Please Illustrate a Mathematical Analysis of This Position

Kirby · Post by **Kirby** » Sat Feb 09, 2013 9:37 am

Magicwand wrote:
Kirby wrote: Maybe there's not a better way.
Yes. Not worrying about meaningless count and ok.
Lets worry about what make you strong not a research paper.

Maybe I should give some context. Awhile back, I attended a workshop held by Kim Myungwan. He explained some endgame techniques, which let you quantify the importance of different local areas on the board. I don't remember how to do it completely, so I asked for an example analysis here.

Maybe I should just see if I can get the information from Kim Myungwan, again, somehow.

Magicwand · Post by **Magicwand** » Sat Feb 09, 2013 9:50 am

Kirby:
your question is not something anybody can quantify.
too many variables and positions will determine the value.
it is better to atari is a fact but you are asking how much better? I dont think there is answer for your question.

RobertJasiek · Post by **RobertJasiek** » Sat Feb 09, 2013 10:09 am

Kirby, if you just want to know the method, then why do you ask with a difficult position? Can't we just study very late endgame examples with exactly 1 iteration step? It seems that you want to run while throwing fireworks (aka privileges) before you can walk:)

jts · Post by **jts** » Sat Feb 09, 2013 10:18 am

Magicwand wrote:Kirby:
your question is not something anybody can quantify.
too many variables and positions will determine the value.
it is better to atari is a fact but you are asking how much better? I dont think there is answer for your question.

In fairness to Kirby, didn't you previously do posts on exactly this subject? Maybe I don't understand what Kirby is asking for.

http://www.lifein19x19.com/forum/viewto ... =11&t=3048

Kirby · Post by **Kirby** » Sat Feb 09, 2013 11:15 am

jts wrote:
Magicwand wrote:Kirby:
your question is not something anybody can quantify.
too many variables and positions will determine the value.
it is better to atari is a fact but you are asking how much better? I dont think there is answer for your question.
In fairness to Kirby, didn't you previously do posts on exactly this subject? Maybe I don't understand what Kirby is asking for.

http://www.lifein19x19.com/forum/viewto ... =11&t=3048

Thanks, jts. That link is useful. Maybe the scenario I posted is too complicated...?

Bill Spight · Post by **Bill Spight** » Sat Feb 09, 2013 3:42 pm

Kirby wrote:Maybe the scenario I posted is too complicated...?

Here it is.

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

At the risk of repeating Robert's points.

It isn't just that it is too complicated. It is relatively undefined. Does the region to the right on the bottom side belong to White? Does the region to the top on the left side belong to Black? Does White need to capture the two Black stones? Does Black need to keep the corner? Without knowing the answers, or without restricting the region of play, assuming that everything outside it is alive, we cannot calculate the size of a play.

Another problem, which is non unsurmountable, is that you do not know where to play.

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

Does Black play the atari or Uberdude's tesuji?

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

Where does White play?

----

Here is something that will help.

Here are your main variations.

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

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

It appears that you think that this position is double sente.

If so, then make the play. The proverb should really be this: Play double sente right away.

But if you want to calculate the size of a play, forget double sente. A double sente is a free lunch. There is no free lunch (in theory

).

So we need to consider these variations.

Click Here To Show Diagram Code: [go]$$Bc $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | . . . . X O O X O . . $$ | . . . . . 1 O X O . . $$ | . . . . . . 3 . . . . $$ -----------------------[/go]

elsewhere.

Click Here To Show Diagram Code: [go]$$Wc $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | . . . . X O O X O . . $$ | . . . 3 1 . O X O . . $$ | . . . . . . . . . . . $$ -----------------------[/go]

elsewhere.

You see how important it is how secure the stones framing the corner are.

----

Actually, we have evidence that this is Black's sente, especially early in the game. If it is not, then it appears that someone has made a mistake. Either Black should not have endangered the two Black stones, or White should not have put them into atari.

If this is Black's sente, then obviously White's reverse sente is large, even if Black controls the left side. The sente is probably urgent.

If this is Black's sente, then Uberdude's play has a lot to recommend it. Its threat is smaller than that of the atari, but as long as White replies it looks better.

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

Click Here To Show Diagram Code: [go]$$Bc Black follower $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | C C C C X O O . O . . $$ | C C C C . X O . O . . $$ | C C C C C 1 . O . . . $$ -----------------------[/go]

Black gets 13 points in the corner.

