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 Post subject: Values of moves
Post #1 Posted: Sat Sep 15, 2018 4:51 am 
Oza
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What is the easiest way to determine a rough value of a move in order to compare alternatives. I am more interested in "ballpark" than "correct." For starters, how about this: black to play: What are a, b and c worth?

Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . a . . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . b . . |
$$ | . . , X . . , . . |
$$ | . . . . c O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

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 Post subject: Re: Values of moves
Post #2 Posted: Sat Sep 15, 2018 5:14 am 
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Whose move is it?

If it's Black to play, then b because b + follow-up would be bigger than a + follow-up.

If it's White to play, then a or a monkey jump from the stone next to c.

The method I am exploring, for what it's worth, is assessing value of plays by counting the move itself plus any afterplays. This automatically takes into account gote and sente (in that, I would play a gote move A ahead of a sente move B, if A + afterplay (even if this were in fact zero) > B + afterplay). I don't suppose this is "correct", by any stretch of the imagination, but it's practical for me. YMMV.

In this case, with Black to play, if b were not answered, then I think an afterplay from it would do more damage to White than an afterplay from a.

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 Post subject: Re: Values of moves
Post #3 Posted: Sat Sep 15, 2018 5:33 am 
Oza
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This is the sort of answer I was hoping for. Two questions: a) When you say "afterplay" do you mean, if your move was not answered and you got to play there again? and b) How would you (or anyone else) count the value of a move at a, b or c?

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Post #4 Posted: Sat Sep 15, 2018 5:40 am 
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daal wrote:
What is the easiest way to determine a rough value of a move in order to compare alternatives.


Since you ask for the easiest way, a) do not distinguish the move from its follow-ups, b) consider at most two values and c) use symbolic values, such as "BIG" versus "NOT BIG".

Then you know that "BIG" is larger than "NOT BIG", two "BIG" moves are roughly equal, two "NOT BIG" moves are roughly equal.

Is this the easiest possible way?:)

Obviously, with such a simplistic evaluation, you often get same values. So to distinguish two "BIG" moves, you need to make the method more complicated than easiest. E.g., consider the same player's follow-up moves ("threats") and compare them in the way described above.

I do not ask for your motivation to create many wrong decisions caused by the imprecision of roughness...


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 Post subject: Re: Values of moves
Post #5 Posted: Sat Sep 15, 2018 6:01 am 
Oza
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RobertJasiek wrote:

I do not ask for your motivation to create many wrong decisions caused by the imprecision of roughness...


I'll tell you anyway. I am not good at calculating, and am even worse at calculating under pressure. I am 100% positive that any method that promises a correct evaluation is too hard for me to use in a game situation. For this reason, I am looking for something that I am able to use, with the hope that it would provide a right answer more often than not, and that this would be better than just guessing. Actually, I do like your big vs. not big method, and big plus big followup > big plus not big follow up is a better method than the one I have now, so thanks. :)

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 Post subject: Re: Values of moves
Post #6 Posted: Sat Sep 15, 2018 6:08 am 
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daal wrote:
This is the sort of answer I was hoping for. Two questions: a) When you say "afterplay" do you mean, if your move was not answered and you got to play there again? and b) How would you (or anyone else) count the value of a move at a, b or c?


Basically, I mean follow-up.

Suppose it is Black to move. Then if he played b and was ignored, say because White played a (attempting mutual damage) then Black's threats to would appear larger than White's here.

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


Of course, I would expect White to answer 1 in this diagram. If White answered, then after exchanging some forcing moves Black could then move onto move a in your original diagram. But if she did ignore, then Black would have serious threats to both the top right and the bottom.

Click Here To Show Diagram Code
[go]$$B If White answered 1 (as expected)
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . 5 . . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . 1 2 . |
$$ | . . , X . . 3 4 . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


If Black went for a first, then I'd expect White go for mutual damage like this:

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


In the first example, I'd expect Black to come out in profit. In the second, I would anticipate a more even outcome.

