This 'n' that

Talk about improving your game, resources you like, games you played, etc.
Bill Spight
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Re: This 'n' that

Post by Bill Spight »

OK, here is one answer to my little problem. Kirby gave another. :)

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


:b1: is a 2 point sente (1 pt. under territory scoring). :b3: gains 2 points, because White is komonster, as explained earlier. :w4: gains 1.75 points and then :b5: gains 1.5 points. Then the players share the dame and protective play. :w10: could be a pass, but it costs nothing and allows us to count territory. White has 10 points of territory and Black has 11, to win by 1 point. (The original position is worth 0.75 for White; Black gained 1.75 in the play.)

The next diagram shows correct play by territory scoring.

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


White wins the ko.

:b1: is a 1 point sente. :b3: gains 0.75 point. :w4: gains 0.5 point, because White is komonster. Each player has 12 points, for jigo. (The original position is worth 0.25 for White. Black gained 0.25 in the play.)

:b3: would be a mistake under area scoring. The next diagram shows best play after that.

Click Here To Show Diagram Code
[go]$$B AGA rules. No komi. Black to play and win.
$$ -------------------
$$ | 6 X O . . . O O O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |
$$ | . X O O 3 . . X . |
$$ | . X 7 8 X X X X . |
$$ | . X O O O O O X . |
$$ | X O O X X O X O 5 |
$$ | X X O . O O X X X |
$$ | . X 1 2 . O O O 4 |
$$ -------------------[/go]

:b9: takes ko.

Click Here To Show Diagram Code
[go]$$Wm10 AGA rules. No komi. Black to play and win.
$$ -------------------
$$ | 3 X O . . . O O O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |
$$ | . X O O X . . X . |
$$ | . X X O X X X X 2 |
$$ | 4 X O O O O O X 1 |
$$ | X O O X X O X . X |
$$ | X X O . O O X X X |
$$ | . X X O . O O O O |
$$ -------------------[/go]

:w14: fills the ko.

:b13: costs nothing. Result: White wins by 1.

:b1: is a 2 point sente. :b3: gains 1.75 point. :w6: gains 2 points. The original position is worth 0.75 for White. Black lost 0.25 in the play.

:b7: and :w8: are a miai pair of dame, which act as a tertiary ko threat. A tertiary threat is a defense against komonster. If :w8: filled the ko, Black would get a dame in the ko exchange.

In this position it did not matter because White had another ko threat, but :w4: was a sente to eliminate Black's tertiary threat at 5.

Kim Yonghoan also discovered komonster and tertiary threats. When we were getting to know each other around 20 years ago, we had a strange exchange of emails. Each of us thought that we knew something the other didn't, and we were a bit coy about our "secret". :)

Why "tertiary" threats? When I was learning go, the beginner literature said that a ko threat was something played to win the ko. OC, the opponent might not answer it. As I began to study ko, I realized that you might play a ko threat in order to make a gain if it were not answered. So a primary threat is one played to win the ko and a secondary threat is one made to gain something in the ko exchange. A tertiary threat is played to prevent a loss to the komonster.

Edit: Kirby's answer.

Kirby wrote:
Click Here To Show Diagram Code
[go]$$B AGA rules. No komi. Black to play and win.
$$ -------------------
$$ | 1 X O . . . O O O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |
$$ | . X O O 3 . . X . |
$$ | . X 7 6 X X X X . |
$$ | . X O O O O O X . |
$$ | X O O X X O X O 5 |
$$ | X X O . O O X X X |
$$ | . X 2 . . O O O 4 |
$$ -------------------[/go]


Black gets pass stone, so 13 points.
White has 12.


OK. Now that we know that White is komonster, we can say that :b1: gains 2 points by area scoring. :w2: gains 2 points in reverse sente. :b3: gains 1.75 points. Then the dame and protective play are shared equally. In the play Black gains 1.75 points to win by 1. :)

In the sequence I gave Black got the last 2 point play, but White got the 1.75 point play. All same same. :)
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Re: This 'n' that

Post by Bill Spight »

I develop my own theory of ko evaluation.

