Author: EdLee [ Fri Jul 26, 2019 3:04 am ] Post subject: Hi Bill,Thanks. So, when we talk about the territorial value of a given local position, what does it mean ?

 Author: EdLee [ Fri Jul 26, 2019 3:15 am ] Post subject: 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 = ( local points) - ( 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 = ( local points) - ( local points) = 9 - 2 = 7swing value = (b) - (a) = 7 - (-1) = 8The territorial value of the original local position (x) is ( (7 + (-1))/2 ) = 3

 Author: EdLee [ Fri Jul 26, 2019 3:29 am ] Post subject: 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 = ( local points) - ( 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 = ( local points) - ( local points) = 7 - 0 = 7swing value = (b) - (a) = 7 - (-1) = 8The territorial value of (x) is ( (7 + (-1))/2 ) = 3

 Author: dfan [ Fri Jul 26, 2019 4:23 am ] Post subject: Re: Please help with this exercise III 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.

 Author: Bill Spight [ Fri Jul 26, 2019 5:02 am ] Post subject: 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.

 Author: Bill Spight [ Fri Jul 26, 2019 5:38 am ] Post subject: Re: Please help with this exercise III 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.pngI 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.

 Author: Jika [ Fri Jul 26, 2019 11:03 am ] Post subject: Re: Please help with this exercise III @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?

 Author: Joaz Banbeck [ Fri Jul 26, 2019 12:00 pm ] Post subject: Re: Please help with this exercise III 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.

 Author: Kirby [ Fri Jul 26, 2019 12:19 pm ] Post subject: Re: Please help with this exercise III 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.

 Author: Bill Spight [ Fri Jul 26, 2019 2:06 pm ] Post subject: Re: Please help with this exercise III 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.

 Author: Bill Spight [ Fri Jul 26, 2019 2:42 pm ] Post subject: Re: Please help with this exercise III OK, Jika, let's get down to basics. How much territory does White have?

 Author: EdLee [ Fri Jul 26, 2019 2:48 pm ] Post subject: 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.

 Author: Bill Spight [ Fri Jul 26, 2019 4:06 pm ] Post subject: Re: Please help with this exercise III 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.

 Author: Bill Spight [ Fri Jul 26, 2019 4:11 pm ] Post subject: Re: 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.

 Author: EdLee [ Fri Jul 26, 2019 6:21 pm ] Post subject: 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. Digesting. Thanks.

 Author: EdLee [ Fri Jul 26, 2019 6:39 pm ] Post subject: 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 ( local points ) - ( 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.