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

elsewhere.

After

-

, White has a sente follower. The usual assumption is that Black cannot afford to play the ko. (Edit: Note that if Black does not control the left side White may play

at 6 or the 3-3.)

Black gets 6 points and White gets 3, for a net of 3 points to Black. The average of the two gote followers in 8 points, which is how we evaluate the result of the Atari diagram.

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

is the orthodox response to

. If

is at 4, then Black can capture

, but takes gote.

Black can wait to play

.

Black gets 10 points in the corner, 2 points better than with the atari.

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

Suppose that White replies with

.

Click Here To Show Diagram Code: [go]$$Bc Black follower $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | C C C C X O O . O . . $$ | C C C C . 1 O . O . . $$ | C C C C C X . O . . . $$ -----------------------[/go]

Black gets 13 points in the corner.

Click Here To Show Diagram Code: [go]$$Wc White follower $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | C C C C X O O . O . . $$ | C C C 2 1 5 O . O . . $$ | C C C 4 3 B C O . . . $$ -----------------------[/go]

Because of

, White cannot play

at 4.

Black gets 10 points in the corner, White gets 3 points, for 7 points net to Black.

The average is still 10 points.

Bravo, Uberdude!

Kirby · Post by **Kirby** » Sat Feb 09, 2013 4:23 pm

Thank you, Bill. This is kind of the type of analysis that I was looking for.

If the problem is not well-defined, then let's assume that the remainder of the board is empty. If this means that black needs to play elsewhere, I'm happy to hear that, too. I just want to know the valuation of doing so.

A couple of responses:

It appears that you think that this position is double sente. If so, then make the play. The proverb should really be this: Play double sente right away.

I do not know if the position is double sente. Maybe it is, but I am not calculating this in a precise way.

Let's say that the value of black playing first, locally, benefits black by A points vs. white playing first locally. Let's also say that if white plays first, locally, white benefits by B points. Let's say there's another place on the board. If black plays first there, he gets C. If white plays first there, he gets D.

If white plays first in the first local position, and gets to play there a second time, the gain from the second play is worth E (for a net of B + E).

If black gets to play twice in the second local position, he gets F on the second play for a gain in that area of (C + F).

It seems that the following are possible:
1.) A > C and B > D. In this case, definitely, black should play in the first local position shown. Both black and white have this as the biggest spot on the board.
2.) A < C and B < D, but E > F . In this case, I'm not really sure. It's bigger for both black and white to play in the second spot, but maybe if (B + E) > (C + F), white gains more from the first local position than black gains from the second, even though both A and B individually were smaller...?

So the idea of "double sente" is hard for me to say that I should definitely play, because it's hard for me to define exactly what double sente is.

I dunno if that makes sense.

---

If this is Black's sente, then Uberdude's play has a lot to recommend it. Its threat is smaller than that of the atari, but as long as White replies it looks better.

I added emphasis to the quote above. I appreciate the analysis of the average points that are gained, and it seems to support the quality of Uberdude's proposed move. But I feel the analysis should take as input something accounting for the fact that the threat is smaller. How is this expressed? It could be that I just don't understand the analysis completely, yet.

And again, let's assume the rest of the board is empty. Or if it makes it easier to consider the local position, feel free to setup the rest of the board however you would like.

This particular position is not important to me. I'm just curious how this analysis takes place.

Thank you.

Bill Spight · Post by **Bill Spight** » Sat Feb 09, 2013 5:40 pm

Kirby wrote:Let's say that the value of black playing first, locally, benefits black by A points vs. white playing first locally.

You have to distinguish between sente and gote. Not to mention kos. That is, you need to take the net number of plays into account.

If this is Black's sente, then Uberdude's play has a lot to recommend it. Its threat is smaller than that of the atari, but as long as White replies it looks better.
I added emphasis to the quote above. I appreciate the analysis of the average points that are gained, and it seems to support the quality of Uberdude's proposed move. But I feel the analysis should take as input something accounting for the fact that the threat is smaller. How is this expressed? It could be that I just don't understand the analysis completely, yet.

Compare the threats yourself.

Kirby · Post by **Kirby** » Sat Feb 09, 2013 9:37 pm

Bill Spight wrote: Compare the threats yourself.

Hmm, ok.