Because of komonster effects, winning (or taking) the ko in my little problem gains 2 points by area scoring, 0.5 point by territory scoring. Neither of these is the "theoretical" value of 4/3 or 1/3. Because the value of plays usually drops over time, kos typically have some komonster effects, although normally not as big as the difference between the dame vs. no dame conditions in area scoring.

Let's look at these effects a little more closely. :)

Aside from dame, the two plays shown are the last on the board. (Just the top few lines of the board are shown.)

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


Under Japanese/Korean (territory) scoring, the no ko threat condition makes the player who does not take the gote komonster. So it does not matter which play is made first, regardless of who has sente. As you may verify. :)

However, in a real game in which the outcome of the ko is uncertain, as a practical matter it is better to take the gote and gain 0.5 point for sure. In this position for Black to fill the ko may gain nothing. She might win it, anyway. :)

Click Here To Show Diagram Code
[go]$$B No ko threats, area scoring
$$ -------------------
$$ | . X O . . . O . O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |[/go]


Under Chinese/AGA (area) scoring komonster effects could make these plays miai. But we need to consider the dame situation to tell.

If there are no dame, then the two plays are miai.

If there is one dame, then they are miai for Black, because Black gets the dame regardless. For example,

Click Here To Show Diagram Code
[go]$$B No ko threats, area scoring
$$ -------------------
$$ | 2 X O . . . O 1 O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |[/go]


:b3: takes dame. :w4: fills ko.

But with one dame they are not miai for White. White should take the gote for a sure 2 point gain plus the dame. If he takes the ko instead:

Click Here To Show Diagram Code
[go]$$W No ko threats, area scoring
$$ -------------------
$$ | 1 X O . . . O 2 O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |[/go]


:w3: fills ko. :b4: takes dame.

When there are two dame Black should take the gote.

Click Here To Show Diagram Code
[go]$$B No ko threats, area scoring
$$ -------------------
$$ | 2 X O . . . O 1 O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |[/go]


:b3: takes dame. :w4: fills ko. :b5: takes dame.

That way she gets both dame, instead of sharing them with White.

And White can take the ko.

Click Here To Show Diagram Code
[go]$$W No ko threats, area scoring
$$ -------------------
$$ | 1 X O . . . O 2 O |
$$ | X O O . O O O X X |
$$ | X X O . O X X X . |[/go]


:w3: fills ko. :b4: takes dame. :w5: takes dame.

Because either way the dame are shared.

OC, as a practical matter either player should take the gote. :)

But what does this example say about evaluating plays in the ko? Let us take the value of a play in the gote as given. Either player gains 2 points, for a swing of 4 points. Then we may evaluate the ko ensemble, including any dame. We use swing values to compare different lines of play, as their difference produces swing values.

Code: Select all

If there are no dame, then either winning or taking the ko swings 4 points.

If there is at least one dame, then

     1) with an odd number of dame

          a) winning the ko swings 4 points,

          b) taking the ko swings 2 points;

     2) with an even number of dame

          a) winning the ko swings 2 points,

          b) taking the ko swings 4 points.


If we do not know the number of dame, then the average swing for winning or taking the ko is 3 points, corresponding to the komonster value for territory scoring. :)

Now, I did not work this out when I started, because I was unaware of area scoring. ;) But I did work out a general way to evaluate prototypical ko ensembles. I have not run across anything like this way of evaluating kos in the go literature, despite its practical value, as evidenced by my little problem. I started writing a book about it in 1989, but that was before finding out about combinatorial game theory and Professor Berlekamp's work on kos. :D
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Re: This 'n' that

Post by Bill Spight »

A bit more on the value of the "half point ko" under area scoring. Also some discussion of komonster.

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


Here we have the ko with the theoretically hotter gote in which whoever plays gains 1.5 points. At the dame stage or with no dame elsewhere they are miai, with a local net score of 0. (The local region is marked.)

