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 Post subject: Counting Influence
Post #1 Posted: Tue Aug 10, 2010 10:34 am 
Judan

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How do you count influence?

I've been thinking of this a bit since I read a recent post, which discussed the following joseki result:

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


If I count the following marked areas as points for black:
Click Here To Show Diagram Code
[go]$$
$$-------------------------------+
$$ . . . . . . . . X X o o o o o |
$$ . . . . . . O X o X o o o o o |
$$ . . . . . . O O X X o X o o o |
$$ . . . . . , . . O O X o X o o |
$$ . . . . . . . . . . . X o o o |
$$ . . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . . |[/go]


I have 25 points for black (counting additional points for captures).

Since this is joseki, one might say that the 5 white stones on the top side are worth 25 points...

To this, I can only think, "Yeah, right".

Then someone might argue, well, black played first in the corner. I heard that a corner play is worth 5 points before. So maybe the 5 white stones on the top are worth 20 points... Again, I think, "Yeah, right".

Ok, so you say, "White has sente". Fair enough. So let's say that the difference between before the joseki, when black just has a stone in the corner, and now is 20 points (the 25 points minus the 5 for having a stone in the corner).

Since white chose to do this joseki, and it ends in sente with him, he gets the benefit of the joseki + the benefit of his move elsewhere since he has sente.

Presumably this should be equal to 20 points, I guess. Since we know nothing about the other move that he plays that he got from his sente, I guess we can assume that the white benefit from the joseki is about 20/2, or maybe around 10 points...

Is this the right way to analyze this? Can we say that we expect white to get at least 10 points from his influence for the result to be even?

In general, how do you count influence? This way?

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 Post subject: Re: Counting Influence
Post #2 Posted: Tue Aug 10, 2010 10:46 am 
Oza
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I don't see how it's possible to evaluate that in the abstract. Presumably white plays that way when the influence does something good on the rest of the board. I can imagine board positions where it's worth 40 points and where it's worth -15 points.

EDIT: only 3 or 4 games on my website get to this position, so I wonder if it's really joseki. Note that they all atari before tenukiing.

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 Post subject: Re: Counting Influence
Post #3 Posted: Tue Aug 10, 2010 11:02 am 
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daniel_the_smith wrote:
I don't see how it's possible to evaluate that in the abstract. Presumably white plays that way when the influence does something good on the rest of the board. I can imagine board positions where it's worth 40 points and where it's worth -15 points.


I agree with this. It's something I considered mentioning in the thread about that joseki - that there are many interesting situations where the frequency of 'joseki' appearance depends solely on the contents of one or both adjacent corners. These patterns are still considered overall joseki, but professional play clearly shows that this is only considered completely true with respect to the rest of the board.

This joseki is an obvious example; if white's thickness is alreay nullified, white just has a cutting point. If white has something of his own facing it, it's black who has 'only' 25 points.

For these reasons I have tremendous difficulty counting influence. I handle it based purely on instinct and by mental comparison to previous games. This probably isn't a good idea in the long run, but it probably also isn't *bad* for my play. The only consistent thought in my head is 'I *know* this is worth more than it looks to be, so I'll handle it accordingly', which only leads to people telling me my moves are rubbish and that there's no threat there. They're probably right :D

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 Post subject: Re: Counting Influence
Post #4 Posted: Tue Aug 10, 2010 11:05 am 
Judan

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I agree that it depends on the overall position. But I guess my question is more of, "how much should I be required to get from the stones so that I don't fall behind"?

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 Post subject: Re: Counting Influence
Post #5 Posted: Tue Aug 10, 2010 11:46 am 
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You can't count influence (seiryoku). You can count the type of thickness known as atsumi. There are different type of thickness, though they all denote a degree of strength. To qualify for the name, the outward facing strength called atsumi - the initial sort that often results from josekis - has to be strong enough to be able to turn into the type of really solid thickness called atsusa. That means it has to have no defects, or otherwise not be attackable.

White in the above position does not yet have atsumi thickness. He just has a conglomeration of stones on the outside which he can turn into atsumi.