Assuming Black has first move, I can see that playing b first would be bigger than playing a first. I'm sure one could be a lot more precise - but is it worth the effort? Both Daal and I play go for a hobby. Of course, it is natural to want to improve, but there are limits as to what pains are worth taking when there are other things to do with one's time.

By the way, I have O Meien's Yose book plus the Nihon Kiin's Yose Sho Jiten (Small Endgame Dictionary) for when I'm in the mood to put in a shift.

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Last edited by Tami on Sat Sep 15, 2018 6:23 am, edited 1 time in total.

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 Post subject: Re: Values of moves
Post #7 Posted: Sat Sep 15, 2018 6:19 am 
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daal wrote:
What is the easiest way to determine a rough value of a move in order to compare alternatives. I am more interested in "ballpark" than "correct."


Start with the rough value of positions. You can figure out the rough value of plays from those.

Here are some helpful guidelines. The first is that, except for kos, the value of a position lies in between the results, played out to the bitter end, when Black plays first and when White plays first. Often the difference between the two results will be larger than you want. But not always. The second, and generally more useful one is that the value of a sente position is the result after the sente has been played. So you just play the sente. And, OC, the value of a gote positions is the average of the results of the two gote moves. So start off by guessing whether a position is sente or gote. You will sometimes be wrong, but, as you say, correctness is not your goal. :)

Quote:
For starters, how about this: black to play: What are a, b and c worth?

Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . a . . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . b . . |
$$ | . . , X . . , . . |
$$ | . . . . c O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


One problem with this small board is that the positions and moves may not be independent. But you have identified them as separate, so go ahead and assume that they are independent. Correctness is not the goal.

Position "b" is a Black sente. So go ahead and play the sente out.

Position "c" may be a White sente. Use you judgement.

Position "a" is a big gote, and the value is around 0, by symmetry. It may be worth a bit for Black, because of the flaws in the White position in the top right. But 0 is a good ball park figure. :)

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 Post subject: Re: Values of moves
Post #8 Posted: Sat Sep 15, 2018 6:29 am 
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Bill Spight wrote:


Position "a" is a big gote, and the value is around 0, by symmetry. It may be worth a bit for Black, because of the flaws in the White position in the top right. But 0 is a good ball park figure. :)


I'm struggling with this...surely getting to play at a is worth quite a bit (12-14 points)?

Or do you mean that when estimating the score, position a has to be reckoned as 0 because that's the average of White and Black playing there?

In fact, this is my current stumbling block with O's book. I'm quite happy to follow his reasoning about the value of a local position being counted as the average of a black or white play there, but I put it aside for the time being when I came to the section concerning the value of actual moves.

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Post #9 Posted: Sat Sep 15, 2018 6:44 am 
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Sad to say, but I am not even sure what is meant by "sente." How does this sound for a definition to fit my purposes: "a sente move is a move whose followup is bigger than any other move on the board, so it will presumably be answered."

Bill wrote:
Start with the rough value of positions.


So you mean: imagine black playing there first to the bitter end, compare white and black territory, imagine white playing there first to the bitter end, compare white and black territory. The difference between these two values is the value of the position?

Click Here To Show Diagram Code
[go]$$B Black goes first
$$ +-------------------+
$$ | M M M M X X O T T |
$$ | M M M M X O O T T |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


Click Here To Show Diagram Code
[go]$$B White goes first
$$ +-------------------+
$$ | M M X O O T T T T |
$$ | M M X X O T T T T |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


So are you saying that the value of the position is 8? I'll stop here, because I think that that is not what you mean.

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Post #10 Posted: Sat Sep 15, 2018 6:51 am 
Oza
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Bill Spight wrote:
Position "b" is a Black sente. So go ahead and play the sente out.

Position "c" may be a White sente. Use you judgement.