Click Here To Show Diagram Code
[go]$$W No ko threats
$$ -------------------
$$ | 2 X O . O . 1 X . |
$$ | X O O . O O O X . |
$$ | X X O . O X X X . |[/go]


If :w1: takes the gote, :b2: wins the ko; each player gets two points.

Click Here To Show Diagram Code
[go]$$W No ko threats
$$ -------------------
$$ | 1 B O . O 4 2 X . |
$$ | X O O . O O O X . |
$$ | X X O . O X X X . |[/go]

:w3: wins ko.

Since White is komonster White may take the ko first. However, Black gets the dame at 4 to stay even.

They are also miai when Black plays first, as you may verify. :)

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


In this case the two plays are not strict miai. In fact, at the dame stage they act like a dame.

Click Here To Show Diagram Code
[go]$$W No ko threats
$$ -------------------
$$ | 2 X O . O 1 3 X . |
$$ | X O O . O X X X . |
$$ | X X O . O X X X . |[/go]


White to play takes the gote to get the dame.

Local net result: 0.

Click Here To Show Diagram Code
[go]$$B No ko threats
$$ -------------------
$$ | 1 X O . O 2 3 X . |
$$ | X O O . O X X X . |
$$ | X X O . O X X X . |[/go]


Black to play wins the ko to get the dame.

Local net result: 2 points for Black.

Neither player can do better at the dame stage, as you may verify.

----

What is the takeaway from all this?

My impression is that most go tournaments in the West use area scoring, and most tournament players are aware that eliminating dame before winning a ko is advantageous. But how many are also aware that the ability to do that means that moves in the ko are worth more than their normal value? As my little problem illustrates. :)

Now, that specific knowledge may not make the difference between winning and losing in many games. OTOH, when it does matter, it is handy to know about, and at the end of the game the reading problems may not be very difficult. IMO, even when komonster effects do not matter to winning or losing the game, there is no reason not to play komonster positions correctly. :)

Besides, komonster effects are not restricted to these positions. They are present any time kos are won at a lower ambient temperature than the theoretical size of ko moves. It is easy, for instance, to replicate area scoring situations for territory scoring. Also, consider the extreme case where one player has an infinite supply of ko threats, having a dead group in double ko. Unless the opponent captures the dead group at the cost of one move and one point, the player with the dead group always has a ko threat. Then the value of moves in other simple kos increases by 50% on average in either area or territory scoring. That can substantially affect correct play.

Most kos have small komonster effects, and it may be best to save ko threats for possible future kos rather than to spend them to pick up 0.5 point or 1 point or so. But be aware of the possibility that correct play may mean playing kos earlier than their theoretical value might indicate.

Playing komonster positions

If you are komonster, you may gain by not winning the ko until it is necessary to do so. If your opponent is komonster, you may gain by winning the ko before its theoretical value indicates. If either player is komonster, it may be correct for each player to take the ko before its theoretical value indicates.

I have spoken. :D
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Re: This 'n' that

Post by tiger314 »

Bill Spight wrote:My impression is that most go tournaments in the West use area scoring, and most tournament players are aware that eliminating dame before winning a ko is advantageous.

As far as I know, with the exception of Britain, France and the Congress, Europe still uses territory scoring for the majority of tournaments. This does create areas where half the tournaments around are area scored and half are territory scored. Poor people living there have to learn the endgame twice :cry: .
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Re: This 'n' that

Post by oren »

Bill Spight wrote:My impression is that most go tournaments in the West use area scoring


At least Seattle uses territory. I am curious what tournaments besides the US Open use AGA on a regular basis.

What does Cotsen use?
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Re: This 'n' that

Post by Bill Spight »

tiger314 wrote:
Bill Spight wrote:My impression is that most go tournaments in the West use area scoring, and most tournament players are aware that eliminating dame before winning a ko is advantageous.

As far as I know, with the exception of Britain, France and the Congress, Europe still uses territory scoring for the majority of tournaments. This does create areas where half the tournaments around are area scored and half are territory scored. Poor people living there have to learn the endgame twice :cry: .