There are two common ways of bolstering such a conglomeration to turn it into atsumi. One is to play a local move that defends the weaknesses and so makes it (for the moment) unattackable. This type of atsumi is hard to count. Two usual processes would either be (a) to do a tewari analysis and, if you are satisfied that all the moves have been efficient, assume that the thickness is worth the size of the other side's corner, or (b) to use a QARTS type evaluation and say something like: "this thickness gives me a good attack on his eyeless group over there, so it must be worth around 20 points" (or 10 points if attacking a one-eyed group). There is, however, a third method as well.

The other way of making an outside shape thick is to play an extension from the wall, i.e. giving it a base for strength. This, to a degree, maps out a territory, too, and so it might seem that this type of atsumi can in some way be counted by looking at the territory. However, that is usually unwise unless you also understand the concept of kakoi (surrounding) moves. It is still best treated by the third method mentioned above.

The basic heuristic of this method is (relying on my memory!) to take the height or length of a sound wall, in stones, as N and calculate (N x (N+1)) / 2. The resulting value is not meant to represent the territory you will get locally, but a territory-equivalent value over the whole game (rather like the Qarts value).

The beauty of this method, mostly associated with Abe Yoshiteru though other pros have variations on it, is that you can use it for walls that go round corners, or kinky walls. There are some modifications to it. For example if you can guarantee certain extra moves you can count them in the size of your wall. It seems also that stones on the first line are not counted. If you have a residual weakness, or an element of overconcentration, you have to reduce the size of the wall. Also some reduction is needed when two walls face each other - I forget the details but basically it's just excluding the overlapped area. There are some other fine points, too.

Note that in this method, you can count the atsumi thickness even if there is no extension from the wall. But there must still be room to make a sensible extension (or to attack an enemy group that dares to come too close). Also, Abe stresses very much the need to have no defects. Even a peep can ruin the value of a wall.

You will know if your atsumi has been used well because it will turn into atsusa - you will be unattackable - and you will pick up point after point either in a moyo or in the endgame while the opponent is busy remedying his defects. If the type of play exemplified by the joseki above continues throughout the game - that is, all moves are equally efficient but Black concentrates on territory now and White on atsumi now - eventually we will reach a stage atsumi has become atsusa and the boundary plays can start. If White achives this blessed state, he will be said to have the thicker endgame (this is a very common way of expressing the evaluation used by pros) and he should win. Of course, turning atsumi into atsusa is somewhat more difficult than just accumulating territory, so it is often hard to make this potential advantage tell in the long journey from the opening to the endgame.

If you have achieved atsusa thickness, of course you count that as normal territory.


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 Post subject: Re: Counting Influence
Post #6 Posted: Tue Aug 10, 2010 11:58 am 
Judan

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John Fairbairn wrote:
You can't count influence (seiryoku). You can count the type of thickness known as atsumi. There are different type of thickness, though they all denote a degree of strength. To qualify for the name, the outward facing strength called atsumi - the initial sort that often results from josekis - has to be strong enough to be able to turn into the type of really solid thickness called atsusa. That means it has to have no defects, or otherwise not be attackable.

....


This is very interesting, John, but it will take some time for me to study it.

For now, I want to just say, thanks for sharing.

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 Post subject: Re: Counting Influence
Post #7 Posted: Tue Aug 10, 2010 12:13 pm 
Judan

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Kirby wrote:
How do you count influence?

I've been thinking of this a bit since I read a recent post, which discussed the following joseki result:

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


If I count the following marked areas as points for black:
Click Here To Show Diagram Code
[go]$$
$$-------------------------------+
$$ . . . . . . . . X X o o o o o |
$$ . . . . . . O X o X o o o o o |
$$ . . . . . . O O X X o X o o o |
$$ . . . . . , . . O O X o X o o |
$$ . . . . . . . . . . . X o o o |
$$ . . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . . |[/go]


I have 25 points for black (counting additional points for captures).

Since this is joseki, one might say that the 5 white stones on the top side are worth 25 points...

To this, I can only think, "Yeah, right".

