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 Post subject: Re: This 'n' that
Post #81 Posted: Wed Oct 28, 2015 11:06 am 
Oza

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For instance, if you show to O Meien and ask him what kind of play :w1: is, he will say gote in a flash. Ask him how much it gains, and he will say 5 points.


Since O Meien had to write a book specially to convey his ideas and felt compelled to give his system a new name (Absolute Counting) this is Alice in Wonderland stuff - words just mean what the Red Queen wants them to mean.

O's book is not specially well written, anyway. He belongs to the Cheshire Cat school of writing - grins at you then disappears - which seems common among mathematicians. But quoting him on this forum seems a bit perverse since there is no English version yet.

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 Post subject: Re: This 'n' that
Post #82 Posted: Wed Oct 28, 2015 11:19 am 
Judan

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John Fairbairn wrote:
Quote:
For instance, if you show to O Meien and ask him what kind of play :w1: is, he will say gote in a flash. Ask him how much it gains, and he will say 5 points.


Since O Meien had to write a book specially to convey his ideas and felt compelled to give his system a new name (Absolute Counting) this is Alice in Wonderland stuff - words just mean what the Red Queen wants them to mean.


Well, traditionally this play is considered a gote with a swing value of 10 points. Some pros might be confused, but I feel sure that O Meien would not be. :) Nor would Takagawa or Shimamura or Hayashi Gembi have been, to name a few. No Humpty Dumpty or Wittgenstein here. ;)

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Post #83 Posted: Thu Oct 29, 2015 7:41 pm 
Judan

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I learn more about sente and gote

Back to ancient times. :) I originally learned about sente from the English version of Korschelt, about the value of taking sente instead of following your opponent around and of keeping sente when possible. I also learned about sente plays, which threaten the opponent with severe loss (according to Korschelt). Later, as an SDK, I learned about the classification of plays as gote, sente, reverse sente, and double sente. I also learned the rule about doubling the swing value of sente, without explanation. I also learned about assuming that sente are played when estimating territory, and the saying that sente gains nothing. (The two go together, and I understood that. If sente gained something, then it would not make sense to assume that sente are played when estimating territory, as that would change the estimate.)

As I said, I began to have doubts about double sente, in particular the double kosumi on the second line. I saw one pro game where it was played in gote, and after that I noticed that pros often left it on the board for some time without playing it, a violation of the saying to hurry to play double sente.

As I also mentioned, on my own I developed a probabilistic understanding of gote and sente, at least in evaluating positions and plays. Since we assume that sente are played, the probability of playing a sente is 100%, and the probability of playing a gote is 50%. That gave me the correct values. I did not think about it, but that did not allow for evaluating double sente, as it implied that each player would get to play the double sente. ;)

I finally understood the rule about doubling the value of sente, when I read somewhere about evaluating a simple ko at 2/3 of its swing value. The point was how much each move gained. There is one move difference in a sente, two moves difference in a gote, and three moves difference in a simple ko. You double the swing value of sente instead of taking one half the swing value of gote because people find it easier to multiply by two than to divide by two. :) I did not think of the implication for double sente, dividing by zero.

I had also forgotten Korschelt’s idea of sente as threatening a severe loss. I told beginners that a play was sente if it carried a threat that was larger than anything else on the board. Not exactly accurate, but close enough. ;)

But I was still operating by the seat of my pants. Often whether a play was sente or gote was obvious, but not always. And what about plays that were sente, but did not carry a threat that was larger than anything else on the board? Obviously they could not be played with sente yet, but presumably they would eventually, with very high probability.

Normally, as the ambient temperature dropped (as we now say), there would come a time when the largest play elsewhere would be smaller than the threat of the sente but larger than the reverse sente. At that point the sente could be played with sente. There might be exceptions, but that was the general rule. So we started with the idea that a play is sente if it carries a threat larger than the largest play elsewhere on the board, and we get a new idea that a play is sente if it carries a threat that is larger than the reverse sente. Eureka! :)

Later that got refined to the idea that a play is sente if it raises the local temperature and initiates a sequence of play that drops below the local temperature with a play by the opponent.

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 Post subject: Re: This 'n' that
Post #84 Posted: Fri Oct 30, 2015 8:24 am 
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A play is sente only if your opponent answers.

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 Post subject: Re: This 'n' that
Post #85 Posted: Fri Oct 30, 2015 9:56 am 
Judan

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Abyssinica wrote:
A play is sente only if your opponent answers.


