As long as one does not specify exactly what is being meant, "territory" is only an informal term. Also Saijo Masataka, then 8p, was aware of the ambiguity, so I explained him my earlier ideas. During scoring, matters are easier than during the middle game (except for difficult rulesets, for which Robert Pauli and I defined territory for the purpose of scoring in 2002-4). Here I discuss territory during the middle game.


There were these conceptual predecessors:
- Cho Chikun's "minimal territory" for global positional judgement (book Positional Judgement).
- The "[territory] count" in endgame evaluations (Black's local territory minus White's local territory).


"current territory" is the fundamental term of territory as used in my middle game concepts.

Compared to Cho Chikun's "minimal territory", which already uses the idea of peaceful replies by the defender, I have invented and added the idea of the attacker's sente sequence. This condition is essential for successive endgame-style reductions to make sense; the attacker, who reduces the opponent's territory regions until they are tightly surrounded, can switch from one direction to another direction next to a territory region, then can switch to the next territory region to be reduced. This is meaningfully possible only if each partial sequence is his technical sente.


My definition of current territory, invented in [1]:
"The opponent is assumed to make all the expected endgame reductions in sente, i.e., the player is assumed to answer everything defensively and the most peacefully. The intersections remaining after that imagined reduction are the _current territory_."

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


Applications of current territory:

1) [Global] positional judgement: The territory count of a quiet position is determined.

A 5 kyu becomes aware that positional judgement is very useful. (E.g., if one is ahead, one simplifies the game. If one is behind, one makes the game complicated.) A low dan
occasionally makes a positional judgement during a game. A high dan is always aware of the current positional judgement; incremental updates allow him to refresh judgements very quickly.

Knowing the territory count is an (if not the most) essential part of global positional judgement. Each player's current territory is determined to get the territory count.

2) Territory efficiency [2]: This is an important measure of local efficiency versus overconcentration. Divide the current territory by the number of stones required to surround and protect it.

3) Generalised territory, n-territory [2]:
http://senseis.xmp.net/?NTerritory

4) General influence definition [2]: It depends also on n-territory and thus on current territory.

5) General thickness definition [2]: It depends also on n-territory and thus on current territory.

6) Method "unsettled group average" [2]: It depends also on the count and thus on current territory. The territorial value of an unsettled group and of a move in it are determined.

7) Some methods of "local positional judgement" [2] rely on current territory.

8) Joseki evaluation method [3]: Stone difference, territory count and influence stone difference are determined, if necessary a transformation to stone difference 0 is performed, the value type is identified and so one knows if a corner sequence's result is equal or favourable for a player. Previously, informal professional consensus had to be sought to judge whether a sequence was a joseki. Now everybody can independently verify and decide this, provided he knows what current territory is and acquires a bit of counting practice.


Conclusion: Current territory is one of the fundamental concepts everybody must know and be able to determine. It has many important applications.


Place of invention:
[1] Joseki 1 Fundamentals
[2] Joseki 2 Strategy
[3] Joseki 3 Dictionary

Can you give an example where the current territory differs from minimal?

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be immersed

Minimal territory, White has 8 points, determined without looking for continued sente:

Click Here To Show Diagram Code

[go]$$B White 4 is pass
$$ ---------------------------------------
$$ | . . . 3 1 2 . O . . 6 5 7 . . . . . . |
$$ | . X . X O . . O . . . O X . X . . . . |
$$ | . . . X O O O O O O O O X . . . . . . |
$$ | . . . X X X X X X X X X X . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . 4 |[/go]

Current territory, White has 10 points:

Click Here To Show Diagram Code

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

Thanks. I can see the distinction you are making, now.

It might be cool to get a large set of games and do some sort of empirical analysis of the two methods, seeing how they perform against one another in terms of estimating the actual result at different points in the game.

There's a lot of variance that can happen in a game, so just because a result differs from the estimation, it doesn't mean the estimation is bad - but it'd still be interesting to compare the two methods empirically in some way, I think.

_________________
be immersed

Why? Minimal territory is a flawed fundament for global positional judgement! It is like saying that one player may make successive plays during the game.

It was in 1993 when I read Cho's book twice, borrowed from a library. So I am not sure how exactly the example sequences looked like, and if they (by "accident") all had an even number of plays. IIRC, Cho did not (or not sufficiently clearly) mention a sente sequence requirement. Maybe he had it in his mind but not so prominently that he could explain such a condition clearly?

IIRC, both Cho and Kajiwara (Direction of Play) suggested 5 points of territory for a 4-4 stone. 5, the komi at that time;) (I have derived 7, but not from the komi.)