Then someone might argue, well, black played first in the corner. I heard that a corner play is worth 5 points before. So maybe the 5 white stones on the top are worth 20 points... Again, I think, "Yeah, right".

Ok, so you say, "White has sente". Fair enough. So let's say that the difference between before the joseki, when black just has a stone in the corner, and now is 20 points (the 25 points minus the 5 for having a stone in the corner).

Since white chose to do this joseki, and it ends in sente with him, he gets the benefit of the joseki + the benefit of his move elsewhere since he has sente.

Presumably this should be equal to 20 points, I guess. Since we know nothing about the other move that he plays that he got from his sente, I guess we can assume that the white benefit from the joseki is about 20/2, or maybe around 10 points...

Is this the right way to analyze this? Can we say that we expect white to get at least 10 points from his influence for the result to be even?

In general, how do you count influence? This way?


First, I don't think that this is joseki.

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


This is joseki. :)

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


Later Black can reach this position in sente. (White should really not neglect the last two moves, I think.)

Now, to evaluate this position we need to add the sente.

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


I have marked points going out about three spaces from the walls, except where the opposing wall is nearby. (Actually, I think that this is somewhat conservative on an empty board, but that is just my opinion.)

That gives Black 17 points plus 4 captured stones, for 21 points. It gives White 28 points. (You can also count the Black stone in ko as 1/3 point for White, but assessing influence is not all that precise. :)) That puts White about 7 points ahead.

Which suggests that Black should not continue by capturing the corner unless she has already taken steps to reduce White's outside influence, or can do so on the next play. :)

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Post #8 Posted: Tue Aug 10, 2010 12:20 pm 
Judan

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Bill Spight wrote:
Kirby wrote:
How do you count influence?

I've been thinking of this a bit since I read a recent post, which discussed the following joseki result:

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


If I count the following marked areas as points for black:
Click Here To Show Diagram Code
[go]$$
$$-------------------------------+
$$ . . . . . . . . X X o o o o o |
$$ . . . . . . O X o X o o o o o |
$$ . . . . . . O O X X o X o o o |
$$ . . . . . , . . O O X o X o o |
$$ . . . . . . . . . . . X o o o |
$$ . . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . . |
$$ . . . . . . . . . . . . . . . |[/go]


I have 25 points for black (counting additional points for captures).

Since this is joseki, one might say that the 5 white stones on the top side are worth 25 points...

To this, I can only think, "Yeah, right".

Then someone might argue, well, black played first in the corner. I heard that a corner play is worth 5 points before. So maybe the 5 white stones on the top are worth 20 points... Again, I think, "Yeah, right".

Ok, so you say, "White has sente". Fair enough. So let's say that the difference between before the joseki, when black just has a stone in the corner, and now is 20 points (the 25 points minus the 5 for having a stone in the corner).

Since white chose to do this joseki, and it ends in sente with him, he gets the benefit of the joseki + the benefit of his move elsewhere since he has sente.

Presumably this should be equal to 20 points, I guess. Since we know nothing about the other move that he plays that he got from his sente, I guess we can assume that the white benefit from the joseki is about 20/2, or maybe around 10 points...

Is this the right way to analyze this? Can we say that we expect white to get at least 10 points from his influence for the result to be even?

In general, how do you count influence? This way?


First, I don't think that this is joseki.

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


This is joseki. :)

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


Later Black can reach this position in sente. (White should really not neglect the last two moves, I think.)

Now, to evaluate this position we need to add the sente.

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


I have marked points going out about three spaces from the walls, except where the opposing wall is nearby. (Actually, I think that this is somewhat conservative on an empty board, but that is just my opinion.)

That gives Black 17 points plus 4 captured stones, for 21 points. It gives White 28 points. (You can also count the Black stone in ko as 1/3 point for White, but assessing influence is not all that precise. :)) That puts White about 7 points ahead.

Which suggests that Black should not continue by capturing the corner unless she has already taken steps to reduce White's outside influence, or can do so on the next play. :)


It's a good point that black has those sente moves, which I ignored in my original diagram.