Even Korschelt did not go that far. ;) A play is made with sente if your opponent answers. :)

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 Post subject: Re: This 'n' that
Post #86 Posted: Fri Oct 30, 2015 10:17 am 
Judan

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I thought it might be fun to use the method of multiples to evaluate one of the so called special rulings of the 1949 Japanese rules, Three Points Without Capturing. :) (See http://senseis.xmp.net/?TorazuSanmoku ). The ruling is attributed to Honinbo Shuwa. Shuwa did not leave a record of his reasoning, but it accords with the result of the method of multiples. :)



When Black plays first, White answers locally, yielding sente but making 3 points in the corner. Black starts in the next corner with the same result: 3 points for White in each corner, as advertised. :)

When White plays first, White gets only 2 points in the corner, but takes gote, so that Black has to start in all of the other corners. Each new corner adds 3 points for White, which is consistent with the ruling.

The fact that White gets only 2 points in gote indicates that the local temperature is -1, that is, that each play loses 1 point. :)

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 Post subject: Re: This 'n' that
Post #87 Posted: Fri Oct 30, 2015 10:43 am 
Judan

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Here is another ruling from the Japanese 1949 rules. Five Points Without Capturing. See http://senseis.xmp.net/?TorazuGomoku



Waddaya know? By the method of multiples, if Black plays first White gets 5 points in each corner, but if White plays first he gets only 3 points in each corner.

A true double sente! :D

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 Post subject: Re: This 'n' that
Post #88 Posted: Fri Oct 30, 2015 12:19 pm 
Dies with sente

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It doesn't seem like the multiples get used much in these examples :)

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 Post subject: Re: This 'n' that
Post #89 Posted: Fri Oct 30, 2015 2:52 pm 
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Bill Spight wrote:

Waddaya know? By the method of multiples, if Black plays first White gets 5 points in each corner, but if White plays first he gets only 3 points in each corner.

A true double sente! :D


Is this like a thousand year double sente.


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 Post subject: Re: This 'n' that
Post #90 Posted: Mon Nov 02, 2015 9:17 pm 
Judan

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I write the rules

When I was a 3 dan I moved to New Mexico, making me the strongest player in the state. Before long I was elected president of the New Mexico Go Association, and I started holding four tournaments a year. I became aware of the problems beginners in the West have with ending the game. I was already aware of the problems they had with telling whether stones were alive or dead at the end. After about a year as president, I drafted and proposed rules that used play to decide questions of life and death. Since at the end of the game each play costs one point, whether by filling in one's own territory, or by playing inside the opponent's territory and becoming a prisoner, my idea, which I had already used with beginners, was to require that each player make the same number of moves in the play to decide life and death. That way the score would stay the same. :)

The rules also had a komi of 6.5 points. We were ahead of our time. :)

Now, I don't know how about how Honinbo Shuwa decided on the score for Three Points Without Capturing, but the New Mexico rules produced the same result. :) Let's see how that would work. In the top right corner we have a group with three points for Black. If the top left position is worth three points for White, then the local score in the combined positions should be zero. How does that play out?



As we already know, if Black plays first White gets three points in the top left after an even number of plays, but if White plays first he only gets two points there, but he has made one more play than Black. When Black makes the required move to make the number of plays the same for each player, the result in the two corners is zero, as advertised. :)

OK. What about the Five Points Without Capturing double sente? Let's take a look. :)



Under New Mexico rules it is worth only three points. To avoid the result of five points for White, Black to play fills a point in the right hand corner. Then White has to start play in the top left corner, and the local net score is again zero. :)

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 Post subject: Re: This 'n' that
Post #91 Posted: Wed Nov 04, 2015 6:03 pm 
Judan

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A couple of bridge anecdotes

A brief snippet of a conversation that I overheard between two bridge partners after a tournament in Albuquerque:

Partner A: I got that bid from Marshall Miles. You know, the guy who wrote All 50 Cards.

Partner B: I always knew you weren't playing with a full deck.

----

It is not unusual in bridge for the declarer to show his hand and declare how many tricks he will make. But occasionally a defender can make a declaration. He cannot show his hand to his partner, but shows it to the declarer.

At a tournament in Arizona my partner and I were playing against a couple who had the classic farmers' look. The husband was tall and gaunt, with a prominent Adam's apple; the wife was a stocky 5' by 5'. The husband was declarer at a contract of Two Diamonds and at trick eight or nine my partner claimed to defeat the contract by two tricks. The declare agreed. At this point his wife piped up: "We'll play it out." Firmly.

