In response to:

To borrow an example from Bruce Wilcox, on this board, black has played exclusively on line 3. He has played 52 stones, to secure 140 points, which is 2.69 points per move.

White has played exclusively on line 4. He has played 44 stones, to secure 121 points, which is 2.75 points per move.

Click Here To Show Diagram Code

[go]$$Bc
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$$ | . . . X X X X X X X X X X X X X . . . |
$$ | . . X , O O O O O O O O O O O , X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . , . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X O . . . . . . . . . . . O X . . |
$$ | . . X , O O O O O O O O O O O , X . . |
$$ | . . . X X X X X X X X X X X X X . . . |
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If black is wrong to settle for a row of stones on line 3 in exchange for giving white a wall on line 4 in the opening, is it due to this slight points-per-move shortfall, or some other reason?

_________________
Regards,

Peter

Hi Peter,

Interesting.

- As we decrease the board size (17x17, 15x15, ...), will W start to lose this contest ?

- As the board size increases (19x19, 21x21, ...), does the difference between B's and W's points-per-stone values converge or diverge ?

(I'm lazy. And it's sleep time. Also, B has 8 more stones on the board than W in Bruce's example. )

As the board shrinks, white should lose more points than black. And vice versa.

This is my preferred theory for why we play on a 19x19 board:

1. On any size board, line 3 is the highest line that secures territory.
2. With this size board, the next line up is worth almost exactly the same points-per-move.

So, the territory-influence trade-off is almost perfectly balanced. No other board size achieves this.

Perfectly good games can be had on smaller or bigger boards, but 19x19 has this special quality.

_________________
Regards,

Peter

Note that in your whole board example there are corners, in Bill's it was just a side position. At the corners the influence of white's stones overlaps so they are less efficient, securing less than the average points per stone. Conversely at the corners the influence of black's stones underlap so they are more efficient here. Your averages are thus biased by the corners. A more relevant calculation would be to increase the bosrd size by one and give each player 4 more stones and see how much more incremental territory each player gets.

I wonder how go would be if we had stuck with 17x17.

Is this even relevant? Since the example uses the wall only for making territory and not for invasions/fighting, so white might actually be better of than the example lets on.

It seems that white used influence to take territory and lost. If only there was a proverb counciling against this.

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- Brady
Want to see videos of low-dan mistakes and what to learn from them? Brady's Blunders

To quote George Bailey, "This is a very interesting situation!"

What if we just focus on the common joseki trade offs near the corners? Isn't the territory/influence balance more-or-less equal by definition of their being joseki?

But white won this game in the sense of being more efficient which makes more sense than absolute score as they didn't play the same number of moves. But if white plays the 4-4 points he loses so it's somewhat arbitrary.

This is also a weird example, because white's territory requires the existence of all 4 sides. Black, however, could lose 3 of his walls, and still be left with territory.

So the lesson is, a 4th line wall is efficient, if you can use it.

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Tactics yes, Tact no...

Imagine that after completing his third wall, black invaded white's moyo. Due to his overwhelming influence, white was able to kill that invasion. Do you think the end result (in terms of points difference) would be very different from the initial example?

_________________
Regards,

Peter

I agree that it is a very contrived example. In many areas (economics, to name one), when faced with an impossibly complicated situation, you start off with a simplified model. Then, you see what its limitations are, and what conclusions you can draw from it.

Do you think that it has any validity when looking at a small wall on one side only? If not, after how many sides/stones does it start to become useful?

_________________
Regards,

Peter

See also the page at SL.

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Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

Is White wrong to give Black 8 extra moves?

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Right, the point I'm making is that the territory looks very solid right now that it's completed, but over the course of the game, that center was significantly more fragile.

_________________
Tactics yes, Tact no...

About the average points per move in a final position, you cannot judge the points per move of early play. At the end of a fairly typical game there will by around 240 stones on the board and around 120 points of territory, for an average of about 1/2 point per stone. But early in the game stones gain around 14 points of territory.

The stones in the middle of a center facing wall on the 4th line early in the game basically gain points in only one direction. That would be around 6 points. However, overconcentration and the difficulty of making territory in the center bring it down. My estimate is a bit over 3 points.

The territory made by stones in the middle of a side facing wall on the 3d line is easier to estimate. Once the wall is safe, each stone makes 2 points of territory.

Later in the game the value of center facing walls is typically less, while the value of side facing walls remains the same.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I think that this is precisely the problem with the contrived theoretical examples. They ignore the time factor. And this goes back to my question about limiting the discussion to a corner sequence between territory/influence. Please correct me if I am completely mistaken but I thought that an important reason for delaying 3-3 invasions against hoshi points is that the territory gained is less than the influence granted during the early game? Though I have no idea when such a balance might swing the other way. (Of course, joseki are not pure 3rd versus 4th line, which complicates the analysis.)

This is correct, and figuring out the correct timing for an invasion, so that you don't help your opponent more than you help yourself, but before they remove the option without giving away too much by losing sente, is tricky.

Generally, you have multiple ways of dealing with a 4-4 stone, of which invading the 3-3 point is only one of them. Ideally, you keep all of your options open, since as the game progresses, you may prefer one or the other. Once you pick one, the others are gone. If you are going to invade, ideally you do so one move before your opponent closes it off to consolidate his moyo. Another good time is when you have a good followup to reduce the influence of the wall he creates, like a good capping move or something, that you would would want to play anyways. If the reduction isn't something you'd consider playing without the influence the invasion would give, don't play the invasion.