Thanks for the info. :)

End of game procedures may differ for different rule sets, but with some exceptions, correct play by territory scoring is also correct by area scoring. :)
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Re: This 'n' that

Post by Bill Spight »

Problems with my theory. The environment.

As I said, I considered part of the environment part of the ko ensemble. For instance, if the environment consists of a number of simple gote with swing values G0 ≥ G1 ≥ G2 ≥ . . . , in deciding whether to take or win a ko I might compare G0 with K - Gn + Gn+1 - Gn+2 + . . . , where K is the swing value of the ko, and the value of n depended on the ko threat situation. In my mind G0 was the swing value of the largest play on the board besides the ko, and therefore K - Gn + . . . was the swing value of the ko ensemble. Kos did not have values independent of the rest of the board.

There is nothing particularly wrong with this theory. After all, it led me to an understanding of komonster. :) But it is unwieldy in practice. How deeply do you look into the environment? 8 moves? 10 moves? (This is related to the famous magic number 7, plus or minus 2 that John Fairbairn often brings up. :)) As a practical matter, at some point you have to stop. (The fact that the environment does not just consist of simple gote is another matter.)

You can estimate the value of Gn - Gn+1 + Gn+2 - . . . by (Gn)/2. So we can decide whether to take or win the ko or not by comparing G0 with K - (Gn)/2, or with K - Gn + (Gn+1)/2, etc. Which estimate we use is up to us. OC, if the difference between Gn and Gn+1 is significant, then we should not use (Gn)/2, as it will probably be an overestimate.

Another problem I discovered with this framework is that it makes the analysis of approach kos difficult.

Fast forward to 1994, when I attended a talk by Professor Berlekamp in which he presented the idea of komaster (which he had developed in the '90s). The komaster is able to win the ko, but is not komonster. After the talk I sent him a note about komonster effects (without using the term) and suggesting a possible modification of his methods. By using the idea of komaster, however, Berlekamp had been able to evaluate approach kos and 10,000 year kos.

The methodology used by Berlekamp, called thermography, utilizes the concept of temperature, or a tax on making a play. For non-ko positions it gets the same results as traditional go evaluation, and also provides additional information. My theory departed from traditional go evaluation, so that is a plus for thermography. :)

It turns out that thermography can be adapted to my approach. For instance, if we decide to stop the analysis at Gn and use (Gn)/2, just set the temperature, t, to (Gn)/2 and treat the larger gote as hot plays. Thus, where my theory says to win the ko if K > G0 + (G2)/2, change that to K > G0 + t. :) This means that G0 is no longer considered part of the environment. The environment consists of G2 and smaller plays. It is a kind of foreground/background distinction.

In 1998 I used the idea of an environment with temperature to redefine thermography and extend it to the evaluation of multiple kos and superkos. :D
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Re: This 'n' that

Post by vier »

Bill Spight wrote:I started writing a book about it in 1989 ...
The original position is worth 0.75 for White ...
In 1998 I used the idea of an environment with temperature to redefine thermography and extend it to the evaluation of multiple kos and superkos.

ONAG is nice and precise. "Winning Ways" is funny and handwaving. "Mathematical Go" is not a pleasure to read for a mathematician. It starts saying too much before giving definitions. I wouldnt mind a current book that is precise.

Your posts are unreadable for me since the background is missing. "Worth 0.75" - in which valuation system?

ONAG describes the disjunctive sum. But the existence of kos means that go positions do not neatly decompose as disjunctive sums. Is there a mathematically precise definition of thermography that applies to go?
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Re: This 'n' that

Post by Bill Spight »

vier wrote:Your posts are unreadable for me since the background is missing. "Worth 0.75" - in which valuation system?

