 
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Jika wrote:
...
PS: How do you quote (multiple) posts, or parts of posts, in one reply? Copy-paste-quoteTag, or something else?


For a partial post, click the quote button, and then delete as necessary. Some of us use ellipses to indicate deletions.

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Post #30 Posted: Fri Jul 26, 2019 12:19 pm 
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Swing value can be confusing, but I think you are on the right track.

It already seems clear to you that black can get 7 points by playing first (3 captures + 1 more point territory). That’s how much black gets, from black’s perspective.

But there’s additional value in playing there: black prevented white from making points. If white had no chance to make points there anyway, blacks would gain the 7 points, and nothing else. But the fact is, if white plays there first, white gets 1 point.

So black didn’t only gain the 7 points - he gained the fact that he denied white 1 point. That’s why you add them together to get 8.

The more points both sides have POTENTIAL to make, the more value there is to play there.

Example: let’s say there are two endgame moves where black can make 7 points by playing first. But in the first one, white gets a point by playing first, as in this example. But in the second one, let’s say that white could t get any points by playing there first anyway. In both cases, black gets the same 7 points by playing first. But it’s better to play the former one, because I’m doing so, black not only gains 7 points- he prevents white from the possibility of getting that extra point.

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Post #31 Posted: Fri Jul 26, 2019 2:06 pm 
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Kirby wrote:
Swing value can be confusing, but I think you are on the right track.

It already seems clear to you that black can get 7 points by playing first (3 captures + 1 more point territory). That’s how much black gets, from black’s perspective.

But there’s additional value in playing there: black prevented white from making points. If white had no chance to make points there anyway, blacks would gain the 7 points, and nothing else. But the fact is, if white plays there first, white gets 1 point.

So black didn’t only gain the 7 points - he gained the fact that he denied white 1 point. That’s why you add them together to get 8.


Please, Kirby, the gain per move is only 4 pts. Gote swing value is about the gain from two moves (one by Black, one by White), not one.

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Post #32 Posted: Fri Jul 26, 2019 2:42 pm 
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OK, Jika, let's get down to basics. :)



How much territory does White have?

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Post #33 Posted: Fri Jul 26, 2019 2:48 pm 
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Hi Bill,
Without using any of the theoretical tools, I can see W has 3 points, from experience: 2 + miai of 1; but I'm very curious to see the formally derived calculations. :)

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Post #34 Posted: Fri Jul 26, 2019 2:56 pm 
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Bill Spight wrote:
Kirby wrote:
Swing value can be confusing, but I think you are on the right track.

It already seems clear to you that black can get 7 points by playing first (3 captures + 1 more point territory). That’s how much black gets, from black’s perspective.

But there’s additional value in playing there: black prevented white from making points. If white had no chance to make points there anyway, blacks would gain the 7 points, and nothing else. But the fact is, if white plays there first, white gets 1 point.

So black didn’t only gain the 7 points - he gained the fact that he denied white 1 point. That’s why you add them together to get 8.


Please, Kirby, the gain per move is only 4 pts. Gote swing value is about the gain from two moves (one by Black, one by White), not one.


I didn’t say per move. I think it is simpler for a beginner to understand the concrete number of points he gets. By playing there, black has 7 countable points, and I think it’s simpler to think about it that way. I understand that there are technical terms here, and we can talk about per move gain, but I don’t think it helps more than confuses someone interested in the basics.

I think the goal here should be to explain as simply as possible, and I’m not sure all of the posts here have that in mind.

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Post #35 Posted: Fri Jul 26, 2019 4:06 pm 
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Kirby wrote:
Bill Spight wrote:
Kirby wrote:
Swing value can be confusing, but I think you are on the right track.

It already seems clear to you that black can get 7 points by playing first (3 captures + 1 more point territory). That’s how much black gets, from black’s perspective.

But there’s additional value in playing there: black prevented white from making points. If white had no chance to make points there anyway, blacks would gain the 7 points, and nothing else. But the fact is, if white plays there first, white gets 1 point.

So black didn’t only gain the 7 points - he gained the fact that he denied white 1 point. That’s why you add them together to get 8.


Please, Kirby, the gain per move is only 4 pts. Gote swing value is about the gain from two moves (one by Black, one by White), not one.


I didn’t say per move. I think it is simpler for a beginner to understand the concrete number of points he gets. By playing there, black has 7 countable points, and I think it’s simpler to think about it that way. I understand that there are technical terms here, and we can talk about per move gain, but I don’t think it helps more than confuses someone interested in the basics.


I agree.

Quote:
I think the goal here should be to explain as simply as possible, and I’m not sure all of the posts here have that in mind.


I agree. But simplicity does not excuse inaccuracy. There is no gain between the two positions, one worth 7 pts. to Black, and one worth 1 pt. to White, because there is no way to move from one to the other. Swing value does not indicate the gain from playing at any point. The belief that it does causes confusion, as I mentioned before. You seemed to agree.

Using Ed's diagram:

Click Here To Show Diagram Code
[go]$$ A
$$ | ? ? O ? ? ?
$$ | ? ? O ? ? ?
$$ | O O O , ? ?
$$ | . X X X X ?
$$ | O O X ? ? ?
$$ | . O X ? ? ?
$$ +------------[/go]


From A Black can move to position B, and White can move to position C, both below.

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


7 pts. for Black in the corner.