Position "a" is a big gote, and the value is around 0, by symmetry. It may be worth a bit for Black, because of the flaws in the White position in the top right. But 0 is a good ball park figure. :)


So of these, you only give a number for a. I am essentially looking for some way of giving a ballpark number to each of a,b and c so I can compare and plonk a stone down at the biggest ballpark number. It is even fine if we say that b being sente is worth an infinite amount of points. But I don't see a way of comparing a b and c from what you wrote.

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Post #11 Posted: Sat Sep 15, 2018 6:58 am 
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daal wrote:
Sad to say, but I am not even sure what is meant by "sente." How does this sound for a definition to fit my purposes: "a sente move is a move whose followup is bigger than any other move on the board, so it will presumably be answered."

Bill wrote:
Start with the rough value of positions.


So you mean: imagine black playing there first to the bitter end, compare white and black territory, imagine white playing there first to the bitter end, compare white and black territory. The difference between these two values is the value of the position?

Click Here To Show Diagram Code
[go]$$B Black goes first
$$ +-------------------+
$$ | M M M M X X O T T |
$$ | M M M M X O O T T |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


Click Here To Show Diagram Code
[go]$$B White goes first
$$ +-------------------+
$$ | M M X O O T T T T |
$$ | M M X X O T T T T |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


So are you saying that the value of the position is 8? I'll stop here, because I think that that is not what you mean.


It's better to make a hanging connection after the hane:

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


Assuming the other player doesn't want to risk the ko, then you get more points.

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Post #12 Posted: Sat Sep 15, 2018 7:38 am 
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daal wrote:
I am essentially looking for some way of giving a ballpark number to each of a,b and c so I can compare and plonk a stone down at the biggest ballpark number.


If I understand what you are asking, it sounds impossible. You don't want to do calculations but want to have numbers.

If I try to think what is best one can do without calculations, I would say:
1) Just guess what is sente by your feeling of whether the opponent will answer, and whether you can play elsewhere after that. Maybe you go wrong sometimes, but then maybe your judgement improves with experience.
2) Try to play sente moves at the last moment before it seems, by your guess, that your opponent should play their reverse sente move to prevent it. Better to err on the side of playing too early. Maybe you only lose a ko threat that way.
3) If the area looks like global double sente, i.e. that both players can play there in sente, consider the value infinite and play it immediately. (However, be suspicious about double sente identification and consider that maybe one or both players' moves are not sente... :) )
4) With gote moves, just try estimate visually what is the difference between you playing there and opponent playing there. Play the biggest moves first, based on where the difference looks the largest. If your gote move looks like reverse sente (i.e. looks like your opponents move there would be sente), assume that they are 2 times bigger than if it is double gote. Though I'm not sure how to multiply by 2 without calculation :) Maybe that can be done as some visual imagination too?
[Edit: tried to make the list more comprehensive and made it more complicated...]

But if you want to have numbers, I cannot see any other way than visualising the positions after your or the opponents first move, and then counting how many points more or less each player gets.

You said you will not have time to calculate during a game. I guess the usual thing is to calculate examples outside your games, and by that train your intuition to better and better guess the values quickly during a game. It's like with tsumego. The more you do them the better you get at guessing how to kill or live in a fast game.


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Post #13 Posted: Sat Sep 15, 2018 8:05 am 
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zermelo wrote:
daal wrote:
I am essentially looking for some way of giving a ballpark number to each of a,b and c so I can compare and plonk a stone down at the biggest ballpark number.


If I understand what you are asking, it sounds impossible. You don't want to do calculations but want to have numbers.

If I try to think what is best one can do without calculations, I would say:
1) Just guess what is sente by your feeling of whether the opponent will answer, and whether you can play elsewhere after that. Maybe you go wrong sometimes, but then maybe your judgement improves with experience.
2) Try to play sente moves at the last moment before it seems, by your guess, that your opponent will play their reverse sente move to prevent it. Better to err on the side of playing too early. Maybe you only lose a ko threat that way.
3) With gote moves, just try estimate what is the difference between you playing there and opponent playing there. Play the biggest moves first, based on where the difference looks the largest.