Click Here To Show Diagram Code
[go]$$B AGA rules.
$$ -------------------
$$ | . # O C C C O O O |
$$ | X O O C O O O X X |
$$ | X X O C O X X X C |
$$ | C X O O . b a X C |
$$ | C X . . X X X X C |
$$ | C X O O O O O X C |
$$ | X O O B B O X W . |
$$ | X X O C O O X X X |
$$ | C X . . C O O O . |
$$ -------------------[/go]


Because the number of Black stones and White stones on the board are equal, the area count and territory count are the same, even if the value for individual points may differ. For convenience and the familiarity of the readers I will use the territory count. The marked points and circled stones indicate territory. Black has 10 points, White has 11. Using probabilistic semantics we can evaluate point “a” as 0.75 point for Black and “b” as 0.5 point. Adding those to the rest of Black’s territory yields 11.25. The ko stone in the top left corner is usually valued as 1/3 point for White. By komonster analysis its value is 1 point for White, which gives White 12 points for a net value of 0.75 for White.

Why is the ko worth 1 point for White? Again, using probabilistic semantics, half the time Black will fill the ko for 0 points of territory, and half the time White will win the ko, as in the next diagram.

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


Because White is komonster he does not have to fill the ko (before the end of play), so the marked point is one point of territory and White gets one point for the captured stone, for a total of two points. The original ko is worth the average, or 1 point for White.

(Historical note: Counting the marked point for White was a possibility for the Japanese rules before they were codified. Both Honinbo Shusai and Go Seigen favored doing that. :))

ONAG describes the disjunctive sum. But the existence of kos means that go positions do not neatly decompose as disjunctive sums. Is there a mathematically precise definition of thermography that applies to go?


The "Extended thermography" paper is where I redefine thermography in terms of play in an environment.

Some references:

Berlekamp, “The economist’s view of combinatorial games,” in Games of No Chance, Richard J. Nowakowski (ed.), Cambridge University Press(1996)

Spight, “Extended thermography for multiple kos in go,” in Lecture Notes in Computer Science, 1558: Computers and Games, Van den Herik and Iida (eds.), Springer (1999)

Spight, “Go thermography: The 4/19/98 Jiang-Rui endgame,” in More Games of No Chance, Richard J. Nowakowski (ed.), Cambridge University Press (2002)

Siegel, Aaron, Combinatorial Game Theory, American Mathematical Society (2013)

Edit: I almost forgot.

Berlekamp, "Baduk+coupons," and

Spight, "Evaluating kos: A review of the research," both in

Proceedings: ICOB 2006: The 4th International Conference on Baduk, Myongji University and Korean Society for Baduk Studies (2006)

I don't know how easily available those proceedings are.
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Re: This 'n' that

Post by vier »

Bill Spight wrote:Berlekamp, “The economist’s view of combinatorial games”
Spight, “Extended thermography for multiple kos in go”
Spight, “Go thermography: The 4/19/98 Jiang-Rui endgame”
Siegel, Aaron, Combinatorial Game Theory, AMS (2013)
Berlekamp, "Baduk+coupons," and
Spight, "Evaluating kos: A review of the research," both in
Proceedings: ICOB 2006: The 4th International Conference on Baduk, Myongji University and Korean Society for Baduk Studies (2006)

I don't know how easily available those proceedings are.

Thanks! I found the Korean proceedings at
http://www.earticle.net/search/pub/?org=106&jour=252
with the two papers mentioned at
http://www.earticle.net/article.aspx?sn=27269 and
http://www.earticle.net/article.aspx?sn=27268
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Re: This 'n' that

Post by Bill Spight »

Click Here To Show Diagram Code
[go]$$ Japanese rules. No komi.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | . O O . O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O . O X |
$$ | . . . O . O O X X |
$$ | . . . . O X . X . |
$$ ------------------[/go]


Black to play. What result with best play?

White to play. What result with best play?

Enjoy! :)

(Board edited later.)
Last edited by Bill Spight on Wed Oct 14, 2015 9:26 am, edited 2 times in total.
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Re: This 'n' that

Post by skydyr »

Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?
Bill Spight
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Re: This 'n' that

Post by Bill Spight »

skydyr wrote:
Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?