I said to her, "He's the declarer." Meaning that it was his decision to make whether to agree with my partner's declaration. (As dummy she had no say in the matter -- although in rare cases she could appeal the result later.)

She replied, "He's my husband and he'll do what I say."

We played the hand out. ;)

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Post #92 Posted: Thu Nov 05, 2015 12:05 am 
Judan

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Territory in the Capture Game

I have mentioned a number of times how the concept of territory is implicit in the capture game. Once the dame are filled, the game can be scored in terms of territory and the winner determined without playing the game out. However, territory in the capture game is not exactly the same as territory in regular go.

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


By symmetry it is plain that each player has the same amount of territory, but the dame are still unfilled.

Click Here To Show Diagram Code
[go]$$B Filling the dame
$$ -----------
$$ | . O 3 X . |
$$ | . O 2 X . |
$$ | . O 1 X . |
$$ | . O 4 X . |
$$ | . O 5 X . |
$$ -----------[/go]


After the dame are filled each player has three safe moves left. Each of those moves is a point of territory. That means that the group tax applies to territory in the capture game. Many people think that the group tax only applies to stone counting, but that is not so. The net score is 0, which means that the second player wins. Since it is White's turn, Black wins.

Click Here To Show Diagram Code
[go]$$Wm6 Playing out the game
$$ -----------
$$ | 3 O X X 4 |
$$ | . O O X . |
$$ | 1 O X X 2 |
$$ | . O O X . |
$$ | 5 O X X 6 |
$$ -----------[/go]


After :b11: White can resign.

In the next example White has surrounded more empty points than Black, but neither player has any territory.

Click Here To Show Diagram Code
[go]$$B No territory
$$ -----------
$$ | . O . O O |
$$ | X X O . . |
$$ | . X O . . |
$$ | . X O O O |
$$ | . X X X X |
$$ -----------[/go]


Click Here To Show Diagram Code
[go]$$B Black wins
$$ -----------
$$ | 1 O 2 O O |
$$ | X X O . . |
$$ | . X O . . |
$$ | 3 X O O O |
$$ | . X X X X |
$$ -----------[/go]


:b3: is like a dame. Because of the group tax, Black has no territory. OTOH, if White played at 3 the result would be seki, with no territory for either player.

After :b3: the net score is 0, as the White eye is seki, with no territory for either player. Since it is White's turn, Black wins.

Click Here To Show Diagram Code
[go]$$B Continuation
$$ -----------
$$ | X O O O O |
$$ | X X O . 4 |
$$ | . X O 5 . |
$$ | X X O O O |
$$ | . X X X X |
$$ -----------[/go]


If :w4:, :b5: maintains the seki. White can resign.

The fact that the White eye on the right is seki instead of dead is because Black cannot sacrifice enough stones to roll up the eye. In Capture 7 Black could possibly roll up the eye.

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Post #93 Posted: Fri Nov 06, 2015 8:27 am 
Judan

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Cats and Dogs

On Monday I attended an interesting talk by Professor Jorge Nuno Silva of the University of Lisbon. He heads a program for the use of intellectual games in the Portuguese schools. One of the games he showed us is Cats and Dogs, in which one player's pieces are cats and the other player's pieces are dogs. In his video these were cartoon characters. The players start with an empty board and take turns placing pieces on the squares of the board. A player may not play a piece rookwise adjacent to an opponent's piece. The first player without a move loses.

OC, it is easy to play Cats and Dogs as a form of no pass go. And yes, it has a form of territory. :)

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


In this diagram each player has 5 points of territory for a net score of 0. Neither player can play on the center line, so those points are not dame. Black to play must start filling in his own territory, so White wins.

Click Here To Show Diagram Code
[go]$$B Game 1
$$ -----------
$$ | . 2 . 1 . |
$$ | . 8 a . . |
$$ | 6 . 7 . 5 |
$$ | . b 9 . . |
$$ | . 4 . 3 . |
$$ -----------[/go]


:w8: and "a" together may be said to form a dame, as do :b9: and "b".

After :b9: the players can stop the game and count the territory.

Click Here To Show Diagram Code
[go]$$B Black +3
$$ -----------
$$ | C 2 . 1 C |
$$ | C 8 . C C |
$$ | 6 . 7 C 5 |
$$ | C . 9 C C |
$$ | C 4 . 3 C |
$$ -----------[/go]


Each player's territory consists of empty points upon which she can play but her opponent cannot. As indicated, Black has 7 points of territory and White has 4 points, for a net score of 3 points for Black.

