Life In 19x19

Plainly the traditional territory value for positional judgement is very conservative, something that might be called solid territory. But how much local territory should we estimate for the 3-3 stone?

One way to answer that question might be statistically, looking at many pro games. Here I will take a different approach.

Click Here To Show Diagram Code

[go]$$W 3-3 stone, estimating territory
$$ ----------------------
$$ | C C C C C . . . . . .
$$ | C C C C C . . . . . .
$$ | . . X . . B . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . W . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .[/go]

Here we have added the and stones. Plainly without the 3-3 stone the position has a value of 0, so we can estimate how much territory the 3-3 stone adds. Using the traditional way we get an estimate of 10 pts. (the points). But we should subtract the territory value of the stone. Since it has no base, we cannot properly estimate its territory value.

Click Here To Show Diagram Code

[go]$$W 3-3 stone, estimating territory (II)
$$ ----------------------
$$ | C C C C C C C C . . .
$$ | C C C C C C C C . . .
$$ | . . X . . B . . X . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . W . . . . . . . .
$$ | C C . . . . . . . . .
$$ | C C . . . . . . . . .
$$ | . . O . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .[/go]

Here we have given the stone a base, adding a counterbalancing Black stone on the top. Now, still using the traditional estimate, we get 16 - 4 = 12 pts. The extra two points come from the two points under the stone. That seems to be an artifact. The extension added 4 pts. to the White position, but 6 pts. to the Black position.

We can adjust for that by adding 1 pt. underneath a stone on the 3d line. Then an extension adds 6 pts. to each position. When we do that we get the following diagram.

Click Here To Show Diagram Code

[go]$$W 3-3 stone, estimating territory (III)
$$ ----------------------
$$ | C C C C C C C C . . .
$$ | C C C C C C C C C . .
$$ | . C X . . B . . X . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . C W . . . . . . . .
$$ | C C . . . . . . . . .
$$ | C C . . . . . . . . .
$$ | . C O . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .[/go]

That estimate yields 18 - 6 = 12 pts.

Now, we expect from the value of komi that a stone on the 3-3 is worth around 14 pts. (Maybe less, as it has gone out of style.) If 12 pts. of that comes from local territory, that leaves 2 pts. for center influence. That seems reasonable.

Is it possible that attempts to find precise values on a near-empty board like this oversimplify the reality of the situation?

Kirby wrote:Is it possible that attempts to find precise values on a near-empty board like this oversimplify the reality of the situation?

Precise values? When you get different estimates of 4, 8, and 12, where is the precision?

Bill Spight wrote:

Kirby wrote:Is it possible that attempts to find precise values on a near-empty board like this oversimplify the reality of the situation?

Precise values? When you get different estimates of 4, 8, and 12, where is the precision?

Hey, they're all within an order of magnitude. If that's not precise, what is?

Bill Spight wrote:Precise values? When you get different estimates of 4, 8, and 12, where is the precision?

Maybe there are some games where you'll get 4 points in the corner, some where you'll get 8, and some where you'll get 12. Maybe it doesn't have to be a single number, because there can be a variety of different board positions in practice.

It's in this mindset that concepts and ideas are more powerful than a formula that tells you F(StoneA, StoneB, StoneC) = 8 points. Simplifying the function to a single number loses details. Instead of reducing StoneA, StoneB, and StoneC to a single value, knowing certain properties of the stones may be more useful and widely applicable to whatever position you may find yourself in.

When there are more stones on the board and the position becomes calculable, at that point, you can apply some function to the stones to come up with a precise number.

But my feeling is that in an empty board, it's too much of a simplification to reduce the complexity of the position to a single, simple number.