You show a number of variations, but do not explicitly answer the questions. :)

For extra credit, evaluate the three gote and the ko. :)
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Bill Spight
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Re: This 'n' that

Post by Bill Spight »

My apologies to anyone who tried the 9x10 board. It has its own charm, though. :D More later.

Edit: I have skipped the discussion of the 9x10 board position, despite its charm. ;)
Last edited by Bill Spight on Thu Oct 29, 2015 9:18 am, edited 1 time in total.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
skydyr
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Re: This 'n' that

Post by skydyr »

Bill Spight wrote:
skydyr wrote:
Click Here To Show Diagram Code
[go]$$ Black by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$ Black is quite ahead
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by 2.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X 6 X . |
$$ | X X O X O X 5 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 3 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 4 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W White by one.
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X . X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]

Click Here To Show Diagram Code
[go]$$W Black by 2
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 2 O O 1 O X . X . |
$$ | X X O X O X . X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 4 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 3 X . |
$$ ------------------[/go]


I feel like I must be missing something, unless it's that the ko is bigger for one side than the other?


You show a number of variations, but do not explicitly answer the questions. :)

For extra credit, evaluate the three gote and the ko. :)

The leftmost play at A7 is 4 points gote for either side.
The next one over at D7 is 5 points gote for either side.
The lower play at G1 is 2 points gote for either side. However, if black takes it, it creates a 5 point ko threat for black.
The ko, if white fills it, saves 6 points and creates a one point sente followup. If black fills it, he takes all 7 points, but he does so over two moves, so each move is 3.5 points. However, the two left side plays are miai-ish and both more valuable than 3.5 points.

Click Here To Show Diagram Code
[go]$$ :w4: at marked, :w6: at :w1: White by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 2 O X . X . |
$$ | X X O X O X 7 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 W X |
$$ | . . . O . O O X X |
$$ | . . . . O X 5 X . |
$$ ------------------[/go]


I suppose the crux of it is that the ko is worth less than either of the two plays on the left, but that they can be used as ko threats because they are almost miai, being a net gain of 1 point for the first side to play and more valuable than an individual move for black in the ko. Also, the total value of the two moves is equal to the total value of the ko and G7.

White has an advantage in the ko in being able to finish it in one move rather than two, as can be seen when white fills the ko for the first move and wins, but black can't take the ko first and win. So, as mentioned earlier, black has to play out the miai-ish moves on the left first. Once black starts that, though, white's play to fill the ko is 7 points vs. 4 points for the gote at A7.

Black starts out 3 points ahead without counting any of the moves, so white has to gain 4 points on black to win but has no ko threats. However, due to the ko, black is 3.5 points behind white locally, and really only half a point ahead before play commences. The key for black is to clear the ko threats first, while white needs to fill first due to the lack of ko threats.

Click Here To Show Diagram Code
[go]$$ Best for black, victory by 1
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 3 O O 1 O X 5 X . |
$$ | X X O X O X 4 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 2 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]


Click Here To Show Diagram Code
[go]$$W Best for white, victory by 1\n :b2: and :w3: can be exchanged
$$ ------------------
$$ | . . . O X X . . . |
$$ | X X X X O X O X . |
$$ | 5 O O 2 O X 4 X . |
$$ | X X O X O X 3 X . |
$$ | O O O X O X O X . |
$$ | . . O . O X O X X |
$$ | . O . O O O 1 O X |
$$ | . . . O . O O X X |
$$ | . . . . O X 6 X . |
$$ ------------------[/go]

If white lets black play at :w1:, black can trade A7 for G1 and the ko threat is enough to win the ko later.

It's hard to use words to explain what's going on, I find. Perhaps it's best to say that every other move on the board affects the value of the ko, or that there's a value that's attached to the ko threat black can create, but it's very hard to define.

Maybe the best way is to say that the two sides appear equal, but white needs to remove the value of the potential ko threat while black needs to create it. However, playing the move that creates the threat isn't valuable enough to play so it needs to be dealt with indirectly. This seems to miss the single/double move required for the ko though.

Did I miss anything? How would you explain this?
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