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This 'n' that

https://lifein19x19.com/viewtopic.php?t=12327

Page 48 of 71

Re: This 'n' that

Posted: Tue May 19, 2020 6:07 am
by Bill Spight
jlt wrote:
Click Here To Show Diagram Code
[go]$$Wc White to play and win. No komi.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O . . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Attempt:
Click Here To Show Diagram Code
[go]$$Wc W32, B31. a and b are miai for White
$$ -----------------------
$$ | . . . . . 9 7 8 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O a O X X . X . . |
$$ | . . O 4 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W31, B30. :w11: is at a ; b and c miai for White.
$$ -----------------------
$$ | . . . . 7 6 8 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 9 b X , . |
$$ | . . O a O X X . X . . |
$$ | . . O 4 X X c X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W31, B30. :w11: is at a ; b and c miai for White.
$$ -----------------------
$$ | . . . . 5 4 6 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 7 9 b X , . |
$$ | . . O a O X X . X . . |
$$ | . . O 8 X X c X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W33, B32. a and b are miai for White
$$ -----------------------
$$ | . . . . 5 4 6 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 7 8 . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 9 X X . X . X . |
$$ | . . O . a O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc White to play and win. No komi.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
:)

Re: This 'n' that

Posted: Tue May 19, 2020 6:45 am
by jlt
OK I failed.
Click Here To Show Diagram Code
[go]$$Wc Fail
$$ -----------------------
$$ | . . . . 7 6 8 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . 9 O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc Fail
$$ -----------------------
$$ | . . . . . 7 5 6 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O 9 O X X . X . . |
$$ | . . O 8 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Let me try something else.
Click Here To Show Diagram Code
[go]$$Wc W34, B33. a and b are miai
$$ -----------------------
$$ | . . . . 3 7 6 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . a O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W31 B30; a and b are miai, c and d too
$$ -----------------------
$$ | . . . . 3 8 6 . . . . |
$$ | . . . . 9 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 7 a X , . |
$$ | . . O c O X X . X . . |
$$ | . . O 4 X X b X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W32 B31; a and b are miai
$$ -----------------------
$$ | . . . . 3 9 7 8 . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O a O X X . X . . |
$$ | . . O 4 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]

Re: This 'n' that

Posted: Tue May 19, 2020 7:24 am
by Bill Spight
jlt wrote:OK I failed.
Click Here To Show Diagram Code
[go]$$Wc Fail
$$ -----------------------
$$ | . . . . 7 6 8 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . 9 O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc Fail
$$ -----------------------
$$ | . . . . . 7 5 6 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O 9 O X X . X . . |
$$ | . . O 8 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Let me try something else.
Click Here To Show Diagram Code
[go]$$Wc W34, B33. a and b are miai
$$ -----------------------
$$ | . . . . 3 7 6 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . a O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W31 B30; a and b are miai, c and d too
$$ -----------------------
$$ | . . . . 3 8 6 . . . . |
$$ | . . . . 9 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 7 a X , . |
$$ | . . O c O X X . X . . |
$$ | . . O 4 X X b X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc W32 B31; a and b are miai
$$ -----------------------
$$ | . . . . 3 9 7 8 . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O a O X X . X . . |
$$ | . . O 4 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc
$$ -----------------------
$$ | . . . . 3 . 4 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O . . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]

Re: This 'n' that

Posted: Tue May 19, 2020 7:49 am
by jlt
Click Here To Show Diagram Code
[go]$$Wc W33, B32; a and b miai
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 8 . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 9 X X . X . X . |
$$ | . . O . a O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc same as second diagram of previous message
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 9 a X , . |
$$ | . . O c O X X . X . . |
$$ | . . O 8 X X b X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]

Re: This 'n' that

Posted: Tue May 19, 2020 9:00 am
by Bill Spight
jlt wrote:
Click Here To Show Diagram Code
[go]$$Wc W33, B32; a and b miai
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 8 . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 9 X X . X . X . |
$$ | . . O . a O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . b X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$Wc same as second diagram of previous message
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 9 a X , . |
$$ | . . O c O X X . X . . |
$$ | . . O 8 X X b X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Well done!
:clap: :clap: :clap:

Re: This 'n' that

Posted: Wed May 20, 2020 8:52 am
by jlt
Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$Bc Endgame corner
$$ -------------
$$ | . . . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
Easy questions.

