Life In 19x19

John Fairbairn wrote:

In both cases (problems R and S) he assumes neither player will respond locally to the initial boundary play with a move that ends in gote.

Yes, that's how I originally took it. But Bill is saying that similarity of treatment masks a slight inaccuracy by O. Which means they should be regarded as different

I guess I just don't really understand why this is an inconsitency. Unless there are situations in which the count by O's method comes out differently then the count is just as useful a tool for deciding where to play. Of course if it's just a local problem then black would immediately respond but I was under the impression counting is used to make comparisons between several moves on the board.

RobertJasiek wrote:The more I study the endgame the richer it unfolds.

This is true with every topic, isn's it ?

For every answer, I get several new questions, o o...

Razor0310 wrote:

John Fairbairn wrote:

In both cases (problems R and S) he assumes neither player will respond locally to the initial boundary play with a move that ends in gote.

Yes, that's how I originally took it. But Bill is saying that similarity of treatment masks a slight inaccuracy by O. Which means they should be regarded as different

I guess I just don't really understand why this is an inconsitency. Unless there are situations in which the count by O's method comes out differently then the count is just as useful a tool for deciding where to play. Of course if it's just a local problem then black would immediately respond but I was under the impression counting is used to make comparisons between several moves on the board.

Here is the difference between the two.

Click Here To Show Diagram Code

[go]$$W S
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . O X X X X O 4 . X . |
$$ . . . 3 1 2 . . . . . . . |
$$ --------------------------[/go]

gains 3 points, and - gains 3 points. Net result: 0 gain.

Click Here To Show Diagram Code

[go]$$W R (Black follower)
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . O X X X 4 . . X . |
$$ . . . . 3 1 2 . . . . . . |
$$ --------------------------[/go]

gains 2 points, but - gains only 1 point. Net result: 1 point gain for White. Black territory: 10 points.

Click Here To Show Diagram Code

[go]$$W R (White follower)
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . O X X X 4 . . X . |
$$ . . . . 7 1 3 5 6 . . . . |
$$ --------------------------[/go]

gains 2 points. Then - gains 1 point. Net result: White gains 3 points. Black territory: 8 points. Average Black territory after : 9 points.

O Meien shows none of these diagrams. For R he shows this diagram, for the result after .

Click Here To Show Diagram Code

[go]$$W Diagram 45
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . O X X X 2 . . X . |
$$ . . . . 5 W 1 4 . . . . . |
$$ --------------------------[/go]

This is not a real life diagram. If White plays , except as a ko threat, he will continue to push in. This is like the sagari-sagari trick. Both sente exchanges, - and - , gain nothing on average. Result: 0 gain from the position after was played.

Edit: O Meien uses the sente-sente trick for position Q.

Click Here To Show Diagram Code

[go]$$W Diagram 42
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . . O X X 2 . . X . |
$$ . . . . . . 1 . . . . . . |
$$ --------------------------[/go]

This diagram shows White's sente, which gains nothing on average.

Click Here To Show Diagram Code

[go]$$B Diagram 43
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . . O X X X . . X . |
$$ . . . . . 2 O 1 . . . . . |
$$ --------------------------[/go]

This diagram shows Black's sente, which also gains nothing on average. Net result: 0. So we count Black's original territory as 9 points.

O uses the sente-sente trick for the original position in Q and for the position after in R. But there is no sente-sente trick for S, neither in the original position nor in the position after . O does treat S differently from the other two.

Hmmmm. I overlooked this before, but actually position Q is ambiguous, as well, but in a different way.

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[go]$$W White sente
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . . O X X 2 . . X . |
$$ . . . . . . 1 . . . . . . |
$$ --------------------------[/go]

White can play as sente and then play elsewhere.

Click Here To Show Diagram Code

[go]$$W Gote
$$ . . . . . . . . . . . . . |
$$ . . . , . . . . . , . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . |
$$ . . . . . . . . . O . . . |
$$ . . . . . . . . . . O O O |
$$ . . . , . . . . O O X X O |
$$ O O O O O O O O X X X . X |
$$ . . . . . O X X 2 . . X . |
$$ . . . . . 5 1 3 4 . . . . |
$$ --------------------------[/go]

Or White can play this sequence, ending in gote.

The ambiguity is clearer, perhaps, with the method of multiples. The SGF file shows play in four copies of Q. Note that when White plays first he should play every one as sente except at the last, when he should take gote. When Black plays first it doesn't matter whether White plays gote or sente. It's ambiguous.

Here is an SGF file with four copies of position S. Note that Black, given a choice, should always take the reverse sente instead of the gote.



Moral: When you are evaluating an ambiguous position, assume that it is played as sente. Doing so preserves the original count.

----

Remember that I said that ambiguous positions are sometimes treated as sente, sometimes as gote in the go literature? O Meien did both in the space of a few pages, treating Q as sente and S as gote.

Thanks bill, I think I understand now. I only have one question. In both of the examples where white plays first there are two outcomes, white keeps sente and the count is unchanged or black is slightly down and gains sente. My question is, if you account for sente in the value of whites last move is the theoretical count unchanged but white at an advantage by playing the last move on the board?

Razor0310 wrote:Thanks bill, I think I understand now. I only have one question. In both of the examples where white plays first there are two outcomes, white keeps sente and the count is unchanged or black is slightly down and gains sente. My question is, if you account for sente in the value of whites last move is the theoretical count unchanged but white at an advantage by playing the last move on the board?

Using the method of multiples for gote (where all the followers are also gote) you can always find some number of multiples such that they are strict miai, and it does not matter who goes first, the resulting score is the same. Dividing the result by the number of multiples gives you the count.

But with sente or ambiguous positions the result will depend upon who goes first. As the number of multiples increases, the average of the two results will tend to the theoretical count.

In the SGF files some of the variations are mistakes. When White plays first and Black replies correctly in the S example, Black always gets an average of 12 points. When White plays first in the Q example, with correct play Black always gets an average of 9 - 1/N, where N is the number of multiples.

See http://senseis.xmp.net/?MethodOfMultiples .

Bill Spight wrote:

Razor0310 wrote:Thanks bill, I think I understand now. I only have one question. In both of the examples where white plays first there are two outcomes, white keeps sente and the count is unchanged or black is slightly down and gains sente. My question is, if you account for sente in the value of whites last move is the theoretical count unchanged but white at an advantage by playing the last move on the board?

Using the method of multiples for gote (where all the followers are also gote) you can always find some number of multiples such that they are strict miai, and it does not matter who goes first, the resulting score is the same. Dividing the result by the number of multiples gives you the count.

But with sente or ambiguous positions the result will depend upon who goes first. As the number of multiples increases, the average of the two results will tend to the theoretical count.

In the SGF files some of the variations are mistakes. When White plays first and Black replies correctly in the S example, Black always gets an average of 12 points. When White plays first in the Q example, with correct play Black always gets an average of 9 - 1/N, where N is the number of multiples.

See http://senseis.xmp.net/?MethodOfMultiples .

Very interesting! I can see your issue with the example. For now I'm just going to be happy knowing how to come up with a count and be aware that ambiguous situations exist. I'm still not totally confident I can find the value of moves properly so I'll try and get my head around that more before I dig into the nitty gritty bits.

Razor0310 wrote:I'm still not totally confident I can find the value of moves properly so I'll try and get my head around that more before I dig into the nitty gritty bits.

Learning proper evaluation will be a feather in your cap.

Bonne chance!