Bill Spight wrote:
You have to distinguish between sente and gote. Not to mention kos. That is, you need to take the net number of plays into account.

It seems to me that sente and gote are used in calculating the value of a local position. In some ways it gives you a limit on the depth in which you need to calculate. You can say, "if black plays here, white will respond, because it is sente." And this information is used to determine the point value. Is this correct? This is my current understanding.

So if that assumption is correct, the determination of sente and gote is a prerequisite for determining local value.

But how do I determine sente and gote if I do not know what the value is of ignoring the play vs. playing the play?

I feel like I've stumbled upon this type of idea before and got confused then, too.

Bill Spight · Post by **Bill Spight** » Sun Feb 10, 2013 1:19 am

Kirby wrote:
Bill Spight wrote: Compare the threats yourself.
Hmm, ok.

Seriously. Show the diagrams.

Bill Spight wrote:
You have to distinguish between sente and gote. Not to mention kos. That is, you need to take the net number of plays into account.
It seems to me that sente and gote are used in calculating the value of a local position. In some ways it gives you a limit on the depth in which you need to calculate. You can say, "if black plays here, white will respond, because it is sente." And this information is used to determine the point value. Is this correct? This is my current understanding.

If you can tell sente and gote, it simplifies your task.

So if that assumption is correct, the determination of sente and gote is a prerequisite for determining local value.

It is not necessary.

But how do I determine sente and gote if I do not know what the value is of ignoring the play vs. playing the play?

You can start out assuming that a play is sente or gote, and if you are wrong, you will get a contradiction.

See http://senseis.xmp.net/?MiaiValuesList%2FDiscussion .

Practice helps.

Kirby · Post by **Kirby** » Sun Feb 10, 2013 1:32 am

Bill Spight wrote:
Seriously. Show the diagrams.

Well, I think this originated from the comment:

Its threat is smaller than that of the atari

which is something that I didn't come up with, but was asking about. My assumption on what you mean here is that

this:

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

threatens to capture the three white stones in a single move:

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

whereas this:

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

threatens to capture the same three stones, but leaves white the forcing move at the marked spot:

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

But I don't think that this forcing move at the end is accounted for in the point average that was calculated earlier. I'd think that there is a way to quantify this numerically and include this in the "real" point average in order to determine the best move to play.

BillSpight wrote:
If you can tell sente and gote, it simplifies your task.
...

It is not necessary.

If this is the case, then sure - you can evaluate the local position since the knowledge of sente and gote are not necessary.

I assume this is to say that "guessing" if something is sente or gote is somewhat like a "hint" in determining the appropriate relative values.

BillSpight wrote:
You can start out assuming that a play is sente or gote, and if you are wrong, you will get a contradiction.

It's not at all clear to me why this is the case, but I guess this is something I'll figure out on my own if I follow the advice provided in your next comment:

BillSpight wrote: See http://senseis.xmp.net/?MiaiValuesList%2FDiscussion .

Practice helps.

Thanks.

Bill Spight · Post by **Bill Spight** » Sun Feb 10, 2013 2:35 am

Contradiction example:

Code: Select all

Here is a simple game tree with Black moves to the left and White moves to the right. Bill Taylor used to argue for an evaluation system that was pure gote.

Let's make the calculations.

Code: Select all

We find that the count of A is 2.5 and each play at A gains 7.5 points. The count of B is 10 and each play at B gains 10 points. Bill Taylor sees no contradiction.

But we do. If Black makes play that gains 7.5 points but gives White the chance to reply and gain 10 points, then Black should not make that play. It gives White 2.5 points for free. If Black never makes a play at A, then it makes no sense to count A as 2.5 points.

OTOH, it makes no sense to wait until the end of play and let White play to -5. By playing first Black can guarantee at least 0. Therefore the count at A is at least 0. And White can prevent Black from getting more than 0; so that is the count at A.

Code: Select all

Voila! This is a Black sente where the reverse sente gains 5 points.

----

Code: Select all

Suppose that we believe that this is a Black sente.

Code: Select all

Then the reverse sente gains 15 points, and a play at B gains 10 points.

Suppose that there are plays elsewhere that gain between 10 and 15 points. Then as a rule Black may play at A to prevent White from playing at A and gaining 15 points. But then as a rule White will make one of the other plays instead of playing at B, so Black's play will not be sente, but gote.