This concept of territory is different from that of regular go, as territory does not have to be surrounded. Cats and Dogs uses a form of proximity scoring. See http://senseis.xmp.net/?ProximityScoring .

Click Here To Show Diagram Code
[go]$$B Game 2
$$ -----------
$$ | . 2 . 1 . |
$$ | . . . . . |
$$ | 7 . 6 . 5 |
$$ | . . . . . |
$$ | . 4 . 3 . |
$$ -----------[/go]


In this game White tries :w6: to prevent Black from playing there, but Black counters with :b7:.

Click Here To Show Diagram Code
[go]$$Wm8 B +3
$$ -----------
$$ | C O . X C |
$$ | . 1 . 4 C |
$$ | X . O . X |
$$ | 2 . 3 . C |
$$ | . O . X C |
$$ -----------[/go]


Next :w8: and :b9: are miai, and then :w10: and :b11: are dame. I have marked the territory. Black still wins by 3. :)

Edit: Another variation.

Click Here To Show Diagram Code
[go]$$B Game 3
$$ -----------
$$ | . 2 . 1 . |
$$ | 7 . 9 . . |
$$ | . 6 . . 5 |
$$ | . 8 0 . . |
$$ | . 4 . 3 . |
$$ -----------[/go]


This time White tries :w6:, which also prevents Black from playing on tengen. :b7: invades. Then :w8: makes 2 points of territory, as does :b9:. Black wins by 4 points, as the reader may verify. :)

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Last edited by Bill Spight on Fri Nov 06, 2015 9:01 am, edited 2 times in total.
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 Post subject: Re: This 'n' that
Post #94 Posted: Fri Nov 06, 2015 8:31 am 
Lives in sente

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Interesting game. Has it been analyzed combinatorially?

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 Post subject: Re: This 'n' that
Post #95 Posted: Fri Nov 06, 2015 8:49 am 
Judan

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gowan wrote:
Interesting game. Has it been analyzed combinatorially?


The video Dr. Silva showed just gave us a taste of the game. There are several games that students play during their education, and there is a rotation, so that not every game is taught each year. The dame correspond to STARS in CGT, and the scoring is surely as I have indicated, but they may not use the term, territory. In both games :b7: has a temperature of 3, and I expect that the students learn about temperature. :) I do not know if more complicated infinitesimals have been discovered.

BTW, I spoke briefly with Silva and asked about go. He said that they tried introducing go into the rotation, but the teachers did not understand ending the game with passes. They may try introducing the Capture Game in the near future. :)

I have edited the previous note to add a third variation. :)

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Post #96 Posted: Fri Nov 06, 2015 4:40 pm 
Dies in gote

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gowan wrote:
Interesting game. Has it been analyzed combinatorially?

It is easy to analyze the 1 x n game. I think the scores of the n x n game are 1, 0, 2, 0, 2 for n = 1, 2, 3, 4, 5.

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Post #97 Posted: Sat Nov 07, 2015 10:50 am 
Judan

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My early bridge career

I learned to play bridge when I was six years old, but did not play much until I was thirteen. That was because other kids did not know how to play bridge, and the local duplicate bridge club met on Thursday nights, a school night. But I played a lot of Oh Hell, which is similar to bridge and whist. I did not start studying bridge until I was twelve.

In those days contract bridge was in its infancy, and the general level of technique was not very high. The hallmark of an expert then was said to be the ability to run a squeeze play. I ran my first one at age thirteen. It was on defense. I put my partner in to run her suit, which squeezed the declarer. I was the only one at the table who understood what had happened. When I was fourteen the local life master said that I was the best player in the club at the play of the hand, but the worst bidder. ;)

When I arrived in Japan I looked up the local duplicate club in Tokyo. The had a game on Tuesday night. I called them up and spoke to a guy named Joe Montalto, who was one of the top level players in Japan at that time, though I did not know that, of course. He said that he would play with me unless another walk-in arrived. We won, and I recall that we defeated a two diamond contract by six tricks for a top score on that hand. He criticized my play on that hand, which surprised me because 1) it worked, and 2) we got a very good result. :)

I started playing frequently at the club, which had a game every afternoon and some nights. I played to make the local life masters look foolish, which was not a very good attitude, I am afraid. :( I played a lot with Yetta Graeler, who was the wife of the concert master of the NHK orchestra, Louis Graeler.