Bill Spight wrote:

$$W 3-3 stone, estimating territory (III)
$$ ----------------------
$$ | C C C C C C C C . . .
$$ | C C C C C C C C C . .
$$ | . C X . . B . . X . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . C W . . . . . . . .
$$ | C C . . . . . . . . .
$$ | C C . . . . . . . . .
$$ | . C O . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W 3-3 stone, estimating territory (III)
$$ ----------------------
$$ | C C C C C C C C . . .
$$ | C C C C C C C C C . .
$$ | . C X . . B . . X . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . C W . . . . . . . .
$$ | C C . . . . . . . . .
$$ | C C . . . . . . . . .
$$ | . C O . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .[/go]

That estimate yields 18 - 6 = 12 pts.

Independently of the question of whether your analysis for this diagram is right, it does not determine the value of the 3-3 point, but it might determine the territory count of this position.

Adding extension stones adds territory, but I do not see your justification for implying a relation between territory amounts in a position without / with an extension. I see only a possible determination of which intersections are added to the set of territory intersections.

(I dislike your artifically added territory marks below part of the stones.)

Kirby wrote:But my feeling is that in an empty board, it's too much of a simplification to reduce the complexity of the position to a single, simple number.

Click Here To Show Diagram Code

[go]$$c 360 point move!!!
$$ ---------------------------------------
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . , . . . . . C . . . . . , . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | C C C C C C C C C 1 C C C C C C C C C |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . , . . . . . C . . . . . , . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ | . . . . . . . . . C . . . . . . . . . |
$$ ---------------------------------------[/go]

From here on out, white can only hope to reduce and win by komi.

RobertJasiek wrote:

Bill Spight wrote: Independently of the question of whether your analysis for this diagram is right, it does not determine the value of the 3-3 point, but it might determine the territory count of this position.

Adding extension stones adds territory, but I do not see your justification for implying a relation between territory amounts in a position without / with an extension. I see only a possible determination of which intersections are added to the set of territory intersections.

(I dislike your artifically added territory marks below part of the stones.)

More seriously, doesn't this suggest that the 8 points you see is really the value of two moves, and that by extension, one should divide 8 points / 2 moves and come up with an average of 4 for each?

Kirby wrote: It's in this mindset that concepts and ideas are more powerful than a formula that tells you F(StoneA, StoneB, StoneC) = 8 points. Simplifying the function to a single number loses details. Instead of reducing StoneA, StoneB, and StoneC to a single value, knowing certain properties of the stones may be more useful and widely applicable to whatever position you may find yourself in.

Sure.

When there are more stones on the board and the position becomes calculable, at that point, you can apply some function to the stones to come up with a precise number.

True. But even then the precise numbers do not tell you unerringly how to play.

But my feeling is that in an empty board, it's too much of a simplification to reduce the complexity of the position to a single, simple number.

Just speaking for myself, to evaluate positions in the opening I think in terms of stones, rarely with more precision than 1/2 stone. However, when comparing plays in the opening I am sometimes sensitive to differences of less than 1 pt., partly based on calculation, on previous knowledge, on experience, and on judgement.

I don't think that people who make precise estimates in the opening are putting too much store in the numbers, but are using them as heuristics. Jowa advised assessing the position at around moves 30, 50, and 100. Steve Fawthrop talks of counting the position every few of moves. (That seems rather often to me.) Anyway, players do find positional evaluation helpful.

Kirby wrote:Maybe there are some games where you'll get 4 points in the corner, some where you'll get 8, and some where you'll get 12. Maybe it doesn't have to be a single number, because there can be a variety of different board positions in practice.

This is not about the value of a 3-3 in an empty quarter, but is about 3-3 in a pretty full board later in the game, when indeed many values become possible for a group including the 3-3 stone or an opposing group around its intersection.

But my feeling is that in an empty board, it's too much of a simplification to reduce the complexity of the position to a single, simple number.

Not a single number. There are territory, influence, turn etc.

skydyr wrote:doesn't this suggest that the 8 points you see is really the value of two moves,

No. When I see a shape with 2 stones, then I determine its territory afresh for both stones together.

and that by extension, one should divide 8 points / 2 moves and come up with an average of 4 for each?

This is not the Territory Count, but is the Territory Efficiency, which is a useful "local" number for studying efficiency.