1) What is the usual territorial value of the corner?

2) How much does a gote or reverse sente gain?
I am not very familiar with the terminology and endgame value calculations, so I will probably get some answers wrong but let me try anyway. I'll start with the easy questions.

If Black plays first, then Black can make two eyes and live with 7 points.
Click Here To Show Diagram Code
[go]$$Bc Black plays first. Score=7.
$$ -------------
$$ | . 1 . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
If White plays first and Black doesn't play the ko, then White gets a seki. White has 1 point and Black has 0 point.
Click Here To Show Diagram Code
[go]$$Wc White plays first. Score=-1.
$$ -------------
$$ | . 3 . X O . .
$$ | O X X X O . .
$$ | 1 . X O O . .
$$ | X 2 X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
So the usual territorial value of the corner is the average (7-1)/2 = 3 points.

:b1: in the first diagram, or :w3: in the second diagram, gain 4 points.

Re: This 'n' that

Posted: Wed May 20, 2020 8:57 am
by Bill Spight
I find that I'm becoming a fan of Yasser Seirawan's lectures. :) Here is a nice one on learning from your mistakes. https://www.youtube.com/watch?v=rgUQBYO ... gs=pl%2Cwn

He also talks about how copycat chess is bad. Mirror go is not obviously bad, and we know that in some cases it is obviously correct. Such cases are specific instances of miai, which is a powerful concept in go.

BTW, miai does not seem to be a concept that Elf learned. It does make miai plays, but not always. This is something that I have believed for a while, first through observation and second through reflecting on the nature of neural networks. It seems to me that the concept of miai is at a level of abstraction that is beyond the capability of today's bots. It a bot may be said to have that concept at all, I think that it would be in the ability, in certain cases of miai, when one of the miai points is taken, the other one is the top choice in reply.

One place that this occurs is at the dame stage of a review when the human players are filling in the dame, but not playing in either of a miai pair of ⅓ pt. kos. In area scoring, which is what Elf and nearly all other top bots are trained on, there is a danger to filling one of a miai pair of ⅓ pt. kos. If the opponent is able to delay filling the other ko until all the dame have been filled, i.e., to be the komonster of that ko, she may be able to gain from that delay. The safe thing to do is to leave the miai on the board until all the dame have been filled. In effect, the miai pair has a temperature of zero at area scoring.

In one example in a game between Chinese pros, with about 20 dame moves left, Elf recommended taking one of the miai pair of kos instead of making a protective play. Taking the ko got 8918 rollouts, while the human protective play got only 594 rollouts. The human, OC, saw that the protective play would eventually be necessary and so played it instead of waiting for the opponent's atari. Elf does not apparently have the concept of sente at the same level of abstraction as humans do, either. ;) OC, taking the other ko was Elf's top choice in the mainline variation, but it got only 8436 rollouts. :o Not really a surprise, but a human would have expected taking the other ko to be a sure thing, even if the opponent were an SDK, because SDKs have learned the concept of miai. Elf does not regard this miai as a sure thing, only as a 95% thing. The kicker is this. Despite the protective play being correct Elf gives it a loss of 6% by comparison with taking the first ko, given its choice to fill the first ko after the protective play.

For years I have been asking about the margin of error of bot winrate estimates. One answer is here in the endgame, where humans can work out correct play. In this case a correct play got an estimated winrate loss of 6% to par. OC, that does not mean that a play that gets an estimated loss of 6% is not an error, but it may well not be. Margin of error. :)

Re: This 'n' that

Posted: Wed May 20, 2020 9:01 am
by Bill Spight
jlt wrote:If Black plays first, then Black can make two eyes and live with 7 points.
Click Here To Show Diagram Code
[go]$$Bc Black plays first. Score=7.
$$ -------------
$$ | . 1 . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
Click Here To Show Diagram Code
[go]$$Bc Only one ko threat
$$ -------------
$$ | . . . X O . .
$$ | O X X X O . .
$$ | 1 . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
The second diagram is slightly preferable, because White has only one possible ko threat instead of two.