But if you want to have numbers, I cannot see any other way than visualising the positions after your or the opponents first move, and then counting how many points more or less each player gets.


I guess you are right, saying that I don't want to calculate, but want numbers is unrealistic. But what about something along the lines of what Robert said, but just a bit more nuanced. For example: Huge, Big, Small and Worthless. What is difficult is that even Big and Not Big depend on sente and followup. Pretty hard to sort out priorities, but I guess that is what makes go interesting. I like what you wrote about choosing without calculations. One question though: How would you go about deciding between a sente move and a big gote move?

Quote:
You said you will not have time to calculate during a game. I guess the usual thing is to calculate examples outside your games, and by that train your intuition to better and better guess the values quickly during a game. It's like with tsumego. The more you do them the better you get at guessing how to kill or live in a fast game.
I wouldn't mind doing this, if there were a list of 10 common positions and their values, but there doesn't seem to be such a list, so I wouldn't know where to start.

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Post #14 Posted: Sat Sep 15, 2018 8:10 am 
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daal wrote:
You said you will not have time to calculate during a game. I guess the usual thing is to calculate examples outside your games, and by that train your intuition to better and better guess the values quickly during a game. It's like with tsumego. The more you do them the better you get at guessing how to kill or live in a fast game. I wouldn't mind doing this, if there were a list of 10 common positions and their values, but there doesn't seem to be such a list, so I wouldn't know where to start.



There is the Nihon Kiin Yose Small Dictionary. ISBN 978-4-8182-0437. There is a section giving values for typical endgame plays. It has a lot of other good things, too, and you only need minimal Japanese to get the gist of it.

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Post #15 Posted: Sat Sep 15, 2018 8:51 am 
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These pages might have some use. Doesn't help much for macroendgame, but not bad for microendgame.

https://senseis.xmp.net/?MiaiValuesList%2F000To099
https://senseis.xmp.net/?MiaiValuesList%2F100To199
https://senseis.xmp.net/?MiaiValuesList%2F200AndMore


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Post #16 Posted: Sat Sep 15, 2018 9:06 am 
Judan

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daal wrote:
Sad to say, but I am not even sure what is meant by "sente." How does this sound for a definition to fit my purposes: "a sente move is a move whose followup is bigger than any other move on the board, so it will presumably be answered."


That is one definition, but for calculating sizes we stick to local sente. I have posted a good bit here on sente vs. gote.

Bill wrote:
Start with the rough value of positions.


Quote:
So you mean: imagine black playing there first to the bitter end, compare white and black territory, imagine white playing there first to the bitter end, compare white and black territory. The difference between these two values is the value of the position?


The value of the position lies between those two values.

Quote:
Click Here To Show Diagram Code
[go]$$B Black goes first
$$ +-------------------+
$$ | M M M M X X O T T |
$$ | M M M M X O O T T |
$$ | . . , X B O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


Click Here To Show Diagram Code
[go]$$B White goes first
$$ +-------------------+
$$ | M M X O O T T T T |
$$ | M M X X O T T T T |
$$ | . . , X W O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


So are you saying that the value of the position is 8? I'll stop here, because I think that that is not what you mean.


I edited the diagrams to show the bitter end. The value of the position lies between 4 and -4, both values from Black's point of view.

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Post #17 Posted: Sat Sep 15, 2018 9:16 am 
Judan

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Tami wrote:
Bill Spight wrote:


Position "a" is a big gote, and the value is around 0, by symmetry. It may be worth a bit for Black, because of the flaws in the White position in the top right. But 0 is a good ball park figure. :)


I'm struggling with this...surely getting to play at a is worth quite a bit (12-14 points)?


That's looks like a pretty good ballpark figure. Miai (Absolute™) counting, OC.

Quote:
Or do you mean that when estimating the score, position a has to be reckoned as 0 because that's the average of White and Black playing there?