Your method of evaluation is more straightforward than I would have imagined.

The only thing I am not certain of is how you selected 3 as the number of intersections to count outward for the influence points.

Can you elaborate on this selection (albeit, probably a fuzzy measure)?

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Post #9 Posted: Tue Aug 10, 2010 1:08 pm 
Judan

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Kirby wrote:
Bill Spight wrote:
Now, to evaluate this position we need to add the sente.

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


I have marked points going out about three spaces from the walls, except where the opposing wall is nearby. (Actually, I think that this is somewhat conservative on an empty board, but that is just my opinion.)

That gives Black 17 points plus 4 captured stones, for 21 points. It gives White 28 points. (You can also count the Black stone in ko as 1/3 point for White, but assessing influence is not all that precise. :)) That puts White about 7 points ahead.

Which suggests that Black should not continue by capturing the corner unless she has already taken steps to reduce White's outside influence, or can do so on the next play. :)


It's a good point that black has those sente moves, which I ignored in my original diagram.

Your method of evaluation is more straightforward than I would have imagined.


Well, as John Fairbairn indicated, there is no developed theory of influence. Even the computer programs that use it use fairly crude and unproven methods (and the Monte Carlo programs do not use it, AFAIK). I actually think that, to a first approximation, influence drops off geometrically, halving with each unit of Manhattan distance. However, for a human to try and calculate even that is absurd in most cases. We need something easier to calculate.

Quote:
The only thing I am not certain of is how you selected 3 as the number of intersections to count outward for the influence points.

Can you elaborate on this selection (albeit, probably a fuzzy measure)?


Given an infinite wall, to a second approximation I reckon the influence for each point distant from the wall to be 1, 1, 0.75, 0.375, ..., which sums to 3.5. Given the uncertainty as you get farther from the wall and the fact that the wall is not infinite, anyway, 1, 1, 1 is not a bad approximation, is it? :)

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Post #10 Posted: Tue Aug 10, 2010 1:15 pm 
Oza

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Kirby wrote:
The only thing I am not certain of is how you selected 3 as the number of intersections to count outward for the influence points.

Can you elaborate on this selection (albeit, probably a fuzzy measure)?


It is basically a matter of experience. Did you see how I evaluate influence in my counting lessons? It is very similar.

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Post #11 Posted: Tue Aug 10, 2010 5:28 pm 
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Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$
$$-------------------------------+
$$ . . . C C C O O X X C X C C C |
$$ . . . C C C O X . X C X C C C |
$$ . . . C C C O O X X C X C C C |
$$ . . . . C C C C O O X X X C C |
$$ . . . . . C C C C C O X C C C |
$$ . . . . . . C C C C O . . . . |
$$ . . . . . . . . C C C . . . . |
$$ . . . . . . . . . C C . . . . |
$$ . . . . . . . . . . C . . . . |
$$ . . . . . , . . . . . , . . . |[/go]

I have marked points going out about three spaces from the walls, except where the opposing wall is nearby. (Actually, I think that this is somewhat conservative on an empty board, but that is just my opinion.)

I would count quite a bit less for W, maybe something like this:

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

Then I would subtract points for the thickness being incomplete (weaknesses at A and B). W would certainly value the position more if he had stones at those points. So my feeling is that, as an isolated "joseki", B is a little better. Of course W will play this way when the thickness faces a useful direction, and then the value depends strongly on the situation.

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Post #12 Posted: Tue Aug 10, 2010 5:39 pm 
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John Fairbairn wrote:
... The basic heuristic of this method is (relying on my memory!) to take the height or length of a sound wall, in stones, as N and calculate (N x (N+1)) / 2. The resulting value is not meant to represent the territory you will get locally, but a territory-equivalent value over the whole game (rather like the Qarts value) ....

Interesting idea. Normally we are taught that fourth-line territory is good, but this heuristic would say that it depends on the length of the line.

For example, here W has 30 points of fourth-line territory, but by your rule, the B wall is worth 45 points. So pushing your opponent along the fourth line might be good, provided you continue it long enough :)

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 Post subject: Re: Counting Influence
Post #13 Posted: Sun Aug 05, 2012 6:57 pm 
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Kirby wrote:
In general, how do you count influence?