So far, so good. :)

Re: This 'n' that

Posted: Wed May 20, 2020 1:15 pm
by jlt
Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$Bc Endgame corner
$$ -------------
$$ | . . . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

3) When Black is komaster, what is the territorial value of the corner?
Let's continue slowly, since I am confused. If Black is komaster, and if White plays first, a sequence like this can be expected
Click Here To Show Diagram Code
[go]$$Wc :b4: ko threat, :w5: answers, :b6: takes ko
$$ -------------
$$ | a . . X O . .
$$ | O X X X O . .
$$ | 1 2 X O O . .
$$ | X 3 X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
The corner can be left like this, but eventually Black will need to settle the ko by playing at a. Black has 5 points of territory and 3 captures but White has captured a stone, so Black got 7 points.

If Black plays first, then Black doesn't need to play anything in the corner right now, but because of the preceding sequence, Black will eventually need to add a move.

So I think that the territorial value of the corner is 7 points.

Re: This 'n' that

Posted: Wed May 20, 2020 2:56 pm
by Bill Spight
jlt wrote:
Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$Bc Endgame corner
$$ -------------
$$ | . . . X O . .
$$ | O X X X O . .
$$ | . . X O O . .
$$ | X . X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]

3) When Black is komaster, what is the territorial value of the corner?
Let's continue slowly, since I am confused. If Black is komaster, and if White plays first, a sequence like this can be expected
Click Here To Show Diagram Code
[go]$$Wc :b4: ko threat, :w5: answers, :b6: takes ko
$$ -------------
$$ | a . . X O . .
$$ | O X X X O . .
$$ | 1 2 X O O . .
$$ | X 3 X O . . .
$$ | O X X O . . .
$$ | O O O O . . .
$$ | . . . . . . .[/go]
The corner can be left like this, but eventually Black will need to settle the ko by playing at a.
Evaluating kos is tricky, because kos involve the rest of the board. I call everything relevant to the ko fight the ko ensemble. Well, Professor Berlekamp developed a strong theory that makes simplifying assumptions, so that you don't have to know much about the ko ensemble; you can focus on the ko itself. It's the komaster theory.

The first assumption is that the komaster can capture the ko without ignoring any of the opponent's threats. So in this case, White has no effective ko threat to make and :w7: plays elsewhere. The second assumption is that at this point the komaster has to go on and settle the ko as soon as possible. IOW, Black cannot afford to leave the corner like that. So :b8: wins the ko.

I was working on my own ko theory when I heard Berlekamp speak on the komaster theory in 1994. It solved problems that I had found intractable. :)
Black has 5 points of territory and 3 captures but White has captured a stone, so Black got 7 points.

If Black plays first, then Black doesn't need to play anything in the corner right now, but because of the preceding sequence, Black will eventually need to add a move.

So I think that the territorial value of the corner is 7 points.
Right. But note that after an even number of plays, White gets a play elsewhere in exchange for losing the ko. This ko exchange is important for evaluating the ko. The exchange is not peculiar to kos. Other plays have exchanges as well. We just don't usually talk about them. ;)

Re: This 'n' that

Posted: Thu May 21, 2020 12:57 am
by jlt
I am still confused. To simplify things, I assume that the board only contains

1) the corner position
2) sufficiently many ko threats for Black
3) gote moves of values E1, E2, E3... The sequence is ordered from the largest to the smallest.

For instance
Click Here To Show Diagram Code
[go]$$B Playing at a is a move of value 2
$$ -----------------
$$ . . X O O a O . .
$$ . . X X X X O . .
$$ . . . . . . . . .[/go]
Suppose first that it's White to play, and that White plays in the corner. Then Black has to choose between the seki variation and the ko variation.

If Black chooses the seki variation, then Black gets -1 point in the corner and after the sequence it's Black to play, so Black will play the move of value E1, etc. so the final score will be -1+2(E1-E2+E3-E4+...)

