Life In 19x19 :: Value of Move vs. Value of Position: Problem #1

Life In 19x19 http://www.lifein19x19.com/

Value of Move vs. Value of Position: Problem #1 http://www.lifein19x19.com/viewtopic.php?f=15&t=4100	Page 1 of 1

Author:	Kirby [ Wed Jun 22, 2011 10:09 am ]
Post subject:	Value of Move vs. Value of Position: Problem #1
One thing that interests me, but I have not perfected, is the idea of the value of a move vs. the "value of the position". I heard about this for the first time a little while back at a workshop with Kim Myungwan. He said that the value of a move is the amount of points that a given move was worth. The value of a position, on the other hand, is the amount of points that a given area of the board was at a given point in time. With this in mind, here is a problem for those that are interested: Click Here To Show Diagram Code `[go]$$W $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . a b . . . . . . \| $$ \| . . O . . O . . . . . O X . . . . . . \| $$ \| . . . , . . . O . , . O X X X X X X X \| $$ \| O O O O O O O O . . . O O O O O O O O \| $$ \| . . . . . . . . . . . . . . . . . . . \|[/go]` What is the value of black's position in the top right? What is the value of black playing at 'a'? What is the value of black playing at 'b'?

Author:	Kirby [ Wed Jun 22, 2011 10:13 am ]
Post subject:	Re: Value of Move vs. Value of Position: Problem #1
It occurs to me that I may have gotten the terminology that he had used wrong. By "value of position", he referred to this as the "value of territory".

Author:	lefuet [ Wed Jun 22, 2011 10:50 am ]
Post subject:	Re: Value of Move vs. Value of Position: Problem #1
I'm not sure about endgame myself, but from what I remember of an endgame lecture I'd guess: value of blacks position is 18 (since it is not clear who will get the endplay at the border just connect each color straight down to the edge)? a play at A is gote for black (hane - block, connect) but the follow up is sente for black and not for white so it is blacks privilege to play it (hane - block, connect - connect) black gains 1 point and white loses 4 (if white were to start at b it would be the other way around) for a total of 10 points?

Author: RobertJasiek [ Wed Jun 22, 2011 11:09 pm ]

Post subject: Re: Value of Move vs. Value of Position: Problem #1

Values can be associated with positions or moves and on a local scale or the global scale. Furthermore different kinds of values can be defined and used. So speaking of "the idea of the value of a move vs. the 'value of the position'" is still too imprecise a distinction because it should be specified WHICH value of a move and WHICH value of a position are being meant. Likewise saying "that the value of a move is the amount of points that a given move was worth" is too imprecise; one must also specify WHICH kind of value is being referred to. Although a one-sided (one colour) view of values is possible (like in your question "What is the value of black's position in the top right?"), it might not always be a sufficient view; taking both colours into account is an alternative. Your example has another problem that Black cannot tenuki arbitrarily often without dying; saying that a first play by White is sente is just a simplifying approach to Black's local territorial value.

Chapter 4 of "Joseki Vol. 2 Strategy" discusses some kinds of values. E.g., we can study the "current territory in Black's quiet group" and let White make the standard sente endgame reduction.

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

Now Black's current territory in the starting position is apparent:

Click Here To Show Diagram Code: [go]$$W $$ --------------------------------------- $$ | . . . . . . . . . . . O O X C C C C C | $$ | . . . . . . . . . . . O X X C C C C C | $$ | . . O . . O . . . . . O X C C C C C C | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

It is 16 points.

There is a good chance that Black b vs. White a is a double sente situation. Double sente escapes value description a bit but nevertheless we can compare current territies. For this, we need to assess also White's:

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

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

White's region is "open ended". So we need tool assistance: Let us define a suitable locale, on which we assess White's territory:

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

After the sequence shown, the territory intersections inside the locale are:

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

White has 42 points in the locale. Exciting. A number that tells us nothing. It is better to consider differences of black and white territories. There are two assumed basic cases: Black first versus White first.