Influence is counted for each intersection in terms of its (i.e., my) definition's degrees of a player's m-connection, p-life and t-territory and the opponent's n-connection and q-life. In other words, the influence of an intersection is tuple of (at least) 5 values. (See Joseki 2 Strategy, p. 71ff).

daniel_the_smith wrote:
I don't see how it's possible to evaluate that in the abstract.


By applying the definition, i.e. determining the degrees for an intersection!

Kirby wrote:
Is this the right way to analyze this [for a joseki]?


For josekis, the appropriate core way of evaluation is described in chapter 3 of Joseki 3 Dictionary. Stone difference, current territory and a simplifying influence value (derived from mobility difference) are determined, the ratio of territory and influence is formed and the membership in a (non-)joseki value class is identified.

Bill Spight wrote:
to evaluate this position we need to add the sente.


Besides stone difference, current territory and influence stone difference, it is indeed useful to assess some further aspects: the player having the turn, whether the current result is stable and other particularly relevant aspects of strategic concepts (such as some important aji).

Quote:
I have marked points going out about three spaces from the walls


Forget about such a naive influence model and instead use "influence stone difference", which (in conjunction with the other mentioned values and the remaining theory described in Joseki 3 Dictionary) works so extraordinarily well that every joseki is identified as being a joseki and every non-joseki is identified as not being a joseki. (I say "every" and not "each" because, of 400 josekis, I have had - only - one joseki related to a big middle game ko exchange that the theory does not explain. Not surprisingly; it is a joseki theory and not a ko exchange theory.)

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 Post subject: Re: Counting Influence
Post #14 Posted: Sun Aug 05, 2012 7:42 pm 
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John Fairbairn wrote:
You can't count influence


When you wrote this in 2010, a good influence definition was not published yet. In 2011, I published it. So, now, one can assess influence numerically.

Quote:
You can count the type of thickness known as atsumi.


In 2011, I published a general definition of thickness. Therefore, each type of thickness can be assessed numerically.

Quote:
There are different type of thickness, though they all denote a degree of strength.


No. Each of them denotes THREE degrees of strength! Namely the degrees of n-connection, p-alive and t-territory.

Quote:
To qualify for the name, the outward facing strength called atsumi - the initial sort that often results from josekis - has to be strong enough to be able to turn into the type of really solid thickness called atsusa. That means it has to have no defects, or otherwise not be attackable.


Such a thickness description can be part of a reasonable informal rough characterisation. However, one must not slavishly exclude all defects; rather the degrees of connection and of life imply a possibility of (preferably non-existing or else marginal) aji.

Quote:
There are two common ways of bolstering such a conglomeration to turn it into atsumi. One is to play a local move that defends the weaknesses and so makes it (for the moment) unattackable. This type of atsumi is hard to count.


It is easy to count by simply counting the number of successive plays to get a desired degree of, say, *-connection, 1-connection or at least 0-connection.

Quote:
Two usual processes would either be (a) to do a tewari analysis and, if you are satisfied that all the moves have been efficient, assume that the thickness is worth the size of the other side's corner,


Tewari is a hopeless overkill for the purpose. Specifying a desired degree of n-connection implies the search for the MINIMALLY necessary number of additional plays to reach that degree and hence implies efficiency WITHOUT EXTRA EVALUATION EFFORT.

Quote:
or (b) to use a QARTS type evaluation and say something like:


QARTS and other symbolic number models are hopelessly unsystematic and imprecise. Such kind of theory is for historians. Now, my theory allows to abandon earlier alchemy and get precise assessments.

Quote:
The other way of making an outside shape thick is to play an extension from the wall, i.e. giving it a base for strength.


This increases the degree of connection of a wall's stones slightly, can increase their life degree significantly and usually increases their territory degree. This is more accurate than saying "making thick".

Quote:
It is still best treated by the third method mentioned above.


Not any longer. Now, t-territory is the choice of evaluation.