Click Here To Show Diagram Code
[go]$$ C
$$ | ? ? O ? ? ?
$$ | ? ? O ? ? ?
$$ | O O O , ? ?
$$ | W X X X X ?
$$ | O O X ? ? ?
$$ | . O X ? ? ?
$$ +------------[/go]


1 pt. for White in the corner.

Black gains something from her move, and White gains something from his. Their average gain is (7 + 1)/2. That is, one half the swing value.

There is no gain for moving from B to C or vice versa, because neither player can do that. The difference between the territory values of B and C is the swing value of playing from A, and can be used to compare plays, But, as I said before, trying to use them for gains and losses leads to confusion and mistakes. I have seen players from beginners to 5 dans make those mistakes.

It is simple and accurate to say that when Black plays first she gets 7 pts., and when White plays first he gets 1 pt. There is no need to talk about gains. Especially as the confusion between swing values and gains is a known problem.

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Post #36 Posted: Fri Jul 26, 2019 4:11 pm 
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EdLee wrote:
Hi Bill,
Without using any of the theoretical tools, I can see W has 3 points, from experience: 2 + miai of 1; but I'm very curious to see the formally derived calculations. :)


All you have to do is look at the four possible variations of correct play. :)

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Post #37 Posted: Fri Jul 26, 2019 6:21 pm 
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Hi Bill,
Quote:
It is simple and accurate to say that when Black plays first she gets 7 pts., and when White plays first he gets 1 pt. There is no need to talk about gains. Especially as the confusion between swing values and gains is a known problem.
That was my mistake ( or at least one of my mistakes ) in post#2: I didn't know, although I had a suspicious feeling, that the term gain has a specific meaning in existing literatures, and may be different from the everyday usage (e.g. in electrical engineering :) ). Also, I didn't know and am still very unclear about swing value. :blackeye:

Digesting. :study: Thanks.

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Post #38 Posted: Fri Jul 26, 2019 6:39 pm 
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Hi Bill,

Thanks for the patience with these 30k questions.
Quote:
1) If the position has a territorial score, that is the territorial value.
...which is defined as ( :black: local points ) - ( :white: local points ), correct ?
Quote:
2) Otherwise, if the position is a non-ko position, it has a mean territorial value, defined as the average result in the alternating play when Black plays first and when White plays first in 2ⁿ copies of the position, either exactly or in the limit as n approaches infinity.
This is the new info from post#16; I haven't looked up mean value theorem as applied to Go, yet. :)

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Post #39 Posted: Fri Jul 26, 2019 7:25 pm 
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Bill Spight wrote:
It is simple and accurate to say that when Black plays first she gets 7 pts., and when White plays first he gets 1 pt. There is no need to talk about gains. Especially as the confusion between swing values and gains is a known problem.


Using the term "gain" is inaccurate only if you take it on to have a particular meaning. You are using "gains" as a specific term, and I think it adds to the confusion, because it requires people to know about this terminology. Maybe "gain" has a specific meaning in some literature, but to somebody that hasn't read this literature, I think it's hard to know that it means something different than "get". In English, the two words are pretty similar. And I agree that it can be dangerous when thinking of this as a plus or minus to your score in actual play. But is it necessary to go into that detail to answer this question?

Jike posted in post #28 that he was still confused. That means there were more than 25 responses that didn't make things clear to him. It means that our approach up until now, albeit precise, isn't clear to a beginner. If you are hung up about my use of the word "gain" instead of "get", I apologize, but I don't think the current discussion is easy for a beginner to digest. We should avoid adding a bunch of terminology for folks to learn, and keep things simple here. We can have a separate thread that's not in the beginner section that goes into all of these terms and nuances.


Local position value, territorial score, ko situations, thermography, fuzzy logic, and possibilities have all been discussed in this beginner thread. Is it really necessary to answer the basic question?

The only reason I am posting in this thread is in an attempt to simplify things - I don't think the current >30 posts are very clear to a beginner, however technically accurate they may be.

---

So I'll try again.

If black plays first in that diagram, black GETS 7 points. If white plays first, white GETS 1 point. It's useful to consider both possibilities in swing values, because by playing first, black can GET 7 points and prevent white from GETTING 1 point. We take both of these benefits into account, and that's why they're summed together.

If white could not GET any points by playing first, but black could still GET 7 points by playing first, then black playing there would still be useful - but not as useful as this scenario, since it doesn't prevent white from GETTING 1 point like it does here.

In contrast, if white could GET, say 2 points by playing first, and black can GET 7 points by playing first, then such a play would be more valuable than this one - even though black can still GET 7 points, it prevents white from GETTING 2 points, which is more than what white would GET if he plays to get the 1 point in this position.

I hope this is more clear.

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Post #40 Posted: Fri Jul 26, 2019 9:36 pm 
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EdLee wrote:
Hi Bill,
Quote:
It is simple and accurate to say that when Black plays first she gets 7 pts., and when White plays first he gets 1 pt. There is no need to talk about gains. Especially as the confusion between swing values and gains is a known problem.
That was my mistake ( or at least one of my mistakes ) in post#2: I didn't know, although I had a suspicious feeling, that the term gain has a specific meaning in existing literatures, and may be different from the everyday usage (e.g. in electrical engineering :) ). Also, I didn't know and am still very unclear about swing value. :blackeye:

Digesting. :study: Thanks.


Ed, I am using gain in its ordinary English meaning. KISS (Keep It Simple, Sister) is my motto. :)

But here and elsewhere people want formality, so I oblige. ;) But the term, gain, is part of KISS.

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