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.)

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.

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?

Sure.



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



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.

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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.



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

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



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.

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.

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be immersed

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.

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be immersed

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.

I've enjoyed reading this discussion quite a bit. It's very interesting that we can get such different answers to a naively simple question. Bills comment



naturally makes me think that perhaps values should also be assigned an error. Why not call a bare 3-3 stone 8 plus or minus 4? Then all the estimates agree. As the game progresses the measurement of it's territory can change, and the error becomes smaller. Is it a useful way to think?

Globally, it is the

Territory Count = Black's territory - White's territory

(there can be prisoners). In my methodology, the kind of territory being determined is the

Current Territory,

see http://senseis.xmp.net/?CurrentTerritory

Except for not stating the sente condition clearly enough, Cho Chikun also uses current territory as the basis of territorial position judgement. We get

Territory Count = Black's current territory - White's current territory



What is ideal for Black is his maximal defense of his already existing territory regions under certain made assumptions, such as peaceful defense and sente for White.

When White's current territory is being determined, the roles are swapped: Black gets the sente, while White defends peacefully his already existing territory regions.



Current territory is NOT (I repeat: NOT) the result of ordinary go playing. When a player's current territory is determined, the study game's objective is exactly this: to determine his current territory.

Think of it as a kind of proof play. When you have a different task, such as determining the life and death status of a black group, you use proof play with the objective for Black to live (or etc.) and for White to kill (or etc.). Other objectives do not exist. Similarly, in territorial positional judgement proof play about a player's territory, the only relevant objective is the determination of his already existing territory.

The move sequences shown do NOT have the objective of increasing the territory. They only have the objective of determining the already existing territory.



Because you would be determining the current territory of this joseki result, instead of determining the current territory of the 3-3 stone.

The influence of the black joseki stones differs from the influence of the lonely 3-3 stone. Therefore, also the territory must be different. Less remaining influence implies (since it is joseki) more territory. IOW, with the joseki you determine, that the 3-3 stone has less current territory than the joseki result's current territory. It is not clear, how much less.

One nice thing about this discussion is that it's finally made me order the Lee Changho book. I'm looking forward to seeing what it has to say in more detail.

Have you noticed that Lee appears to proclaim "4 + alpha" (for some, by the used method, obviously relatively big alpha), while I proclaim "8" (i.e., I determine the alpha as 4)? A "method" with a rough error is not just of the same quality as a method with an apparently small error, even in your simplistic view.

EDIT:



It is a principally interesting other study question. (And the methods are applicable again.)

Based on the example at sensei's library, at least, it seems like it's only relevant when a group is relatively sealed in. On the whole board, for example, white could just mirror black's moves in opposite corners, and until the symmetry is broken, after white's moves the territory count should be zero, no?

More to the point, I don't understand why the initial white move you chose is the correct one, and why black's response is correct, when black could just as well respond with a keima or the like, claiming either more territory or the threatened capture of white's original stone. It seems just as accurate to say that the 3-3 point doesn't enclose any territory, because after a few white moves, black is left without a living shape.

EDIT:
Also, that page makes it pretty clear that the Current Territory count is only really applicable to the middle game.

New territory is not obtained, but already existing territory is being defended as territory. Even though you are sometimes surprised when it is bigger than you thought, because the defender is so cute to survive.

Never has a barely living group, whose only living possibility is a change of direction, less territory than it can show by maintaining life by indeed changing the direction! A barely living group never has only the small territory of its unnecessarily dying shape.

The error is not 4, but - I claim (but cannot prove beyond doubt) - is smaller than the rounding error 0.5.

Whose view is the "simplistic view"? Without knowing the exact value, the amount of error is unknown.

So even in your simplistic view, you have not proven that your method provides an apparently smaller error.

_________________
be immersed

For moyos, determine current territory and half territory!



- It is reasonable.
- It lives.
- It minimises while fulfilling the other conditions.



- It is reasonable.
- It is peaceful (not claiming an unprotected, open side).
- It maximises while fulfilling the other conditions.



That would violate in particular the "peaceful defense" condition.



Wrong, because that would NOT be a sente reduction sequence. The attacker's sente in the sequence is one of the requirements (as well as the defender's requirement to block the sente moves (except when an exception applies)).


EDIT:



The SL page is just initial food and does not demonstrate all the power of application. See the literature for that.

There is a difference. Later in the game, the methods can be shown to be correct. When there are many variations, the methods result in simply a guess, no better than other guesses (until you have proven their accuracy).

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be immersed