Quote:
The basic heuristic of this method is (relying on my memory!) to take the height or length of a sound wall, in stones, as N and calculate (N x (N+1)) / 2.


Alchemy. - The proper way is to identify, for each intersection, the t degree of t-territory. Optionally, a sum can be formed: 0-territory (aka "current territory") counting 100% and 1-territory 50%. (2-territory tends to be overkill.)

Quote:
The resulting value is not meant to represent the territory you will get locally, but a territory-equivalent value over the whole game


Now, it is easier to assess the current estimate of local territory. (For the other kind of territory estimate, one would want to determine per-move values, but in practice this is too tough during the middle game, except for specialised application such a average value of a particular unsettled group).

Quote:
The beauty of this method, mostly associated with Abe Yoshiteru though other pros have variations on it, is that you can use it for walls that go round corners, or kinky walls.


There is no beauty in flawed, imprecise theory!!! Replace it (and the professionals should also replace it) by my theory!

Quote:
There are some modifications to it. For example if you can guarantee certain extra moves you can count them in the size of your wall. It seems also that stones on the first line are not counted. If you have a residual weakness, or an element of overconcentration, you have to reduce the size of the wall. Also some reduction is needed when two walls face each other - I forget the details but basically it's just excluding the overlapped area. There are some other fine points, too.

Note that in this method, you can count the atsumi thickness even if there is no extension from the wall. But there must still be room to make a sensible extension (or to attack an enemy group that dares to come too close).


Luckily, my much mightier theory does not need such exceptions related to shapes or position relative to the edge.

Quote:
Abe stresses very much the need to have no defects. Even a peep can ruin the value of a wall.


He is wrong. It is not a necessity - rather it is an aspect of degree. Typically, a wall allowing a peep is 0-connected and not *-connected. After the peep, the influence on nearby intersections is worse than before for the wall's player and improved for the peep's player. However, "ruin" the value of a wall is an exaggeration. As a better description, the values decrease. This can have significant impact, but not to the extent of necessity in general.

Quote:
You will know if your atsumi has been used well because it will turn into atsusa - you will be unattackable -


Instead of continuing usage of such rough terms, it is more meaningful to speak of 1-connection or *-connection instead of 0-connection (similar for life). Your stones are pretty much unattackable if they are at least 1-connected and 1-alive and even less attackable for higher degrees.

Quote:
and you will pick up point after point either in a moyo or in the endgame while the opponent is busy remedying his


Correct.

Quote:
defects.


It is not just aji. Rather the opponent can also be busy defending his stones with too small degrees of connection or life.

Quote:
eventually we will reach a stage atsumi has become atsusa and the boundary plays can start.


Boundary plays need not start at a particular moment of the game; a few are best played early.

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Post #15 Posted: Sun Aug 05, 2012 7:59 pm 
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Bill Spight wrote:
there is no developed theory of influence.


In the meantime, I have invented some theories of influence:

1) The precise definition of "influence".

2) The concept of Mobility Difference. (And derivates of this.)

3) A few special aspects of Local Positional Judgement.

4) Influence Stone Difference as part of my joseki evaluation theory.

Quote:
We need something easier to calculate.


We can use the easiest of my methods above that is a) applicable and b) in practice sufficiently accurate for a purpose of usage. E.g., one does not always need to determine all influence degrees for each intersection; it often suffices to know roughly where a particular player has more influence than the opponent. This can almost always be "calculated" by visual heuristic. When necessary, more precise degrees can be assessed, such as "If I play a stone here, is it [0-]connected?".

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Post #16 Posted: Sun Aug 05, 2012 8:01 pm 
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DrStraw wrote:
It is basically a matter of experience.


mitsun wrote:
I would count quite a bit less for W


Quote:
this heuristic would say


Replace experience by knowledge! Replace imprecise guesses (by imprecise old models) by precise numbers!

Quote:
my feeling is that, as an isolated "joseki", B is a little better.


Instead of feeling, apply my theory of joseki evaluation!