Case Black first:

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

In the locale (and for Black in the corner), the black minus white territories are 18 - 42 = -24. (By convention, negative numbers favour White.)

Case White first:

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

In the locale (and for Black in the corner), the black minus white territories are 16 - 44 = -28.

Exciting. Big numbers that still tell us little. We need to form yet another difference: case Black first minus case White first:

-24 - (-28) = 4.

This we can call "the local move value of the double sente" is 4 points [in double sente].

As a double sente, it is "[a difference of] 4 points for free" but otherwise comparison to values of gote moves does not make much sense.

As you could see, it is possible to calculate some positional and some move values. However, one also needs to state WHICH kinds of positional / move values one is determining.

Author: RobertJasiek [ Wed Jun 22, 2011 11:23 pm ]

Post subject: Re: Value of Move vs. Value of Position: Problem #1

Locale can be used more ingeniously: Let us define the following locale:

Click Here To Show Diagram Code: [go]$$B $$ --------------------------------------- $$ | . . . . . . . . . . C C C C . . . . . | $$ | . . . . . . . . . . C C C C . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Now we study points made or not made only inside the locale.

Case Black first:

Click Here To Show Diagram Code: [go]$$B $$ --------------------------------------- $$ | . . . . . . . . . . O X X C . . . . . | $$ | . . . . . . . . . . O O X C . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

In the locale, Black makes 2 points, White makes 0 points, the difference is 2 - 0 = 2.

Case White first:

Click Here To Show Diagram Code: [go]$$W $$ --------------------------------------- $$ | . . . . . . . . . . C O O X . . . . . | $$ | . . . . . . . . . . C O X X . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

In the locale, Black makes 0 points, White makes 2 points, the difference (by convention, always subtract White from Black) is 0 - 2 = -2.

Both cases joined by forming the overall difference:

2 - (-2) = 4.

Surprise! Even when using a tiny locale, we get the correct number [of a double sente move value].

BTW, although the concept locale was used for a very long time, I do not recall any term for it. So I introduced it and its definition from page 12 of my book is:

The locale is a local region of the board suitably chosen for counting stones, intersections or points conveniently.

Author: Bill Spight [ Fri Jun 24, 2011 7:31 am ]

Post subject: Re: Value of Move vs. Value of Position: Problem #1

Kirby wrote:

One thing that interests me, but I have not perfected, is the idea of the value of a move vs. the "value of the position". I heard about this for the first time a little while back at a workshop with Kim Myungwan.

He said that the value of a move is the amount of points that a given move was worth.

That's uninformative.

Quote:

The value of a position, on the other hand, is the amount of points that a given area of the board was at a given point in time.

With this in mind, here is a problem for those that are interested:

Click Here To Show Diagram Code: [go]$$W $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . a b . . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

What is the value of black's position in the top right? What is the value of black playing at 'a'? What is the value of black playing at 'b'?

This is a rather difficult position to evaluate. I am not at all sure of the optimal sequences of play.

For the average value of the top right, with the usual assumption that Black cannot afford to fight a big ko there, I get 15.5 points.

A Black play at "a", I think, is not optimal play, and is a neutral sente, which loses nothing on average.

A Black play at "b", I think, is a reverse sente that gains around 10 to 11 pts.

I would not at all be surprised if Kim says different.

White sente

Click Here To Show Diagram Code: [go]$$W White sente $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . 1 2 . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

As I have said before, this type of situation is usually sente for one side or the other. In this case I think that it is White's sente.

Here is how I evaluate the top right corner.

Black follow-up

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

(

come later.)

Edit: I showed an incorrect follow-up after :b3:

before,

, which does not affect the estimate of Black territory.

Black has 19 points.

White follow-up

Click Here To Show Diagram Code: [go]$$W White follow-up $$ --------------------------------------- $$ | . . . . . . . . . . . 1 7 3 5 6 . . . | $$ | . . . . . . . . . . . . O X 4 8 . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

After

White has a sente follow-up. As per the usual assumption, Black avoids ko. Black has 12 points.