If you can write out a definitive proof that current territory is always superior for estimation purposes, I suppose empirical analysis is not necessary.

I'm just not sure I see it definitively right now. I can't yet rule out the possibility that the conservative minimal territory won't be better in some cases. Maybe it is... I just don't know for sure.

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be immersed

NB I'm not well-versed in this.

In mid-game positional judgements, isn't determining one side's sente difficult? Of course, in late endgame correct play is often pretty solvable in practice.

Some diagrams from Cho's book, slightly abridged:


I'd like to add that I cannot endorse Cho Chikun's Positional Judgement High-speed Game Analysis enough.

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Revisiting Go - Study Journal
My Programming Blog - About the evolution of my go bot.

I do not claim such for all estimation purposes. (E.g., there can be endgame studies where locally only gote sequences can be a good assumption if the opponent makes gote sequences elsewhere.)

I do claim (because of the stated reason of violated implied alternation) it for the general purpose of estimating territory of a global positional judgement, a locally applied global positional judgement or a similar territorial joseki result judgement.



During the middle game, you can't violate the rule of alternation. Artifically violating it and allowing the opponent to violate it elsewhere works only in special cases (such as each player has exactly one territory region open for reduction from exactly one direction) and such a construction would be unnecessarily artificial.

Not at all. Sente is assumed by definition! What can sometimes be a bit difficult is finding reasonable reduction sequences that fulfil this condition.



Also during the opening, if one imagines likely later nearby stones, from which connected endgame reductions can be imagined.



Thank you, but I am afraid, these are the wrong diagrams. What I want to know about is diagrams with basic reduction sequences (not the special mutual damage topic), which reduce several territorial regions of a player and a territorial region from several directions.



This is a different "sente" topic.

***

Can you find something in the book that sets requirements for reduction sequences? I recall the "minimal" criterion and, IIRC, also an implied peaceful reply. Are there more?

The way I see it, both methods are heuristics, which attempt to model the reality of the territory count.

It also sounds like your model tries to add more precision to the heuristic. This may improve its performance, but this is not guaranteed without further proof.

An example that I can think of is regression. If you have a bunch of datapoints you want to model, you might try to do so with a linear polynomial. You get a line that passes through the data. Maybe it becomes a more accurate model if you use a quadratic polynomial, or perhaps a fifth order polynomial.

But it doesn't follow that adding degrees to you polynomial's model necessarily improves it. In the case of overfitting the data, you start to model outliers and/or data that isn't corresponding to the variable you are trying to model.

So it could be that a more precise heuristic will give better performance. But I don't think this can be absolutely implied without some sort of analysis against what you're actually trying to estimate.

That being said, I think the idea is an interesting contribution regardless.

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be immersed

Sure. If, on average, the numbers are 0 to 2 points off, they are ok.



So far I have "only" empirical proof for

- many thousands of my games: current territory works very well. I know from having watched the changes of territory estimates during the game and comparing it with the final score and move mistakes made.

- the 400 josekis in Joseki 3 Dictionary.



Sure.

If I wanted to test different heuristics, I would not start with something illogical (such as the gote sequences of minimal territory) but I would rather alter the peaceful defense and allow tougher and yet tougher counter-attacks. This would introduce another problem though: One would be evaluating an unknown fraction of the territorial impact of influence. With current territory, that fraction can be estimated as almost 0%, i.e., by measuring influence one knows that one is measuring about ALL the influence.

If I included a fraction of influence in the territory values (to test your "regression" doubt), I would destroy the assumptions I have made for my general joseki evaluation method, all the theory would break down and it could no longer be successfully applied to ALL the josekis. By your suggested attempt to possibly measure territory better, influence would be measured worse. The simple ratio of (only) territory and (only) influence (as represented by the influence stone difference heuristic) could not be formed.

Besides, peaceful defense is identified easily while counter-attacks allow a great variation and it would be very hard to identify the most suitable sequences. It would become a global "find the perfect play" task and estimating territory would be a side product of (dreaming of) finding perfect play.

Rather I am proud to have provided such mighty (because of the broad functional variety) empirical evidence: that current territory works for all the 400 josekis I have tested. The next heroic step would be to take a couple of thick dictionaries with their additional 40,000 josekis and apply my method to also them. This is a faster empirical approach than studying in writing global positional judgement (relying on current territory) after EVERY move of 40,000 example games. (For verbal study, see above for my watched games.)

Cool that current territory not only seems to be a logical approach to evaluating score, but also that you've seen good results when applied to joseki and real games.

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be immersed

Whether this is sufficiently clearly is IMO a matter of taste. I gladly admit that reading Roberts book increased my understanding of this concept.