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Post #17 Posted: Sun Aug 05, 2012 11:48 pm 
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There is a certain logic to the Nx(N+1)/2 formula,

That's simply the formula for the sum of the first N integers,

In this case I believe the explanation would be that a wall of height N creates a right triangle of influence, that sum would then be the area of that triangle measured in grid points.

However, since I believe influence reflects off walls ans passes through loose positions, I think this is, at best a heavy simplification

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Post #18 Posted: Mon Aug 06, 2012 3:58 am 
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I would love to see some more serious opposition against your theories. Unfortunately I am too weak a go player to throw a stone. Influence like other concepts you define as having several components. One position can count for more influence in some respect than another but less in other respects. So there is no order relation. Bill defines influence as a scalar. Scalars are much easier to handle and to compare. So if possible give me a scalar theory. And if possible give me a theory where influences of individual stones can simply be added. ( That is an additive theory ). And even more nice if oppenent's influence can be subtracted. But OC the proof must be in the pudding. Pudding: the ability to evaluate a position numerically or to calculate the optimal move. Well, that might be the same thing.

For example. A concept like weather cannot be defined by one number. It involves temperature, sunshine, rain, wind, humidity and so on. Weather is a useful concept but not easily used for practical purposes. Your influence definition reminds me of weather but I am not convinced that it's compoundness is necessary.

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Post #19 Posted: Mon Aug 06, 2012 6:53 am 
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cyclops wrote:
I would love to see some more serious opposition against your theories.


Good theories do not generate opposition:) Anyway, it is easy to create test opposition by myself:

- Assume that either aspect "connection", "life", "territory", "view from both players' perspective" were unnecessary. See below for some counter-arguments.

- Assume that some earlier characterisation of "influence" would have been better. All you get is great shame for everybody else having overlooked the simplest possible and complete characterisation by the mentioned aspects from both players' views. In particular, I do not recall any clear, distinguished mentioning by others of connection and life as being essential components of influence. Various, varying and ambiguous aspects were mentioned. E.g., aji was one of them. Aji is a concept more difficult than the concepts connection or life. Not only is my theory better, but it is also simpler and clearer. Simpler because it relies on simpler basic concepts and clearer because it states the necessary concepts explicitly and even in terms of numbers.

- Assume that there could be any more accurate but still practical assessment of connectivity. You will have problems to find anything else. Possible number of omissions is the (only?!) second candidate but it has disadvantages: a) It was not designed specifically for connection. b) It does not explain negative degrees.

- Similar for life, except that (a) was given for possible number of omissions.

- Assume that "current territory" would not be the best basic kind of territory concept for describing influence. Some centuries later, maybe per-move value theory can become a better candidate. Even then, it is hard to find a more practical and more successful (see next point) description of a territory concept for describing influence. It is so practical because its determination is straightforward (for those players 3 kyu or stronger who do reasonably accurate positional judgement several times every game)

- Assume influence stone difference would not be the most successful influence model for josekis. Go ahead, invent some alternative and prove that it applies in more than 399 of 400 cases!

- Assume there could be a more practical first approximative method than mobility difference for determining almost precisely the player who has more center influence and how much more he has. Difficult! The method is so beautifully simple and elegant! Have you ever seen any professional becoming more "accurate" than saying "this player has the thicker position"? I have not. My method is more precise and the only method I have seen so far that attempts reasonable accuracy at all.

There is so little attractive alternative theory that I do not only not see opposition but seriously doubt whether anything else reaches at least half the quality of my influence theories, as far as defining influence is the objective. The best alternatives mentioned so far were highly partial descriptions such as very doubtful symbolic number alchemies (I would not even call it theories). My theories are essentially always applicable. Alternative theories had only limited scopes.

You ask for opposition? I ask for approval and application! Which other go theory is equally mighty, equally accurate AND applicable for human players? I have a candidate for mighty and applicable: Go Seigen's New Fuseki insight and practical proof that 3-3 and 4-4 are equally valid first corner plays. Unfortunately, that candidate does not offer any accuracy. There is another candidate fulfilling all three criteria: miai counting endgame theory in combination with basic knowledge on gote and sente (where sente is unambiguous). Even older theories of positional judgement pale without my explanations of influence because an accurate and correct description of influence was missing entirely. You can judge the quality of my theory by comparing it with other go theory. Please show all the equally good or better mighty, accurate and applicable theories (about any important go theory topic)! I want to learn! If you can't, then why ask for opposition? Can you appreciate theory lying before you as much as it deserves?