Average score for Black: (19 + 12)/2 = 15.5.

Author: emeraldemon [ Fri Jun 24, 2011 10:12 am ]

Post subject: Re: Value of Move vs. Value of Position: Problem #1

Here's how I was thinking of it:

White gote w/ sente followup

Click Here To Show Diagram Code: [go]$$Wcm1 White gote w/ sente followup $$ --------------------------------------- $$ | . . . . . . . . x x x x 7 5 6 . . . . | $$ | . . . . . . . . x x x 3 1 2 8 . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Black gote w/ sente followup

Click Here To Show Diagram Code: [go]$$Bcm1 Black gote w/ sente followup $$ --------------------------------------- $$ | . . . . . . . . 8 7 5 9 x x x . . . . | $$ | . . . . . . . . 0 6 2 1 3 x x . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

x's mark territory differences. I count as 12 points gote, or 6 points using miai (move value) counting. Obviously I'm missing something, but could someone explain why these sequences arent optimal?

Author: Bill Spight [ Fri Jun 24, 2011 10:59 am ]

Post subject: Re: Value of Move vs. Value of Position: Problem #1

emeraldemon wrote:

Here's how I was thinking of it:

White gote w/ sente followup

Click Here To Show Diagram Code: [go]$$Wcm1 White gote w/ sente followup $$ --------------------------------------- $$ | . . . . . . . . x x x x 7 5 6 . . . . | $$ | . . . . . . . . x x x 3 1 2 8 . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Black gote w/ sente followup

Click Here To Show Diagram Code: [go]$$Bcm1 Black gote w/ sente followup $$ --------------------------------------- $$ | . . . . . . . . 8 7 5 9 x x x . . . . | $$ | . . . . . . . . 0 6 2 1 3 x x . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

x's mark territory differences. I count as 12 points gote, or 6 points using miai (move value) counting. Obviously I'm missing something, but could someone explain why these sequences arent optimal?

OK, let's take the second one. Let's assume that Black's play is not sente.

Hane and connect

Click Here To Show Diagram Code: [go]$$Bcm1 Hane and connect $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . 2 1 3 . . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Descent

Click Here To Show Diagram Code: [go]$$Bcm1 Descent $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . 1 . . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Which is better for Black? (I'll hide the next diagram for people who want to think about it.)

Author: mitsun [ Fri Jun 24, 2011 3:33 pm ]

Post subject: Re: Value of Move vs. Value of Position: Problem #1

A while back there was a series of posts on "Boundary Plays", based on a book by O Meien. I think if this series had continued, we might have an authoratative approach to analyzing positions like this. I for one would love to see that series revived.

Here is my take on this. The value of a position is an interesting concept, which has two related uses: 1) estimating the score, 2) calculating the value of a local move. The second case is probably more interesting.

The position below is a good example, simple enough to analyze, but complex enough to have many variations.

Click Here To Show Diagram Code: [go]$$W $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

For purposes of calculation, let's compare all future results to the following symmetric base result. By the way, this ending position also provides a fair estimate of the value of the starting position, assuming different plays by both sides are about equally large, even though it will never occur in an actual game.

Click Here To Show Diagram Code: [go]$$W $$ --------------------------------------- $$ | . . . . . . . . . . . O X . . . . . . | $$ | . . . . . . . . . . . O X . . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

First, suppose there are no other large plays on the board. If W starts with the hane and hanging connection, B will have to block, letting W end in sente:

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

Later we can assume (see digression below) that B will get to atari and W will have to connect. Compared to the base diagram, W has the same points, while B has 2 fewer points.

(Digression -- this is one of many simplifying assumptions we will make in this analysis. If we were mathematical purists, we might consider that there is a finite probability for W to connect before B gets to atari, and we could then credit W with some small fraction of that one point reverse sente play. But as practical Go players, let's agree to dispense with complicated fractional points.)

W could also start with the straight descent. Again if there are no other large plays on the board, B will have to block, letting W end in sente:

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

The net result here is the same as for the hanging connection.