One day Joe asked me to play with him that coming Sunday afternoon. On one hand I played a trump squeeze, which I thought nothing about, but Joe was suitably impressed. :) After the game he told me that he was thinking about asking me to join his team, and that if I was amenable, there was a tournament the next month that we could play in and he would decide after that. Of course I agreed, and we got together socially with the rest of his team that evening. BTW, Joe was very good at the play of the cards. It was said that he could play the hand one trick better than everybody else, but unfortunately, he overbid by two tricks. ;)

One member of Joe’s team was Lou Schaefer, the Philippina wife of an American Colonel. There was another guy at the club, Kunio, who was a couple of years older than I. Lou used to tell people that we were her sons. She said, “I had Kuni when the Japanese invaded, and Bill when the Americans came back.” ;) After the initial team get together Lou took me aside and told me to ignore Joe’s criticisms. “He criticizes everybody,” she said. It soon became apparent that Joe was asking me to possibly join his team because his teammates were tired of his constant criticism, and no longer wanted to be his partner. On the team they would play at the other table.

Joe and I played often in the weeks before the tournament, and his constant criticism was wearing. The trouble is, he was often right, or his critiques fell into a gray area that you could argue with. I never did. Yetta was also hypercritical, but she was not in Joe’s league, and it was easy to sluff off her complaints. Later, in New Mexico I also played with a woman who was also hypercritical, but she never criticized me. One player dubbed us Spight and Malice. ;) (What is it with these hypercritical bridge partners? Bad karma?)

In those days Japanese tournaments were one day affairs, as the Japan Contract Bridge League did not have a whole lot of players. Early in the first session Joe criticized my play on the previous hand. But this time there was no gray area, his analysis was simply wrong. I saw my chance and I took it. I set my cards face down on the table and said, “Joe, you are wrong and you know it.” Then I got up and went to the men’s room. I waited around for a couple of minutes and then returned to the table. We finished the round in silence, except for the talk necessary to play the game. Later I told Lou and she said, “You said that to Joe Montalto?!” Joe never criticized me again. :) A couple of months later he remarked to someone, “Bill is a fine young player, but temperamental.” ;)

About six months after I arrived in Japan Yetta's son Johnny came back from Czechoslovakia. He is the 5 kyu who got me started playing go and was my first teacher. We played once a week, and sometimes more often, for about 11 months. :)

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Post #98 Posted: Wed Nov 11, 2015 7:45 pm 
Judan

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Evaluation through (hypothetical) play in the environment

We have already seen how we might evaluate plays in special, ideal environments, such that each player is indifferent whether to make the play or to play in the environment. These environments are special only in the sense of being engineered to produce exact results. But they are meant to mimic normal conditions on the go board. A randomly chosen environment from real games would produce approximately the same results.

We have also seen how environments consisting only of duplicate positions can be used to evaluate them.

We have also seen how an environment of plays that lose one point by territory scoring can be used to score local positions. A key point is that each side must make the same number of plays; otherwise the first player loses one point — or more if free passes are allowed.

We can also evaluate non-terminal plays in a similar fashion. The logic is simple. If Player A makes a play that gains X points and then the other player, Player B, makes a play in another position that gains X points, the value of the combination of positions remains the same. Let’s use that idea to evaluate the following position.

Click Here To Show Diagram Code
[go]$$ Outer stones alive
$$ . . . . . . .
$$ . X X X X X .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O . O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


Now, experienced players know that we evaluate this corridor as 2.5 points of territory for White. Let’s derive that from hypothetical play in an environment.

Click Here To Show Diagram Code
[go]$$W White first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O . O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


:b2: elsewhere

Let us assume that the play elsewhere, in the environment, gains t points for either player and its local value is 0. (We use t for historical reasons.) Locally White gets 5 points and Black gets t, for a result of t - 5, from Black’s point of view. (By convention we take Black’s point of view.)

Click Here To Show Diagram Code
[go]$$B Black first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O . O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


:w2: elsewhere

Now the result is 0 - t = -t.

If the result is the same regardless of who plays first, then we have the equation,

t - 5 = -t

and so

t = 2.5.

Each play gains 2.5 points.

Furthermore, the value of the local position is -2.5, as advertised. :)

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Post #99 Posted: Thu Nov 12, 2015 11:58 am 
Judan

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Evaluation through (hypothetical) play in the environment, II

Now let’s evaluate a position with a follower.

Click Here To Show Diagram Code
[go]$$ Outer stones alive
$$ . . . . . . .
$$ . X X X X X .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


Even experienced players might have to think a bit to evaluate this corridor. :)

Click Here To Show Diagram Code
[go]$$W White first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O B O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


:b2: elsewhere

As before, White gets 5 points locally and Black gets t0, for a result of t0 - 5, from Black’s point of view. (I use t0 because we are going to find another environmental value for the follower.)