Quote:
Influence like other concepts you define as having several components.


Are you surprised? I am not. Influence is not a basic concept but an intermediate strategic concept presuming lower level theory knowledge.

Quote:
One position can count for more influence in some respect than another but less in other respects.


Yes. Surprised?:) This can be understood easily: Compare different influences by these types of walls:

1) surrounding territory, no effect for later strategy

2) outside wall adjacent to huge empty space, great effect for later strategy

3) ultimate thickness wall adjacent to neutral space, looks great but has no relevant effect for later strategy

The influence protects territory in different forms:

1) already made territory

2) potential additional territory

3) not at all

As you can see, territory is a parameter of influence! So it is necessary to allow influence to have different degrees in territory.

Similarly, connection and life can vary in degrees when considering influence (or thickness).

Quote:
So there is no order relation.


Right. Go is not simple. E.g., in general, endgames also do not have a simple order relation.

Quote:
Bill defines influence as a scalar. Scalars are much easier to handle and to compare.


Simplicity of a model is not evidence of its quality. A model must describe reality. The reality of influence is: It is not a scalar concept.

Quote:
So if possible give me a scalar theory.


It is easy to refer to simplifications. My models "mobility difference" and "influence stone difference" are scalar theories. You can use either IF A SIMPLIFICATION IS SUFFICIENT for a purpose of application.

For in particular these applications, a simplification is sufficient:

1) determining the player with the greater (center) mobility during the middle game

2) influence evaluation as a part of the joseki evaluation theory

For in particular this application, a simplification is insufficient:

- comparing the quality of two different walls

Quote:
And if possible give me a theory where influences of individual stones can simply be added.


More meaningfully, influences of both Black and White are considered; after forming a player's sum, one must then compare both colours. For a typical application, a difference of Black's and White's sums must also be formed. Supposing you can swallow that pill, I have given you simplifying theories with such a small calculation effort; in particular, "mobility difference" and "influence stone difference".

However, it would be a bad idea to pretend simplicity for applications where it is impossible.

What you can do in your games is a PARTIAL and ROUGH application of a mightier theory. E.g., you might consider only connectivity, presume a sufficiently good life degree and ignore different territory potentials. E.g., it is already very instructive to compare examples of outside joseki groups that are 0-, 1- versus *-connected. But..., as much as you might like simplicity, a solid wall with its *-connection can still be worse than a 0-connected wall if the former does not have an extension but has a negative life degree. A partial application gives you partial but insufficient insight!

Quote:
And even more nice if oppenent's influence can be subtracted.


This is being done in my simplifying influence models "mobility difference" and "influence stone difference". It is nice but application is restricted because either model is simplifying.

Quote:
Your influence definition [...] I am not convinced that it's compoundness is necessary.


See above. Each of connectivity, life and territory is a necessary component. Both players' views are necessary. All unnecessary aspects, which can be implied from the necessary aspects, I have omitted! Eye value, thick shape, aji, board division lines, traditional names for specific degrees, active versus passive, further strategic concepts etc.


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Post #20 Posted: Mon Aug 06, 2012 1:47 pm 
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I appreciate your answer, Robert, though it is a bit overwhelming. I disagree that good theories don't generate opposition. Relativity, both special and general, got a lot of opposition. Because of that the confirmation in 1919 by Mercury's eclipse after much debate was glorious for Einstein. I would be really happy for you if your theories would prevail likewise in serious discussions among your peers. In the mean time I am going to finish reading your joseki book. Enough effort for the time being.

RobertJasiek wrote:
........... Supposing you can swallow that pill, I have given you simplifying theories with such a small calculation effort; in particular, "mobility difference" and "influence stone difference". ..........

Thx for allowing for that possibility :blackeye:

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