Another way of looking at it is to say that by not replying, White makes the count at A equal -2.5, which is better for White than 0.

Code: Select all

This is the correct evaluation. A play at A is gote, gaining 12.5 points.

RobertJasiek · Post by **RobertJasiek** » Sun Feb 10, 2013 3:18 am

Bill Spight wrote:
Code: Select all
               -2.5
               /   \
             10    -15
            /  \
           20   0
This is the correct evaluation. A play at A is gote, gaining 12.5 points.

This is like

Code: Select all

               -2.5
               /   \
             10    -15

From a position worth -2.5, Black can increase by 12.5 to get 10. From a position worth -2.5, White can decrease by -12.5 to get -15. I.e., -2.5 is the average of the immediate followers.

Uberdude · Post by **Uberdude** » Sun Feb 10, 2013 7:17 am

Kirby, whilst it might be an interesting intellectual exercise to try to express the difference in size of follow-ups of the atari versus placement in a single number, it's unlikely to help you play good Go. In the vast majority of cases they will be both be sente at an easy to judge time of the game. If the difference is relevant, it is likely that using the "calculate the miai value of a move and play them in decreasing order" strategy will not lead to optimum play, as it is based on there being a continuum of slightly decreasing sized miai plays available which is never quite true, and those cases where there is a difference between the atari and placement will likely be exactly those where the 'lumpiness' of the size of remaining moves is large resulting in tedomari etc being a very important factor. In such cases thinking of positions in terms of the tree of swing values and how these can interact for the various positions on the board is what you need to do to find optimum play.

P.S. I've not actually studied this rigourosly, so maybe Bill or someone else may correct me, but that's my understanding of it and how I try to play the best yose on OGS and it works well for me.

Bill Spight · Post by **Bill Spight** » Mon Feb 11, 2013 1:25 pm

Kirby wrote:
Bill Spight wrote:
Seriously. Show the diagrams.
Well, I think this originated from the comment:
Its threat is smaller than that of the atari
which is something that I didn't come up with, but was asking about. My assumption on what you mean here is that

this:
$$Bc
$$ | . . . . . . . . . . .
$$ | . . . X X X X O O . .
$$ | . . . . X O O X O . .
$$ | . . . . . B O X O . .
$$ | . . . . . . . . . . .
$$ -----------------------
Click Here To Show Diagram Code
[go]$$Bc $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | . . . . X O O X O . . $$ | . . . . . B O X O . . $$ | . . . . . . . . . . . $$ -----------------------[/go]
threatens to capture the three white stones in a single move:
$$Bc
$$ | . . . . . . . . . . .
$$ | . . . X X X X O O . .
$$ | . . . . X C C X O . .
$$ | . . . . . X C X O . .
$$ | . . . . . . X . . . .
$$ -----------------------
Click Here To Show Diagram Code
[go]$$Bc $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | . . . . X C C X O . . $$ | . . . . . X C X O . . $$ | . . . . . . X . . . . $$ -----------------------[/go]
whereas this:
$$Bc
$$ | . . . . . . . . . . .
$$ | . . . X X X X O O . .
$$ | . . . . X O O X O . .
$$ | . . . . . . O X O . .
$$ | . . . . . B . . . . .
$$ -----------------------
Click Here To Show Diagram Code
[go]$$Bc $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | . . . . X O O X O . . $$ | . . . . . . O X O . . $$ | . . . . . B . . . . . $$ -----------------------[/go]
threatens to capture the same three stones, but leaves white the forcing move at the marked spot:
$$Bc
$$ | . . . . . . . . . . .
$$ | . . . X X X X O O . .
$$ | . . . . X O O X O . .
$$ | . . . . . . O X O . .
$$ | . . . . . X . B C . .
$$ -----------------------
Click Here To Show Diagram Code
[go]$$Bc $$ | . . . . . . . . . . . $$ | . . . X X X X O O . . $$ | . . . . X O O X O . . $$ | . . . . . . O X O . . $$ | . . . . . X . B C . . $$ -----------------------[/go]
But I don't think that this forcing move at the end is accounted for in the point average that was calculated earlier. I'd think that there is a way to quantify this numerically and include this in the "real" point average in order to determine the best move to play.

OK, that's a start.

How do you assess the positions where Black completes his threat?

Life In 19x19

Please Illustrate a Mathematical Analysis of This Position

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