Click Here To Show Diagram Code
[go]$$B Black first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O X O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


:w2: elsewhere

Now the result is v1 - t0, where v1 is the value of this follower.

Experienced players know that v1 = -1, and that t1 = 1. Black to play saves the :bc: stone for a local score of 0, and White to play captures it for a local score of -2. Each play gains 1 point.

For the original position we have the equation,

t0 - 5 = —1 - t0

and so

t0 = 2.

Each play gains 2 points.

The value of the local position is -3. :)

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 Post subject: Re: This 'n' that
Post #100 Posted: Fri Nov 13, 2015 7:59 am 
Judan

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Evaluation through (hypothetical) play in the environment, III

Now let’s evaluate a slightly different position.

Click Here To Show Diagram Code
[go]$$ Outer stones alive
$$ . . . . . . .
$$ . X X X X X .
$$ . . O . O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


This is obviously a sente, but let’s not start with that idea. :)

Click Here To Show Diagram Code
[go]$$W White first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


:b2: elsewhere

As before, White gets 5 points locally and Black gets t0, for a result of t0 - 5.


Click Here To Show Diagram Code
[go]$$B Black first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


:w2: elsewhere

Now the result is v1 - t0, where v1 is the value of this follower.

Experienced players know that v1 = -2, and that t1 = 2. Black to play saves the :bc: stones for a local score of 0, and White to play captures them for a local score of -4.

For the original position we have the equation,

t0 - 5 = —2 - t0

and so

t0 = 1.5.

Wait! t1 > t0 (2 > 1.5). That means that White’s reply gains more than t0, so White will reply instead of playing elsewhere. :b1: is sente.

Click Here To Show Diagram Code
[go]$$B Black sente
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O 2 O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]


The result after :w2: is -4. That gives us this equation.

t0 - 5 = -4

and so

t0 = 1.

The reverse sente play gains 1 points.

The value of the original position is -4. :)

Note that we could have started with the assumption that the play was sente and confirmed that by the fact that t1 > t0 (2 > 1).

There is another way that we could have figured out that this was a Black sente, one I often used way back before I found out about solving for t0 and t1. I calculated the value of the position after :b1:, which is -2 and used that to calculate the value of the original position as if it were gote. That comes to -3.5. The value if it is a Black sente is -4. White would certainly prefer it to be -4, and therefore will make it sente by replying to :b1:. ;)

As simple as the material in this note may seem, it is very important for understanding local sente and gote. It illustrates why we call this a one point sente. Not because, as it sounds, the sente gains 1 point, but because it tells us when each player is indifferent between playing locally or playing in the environment. (OC, in a non-ideal environment that may not be the case. :)) It is the reverse sente that gains 1 point.

It also illustrates why we say that the sente player has the privilege of playing the sente. When plays in the (ideal) environment gain less than 2 points and more than 1 point, Black may play locally with sente, while White has to wait until the plays in the environment gain 1 point or less.

It also illustrates why we say that sente gains nothing. The reverse sente gains 1 point with a play to a value of -5, which means that the original value is -4, the same as after Black’s sente and White’s reply.

The material in this note is also important because it shows us how to distinguish between local sente and gote. As I said, that was something that was never explained to me when I was learning. I had to figure it out for myself. Probably that was because there are other meanings of sente and gote, and so there was some confusion among the writers about their meaning. Before I figured out how to tell the difference, I did what I think most players do, I made an educated guess about whether a play was sente or gote and did the calculations accordingly. With some experience, that usually works, or the errors are small.

However, the calculated values in yose books are often wrong, and sometimes the lines of play are wrong, or if they are not wrong from the point of view of tesuji, they give the wrong impression of when to play elsewhere. I show an example on Sensei’s Library. here ( http://senseis.xmp.net/?YoseErrorsInMagicOfGo ) and here ( http://senseis.xmp.net/?TenukiIsAlwaysAnOption ). Very often the calculations are wrong because the play is misidentified as sente or gote. That suggests that the writer (often a strong amateur ghost writer) did not check, or did not know how to check. Now you do. :)

Even if the textbooks often get it wrong, that does not mean that strong players do. I remember once figuring out that a play that the textbooks said was sente was actually gote, and the next day I was playing over one of Sakata’s games, I think with Fujisawa Hideyuki, and the play came up. They played it as gote. :D

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

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