RobertJasiek wrote:

skydyr wrote:doesn't this suggest that the 8 points you see is really the value of two moves,

No. When I see a shape with 2 stones, then I determine its territory afresh for both stones together.

and that by extension, one should divide 8 points / 2 moves and come up with an average of 4 for each?

This is not the Territory Count, but is the Territory Efficiency, which is a useful "local" number for studying efficiency.

I think I'm confused about what exactly you are trying to count, then, because it seems that if you are granting white all the moves in your additional example in sente, it's hardly ideal play for black. Without looking at the whole board, it's hard to say that black wouldn't get compensation elsewhere in exchange for being relatively sealed in in gote. Why not choose this joseki as representative to get a value for the 3-3 stone, since it removes most of the potential influence from the equation?

Click Here To Show Diagram Code

[go]$$Wc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . 6 . . .
$$ | . . B 2 . . . . .
$$ | . . . 1 3 . . . .
$$ | . 4 . . . . . . .
$$ | . . . . . . . . .
$$ | . . . 5 . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Edited for grammar.

Bill Spight wrote:I don't think that people who make precise estimates in the opening are putting too much store in the numbers, but are using them as heuristics.

This makes sense, but it would seem then, that if the "precise estimate" is intended to be used as a heuristic in the first place, it is less meaningful to criticize a "less precise estimate" obtained in a less mathematical manner.

That is to say, if you have a localized position for which you can prove that your precise numerical technique yields exactly the correct answer, then I agree that you can argue of the benefits of using such a calculation above other methods - it provides exactly the correct answer.

But if you use a similar method early on in the game, only to come up with a rough estimate in the first place, then I don't see how the method is necessarily superior to other methods of positional judgment.

When multiple methods of positional judgment (eg. Lee Changho's, Robert Jasiek's, etc.) lead to estimates and not provably correct judgments, it becomes difficult to argue for one method over another in objective terms. As a result, I am inclined to put more weight into estimations that have held track record in game results.

Ie. If we have this pro estimates with this methodology, I cannot prove that he is correct given the empty state of the board. But given the absence of proof in a superior methodology, it seems like a weak argument to argue with the pro's estimation - the adversary methodology is an estimation, just the same.

RobertJasiek wrote: This is not about the value of a 3-3 in an empty quarter, but is about 3-3 in a pretty full board later in the game, when indeed many values become possible for a group including the 3-3 stone or an opposing group around its intersection.

Then why not discuss the position later in the game, when a pretty full board arises? When you have a pretty full board, you can use a precise methodology to calculate exactly the value of the 3-3 territory claimed by the 3-3 stone in the corner.

But since the board is open and many possibilities exist, it seems difficult to argue for one estimation over another.

RobertJasiek wrote:
Justification for 8 points:

Using Jasiek's methods of positional judgement [3], current territory expresses the territory value and is defined via the opponent's expected endgame reductions in sente and the player's peaceful answers with the following, relevant exception: "The defender switches direction only if a) this is necessary for maintaining life [...]" Other principles are relevant for White's first reduction move: "Construct reasonable peaceful reductions from the outside [...]" and "If the attacker has only remote support by friendly stones, his early reduction plays are accordingly reasonable."

What if black had played twice more in the corner first, then by my reading of your system:

Click Here To Show Diagram Code

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

Black no longer needs to switch directions to live, so adding that corner eye has cost him 6 points? You could, I suppose, quibble that 1 and 3 are no longer "reasonable reductions", that black can too easily attack those stones, but that objection also existed without the additional stones.

Essentially, you seem to hit upon a loophole in your territory system. It is often the case where switching directions, perhaps sacrificing territory on one side to expand further on the other side, is beneficial. You could allow it unconditionally, and get a more accurate estimate at the cost of more reading required to evaluate a position. Or you could remove it, and accept that when a reduction kills, the number does not take that into account. But allowing a change of direction only when necessary for life creates this sort of situation where a barely living group is worth more than a strong one, because only the weak group is allowed to expand in the other direction to obtain territory.