If Black chooses the ko variation, then :w7: plays the move of value E1, :b8: settles the ko, :w9: plays the move of value E2, etc. so the final score is 7+2(-E1-E2+E3-E4+...)

The difference between the second and the first is 8-4E1, so

If E1<2 then Black chooses the ko variation
If E1>2 then Black chooses the seki variation
If E1=2 then Black chooses either one.

These considerations don't help me much.

Re: This 'n' that

Posted: Thu May 21, 2020 3:08 am
by Bill Spight
jlt wrote:I am still confused. To simplify things, I assume that the board only contains

1) the corner position
2) sufficiently many ko threats for Black
3) gote moves of values E1, E2, E3... The sequence is ordered from the largest to the smallest.

For instance
Click Here To Show Diagram Code
[go]$$B Playing at a is a move of value 2
$$ -----------------
$$ . . X O O a O . .
$$ . . X X X X O . .
$$ . . . . . . . . .[/go]
This is how I built my theory of ko. :)
Suppose first that it's White to play, and that White plays in the corner. Then Black has to choose between the seki variation and the ko variation.

If Black chooses the seki variation, then Black gets -1 point in the corner and after the sequence it's Black to play, so Black will play the move of value E1, etc. so the final score will be -1+2(E1-E2+E3-E4+...)
1) If Black chooses the seki variation, and if the value of E1 is less than or equal to 4, then White moves to -1 in the corner, and Black plays in the Es. The result will be

-1 + E1 - E2 + ....

plus some constant.
If Black chooses the ko variation, then :w7: plays the move of value E1, :b8: settles the ko, :w9: plays the move of value E2, etc. so the final score is 7+2(-E1-E2+E3-E4+...)
2) If Black chooses the ko variation and E1 is less than the value of a move in the ko, then after White takes the ko, Black plays a threat, and White answers it, and then Black takes the ko back, White plays in E1, Black wins the ko, and then play continues in the Es.

The result is 7 - E1 - E2 + E3 - ....
plus the same constant.

The difference in the results is 8 - 2*E1. But we know that E1 <= 4, so Black should make the ko.

3) But what if E1 > 4? Then if Black chooses the seki option, White does not make a seki but plays in E1.

Now, we do not know the size of the rest of the Es, so we do not know whether the corner will become seki or not. We can estimate the result, however as

3 - E1 + E2/2
plus the same constant.

If we change the result of making the ko to a similar estimate, we get

7 - E1 - E2/2

The difference is 4 - E2.

But if E2 < 4, we do know that if Black does not make ko, White will play in E1 and then Black will make life. So E2 >=4, and Black should choose the seki option.

Berlekamp's theory ignores the differences between the Es and comes to the same conclusion more easily. :)

Re: This 'n' that

Posted: Thu May 21, 2020 8:20 am
by RobertJasiek
An Alternating Sum should be abbreviated:

∆E1 := E1-E2+E3-E4+...

-∆E1 := -E1+E2-E3+E4-...

Re: This 'n' that

Posted: Thu May 21, 2020 2:24 pm
by jlt
An elementary question: why do your formulas differ from mine by a factor 2?

For me, E1=2 corresponds to a move like this
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ . . X O O a O . .
$$ . . X X X X O . .
$$ . . . . . . . . .[/go]
If Black plays there, Black gets 2 points of territory + 2 prisoners = 4 = 2E1 points, that's why I wrote a factor 2 but you didn't??

Re: This 'n' that

Posted: Thu May 21, 2020 3:00 pm
by Bill Spight
jlt wrote:An elementary question: why do your formulas differ from mine by a factor 2?

For me, E1=2 corresponds to a move like this
Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ . . X O O a O . .
$$ . . X X X X O . .
$$ . . . . . . . . .[/go]
If Black plays there, Black gets 2 points of territory + 2 prisoners = 4 = 2E1 points, that's why I wrote a factor 2 but you didn't??
You always start, as one of my philosophy profs pointed out to a chorus of boos, from where you are. ;) Before either player plays from this position, what is its territorial value? After either player plays here, how much has she gained (on average)? That's the question. Gains are what add and subtract correctly.
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