So we may be tempted to say that either side has a 4 point sente play in this position. But things are not so simple ....

Suppose there are other large plays on the board, so that taking sente has significant value. This is the usual assumption for endgame position analysis. Again we have to consider two possible moves for each side, hane and straight descent, but with more involved continuations.

B4 tenuki

Click Here To Show Diagram Code: [go]$$W B4 tenuki $$ --------------------------------------- $$ | . . . . . . . . . . . 3 . . . . . . . | $$ | . . . . . . . . . . . . 1 2 . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

The hane and connection may be gote, but it leaves a large follow-up for later. Let's assume that this follow-up is not so large that B must prevent it now (B wants sente to play somewhere else), but large enough that W will get to play it later in sente. This is a judgement call, but again it is a common assumption in endgame analysis. Then the hane it is worth more than our previous calculation, because we assume that taking gote now earns a follow-up sente play:

B tenuki

Click Here To Show Diagram Code: [go]$$W B tenuki $$ --------------------------------------- $$ | . . . . . . . . . . . O 5 1 3 4 . . . | $$ | . . . . . . . . . . . . O X 2 6 . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Note that the hanging connection is better than a solid connection, because it leaves a larger follow-up for later, under the usual assumption that the other side cannot afford a large ko.

Compared to the base position, W has 1 more point and B has 6 fewer points. The sequence is similar if B gets to play first, so we can say that in this situation the hane is worth 14 points in gote for either player.

Now let's consider the straight descent. What happens if the other side ignores the descent? Then there is an enormous follow-up, either a one-space jump or a monkey-jump. These continuations are probably sente, because they threaten further large incursions (or even death). For example:

Click Here To Show Diagram Code: [go]$$W $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O . 1 . 2 . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code: [go]$$B $$ --------------------------------------- $$ | . . . . . . . . . 1 . . . . . . . . . | $$ | . . . . . . . . 2 . . . X . . . . . . | $$ | . . O . . O . . . . . O X . . . . . . | $$ | . . . , . . . O . , . O X X X X X X X | $$ | O O O O O O O O . . . O O O O O O O O | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

We can debate the proper continuation in either case, and we would have to work out detailed sequences to calculate the numerical result. (This might make an interesting discussion by itself, maybe for another thread.) But in practice this is probably not necessary -- we can assume that by the time a play here becomes profitable, the territorial loss incurred by not answering will be too large for either side to allow. Put another way, it is likely that someone will be able to time their play here to make the descent in sente.

So to summarize:

Assuming no other large plays available (unlikely):
Hane and hanging connection = 4 points sente
Straight descent = 4 points sente

Assuming other large plays available (normal situation):
Hane and hanging connection = 14 points gote
Straight descent = even larger gote, probably so large that it is actually sente

Exercise for the reader: construct a full board position, with B to play, where the descent is correct but gote.

Author:	flOvermind [ Sun Jun 26, 2011 5:19 am ]
Post subject:	Re: Value of Move vs. Value of Position: Problem #1
mitsun wrote: Straight descent = even larger gote, probably so large that it is actually sente Exercise for the reader: construct a full board position, with B to play, where the descent is correct but gote. I think that's rather easy. You just have to have a play on the board that's smaller than the value of the straight descent (I haven't calculated it myself, but Bill says in his post that it's 10 or 11 points), and larger than the followup monkey jump (around 5 or 6 points). It's not that unlikely that not answering the descent is correct play.

Author:	RobertJasiek [ Sun Jun 26, 2011 8:12 am ]
Post subject:	Re: Value of Move vs. Value of Position: Problem #1
mitsun wrote: a book by O Meien. I think if this series had continued, we might have an authoratative approach to analyzing positions like this. The book appears to discuss one approach but there are also other approaches. Besides it depends on context whether sente or gote should be chosen and when follow-up moves should be considered sente. So there is not the one authoratative approach but rather a collection of several possible approaches.

Page 1 of 1	All times are UTC - 8 hours [ DST ]
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/