Just eyeballing it, it's pretty symmetrical, eh?

Quote:
In fact, this is my current stumbling block with O's book. I'm quite happy to follow his reasoning about the value of a local position being counted as the average of a black or white play there, but I put it aside for the time being when I came to the section concerning the value of actual moves.


The value of a play depends upon the difference in value between two positions. The value of positions is basic.

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Post #18 Posted: Sat Sep 15, 2018 9:33 am 
Oza
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Bill Spight wrote:
I edited the diagrams to show the bitter end. The value of the position lies between 4 and -4, both values from Black's point of view.


Ok, the value of that position is 0. So what does the value of the position tell us about whether to move there or not? Does it make sense to compare it to the value of another position, for example this one:

Click Here To Show Diagram Code
[go]$$B black first
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | T T T T X O M O M |
$$ | T T T X O O M M M |
$$ +-------------------+[/go]


Click Here To Show Diagram Code
[go]$$B white first
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | T X X . . O M O M |
$$ | T X O O O C M M M |
$$ +-------------------+[/go]


Here we have +2 if black goes first and -3.5 if white goes first. Aack, a fraction! (Prolly wrong anyway). Any further fractions no longer qualify as easy! So lets just say that the middle is less than 0 and more than -1, which is different from the 0 that we get from the position at the top. What does that tell us about where to move?

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 Post subject: Re: Values of moves
Post #19 Posted: Sat Sep 15, 2018 9:59 am 
Judan

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daal wrote:
Bill Spight wrote:
I edited the diagrams to show the bitter end. The value of the position lies between 4 and -4, both values from Black's point of view.


Ok, the value of that position is 0. So what does the value of the position tell us about whether to move there or not? Does it make sense to compare it to the value of another position, for example this one:


Not that one, but this one.

Click Here To Show Diagram Code
[go]$$B After White plays gote
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . W . . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


Playing in the top left, because the three moves (a, b, and c) and positions are assumed to be independent (even if that's not quite right).

For instance, let's guess that this position is a White sente.

Click Here To Show Diagram Code
[go]$$W White sente
$$ +-------------------+
$$ | . . . 3 . C C C C |
$$ | 6 5 1 2 W . C C C |
$$ | . 4 7 X . O C C C |
$$ | S 8 . X . O C C C |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]


Then we can make a ball park estimate that this position is worth 12 pts. to White. That means that we can estimate that :wc: has gained 12 pts. Like Tami said. :)

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Post #20 Posted: Sat Sep 15, 2018 11:48 am 
Honinbo
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Quote:
It's better to make a hanging connection after the hane:
Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | . . . 3 9 5 7 8 . |
$$ | . . . . 1 2 6 0 . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]
Assuming the other player doesn't want to risk the ko, then you get more points.
Hmm... something seems off ? :scratch:
And :w4: tenuki (above variation) causes different calculations.

Click Here To Show Diagram Code
[go]$$B var 2
$$ +--------------------
$$ | . . . . 5 3 4 . . |
$$ | . . . . 1 2 6 . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +--------------------[/go]
If :w4: simply replies with descend, then locally B has fewer points than B's hane & solid connect in var 2.
Click Here To Show Diagram Code
[go]$$B var 3
$$ +--------------------
$$ | . . . 3 . 4 . . . |
$$ | . . . . 1 2 . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +--------------------[/go]

This :b5: tiger's mouth is after :b3: hane, but leads to yet different calculations
( but locally B still seems worse off than var 2 ):
Click Here To Show Diagram Code
[go]$$B var 4
$$ +--------------------
$$ | . . . 5 6 3 4 . . |
$$ | . . . . 1 2 . . . |
$$ | . . , X . O , . . |
$$ | . . . X . O . . . |
$$ | . . X . , . O . . |
$$ | . . . . X . . . . |
$$ | . . , X . . , . . |
$$ | . . . . . O . O . |
$$ | . . . . . . . . . |
$$ +--------------------[/go]

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