Line 3 v line 4 in the opening

[PeterPeter]

In response to:

Each step by White adds only 2 points of territory in the limit, while each step by Black (this early in the game) adds more than 3 points worth of influence. (Dr. Straw and I are in close agreement about that.)

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.

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Click Here To Show Diagram Code

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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?

[EdLee]

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. )

[PeterPeter]

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.

[Uberdude]

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.

[Abyssinica]

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

[paK0]

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.

[wineandgolover]

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

[Aidoneus]

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.

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?

[Uberdude]

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

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.

[shapenaji]

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.

[PeterPeter]

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.

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?

[PeterPeter]

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?

[ez4u]

See also the page at SL.

[Bill Spight]

In response to:

Each step by White adds only 2 points of territory in the limit, while each step by Black (this early in the game) adds more than 3 points worth of influence. (Dr. Straw and I are in close agreement about that.)

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.

$$Bc
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X X X X X X X X X X X X X . . . |
$$ | . . 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 . . |
$$ | . . . X X X X X X X X X X X X X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+

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 . . |
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$$ +---------------------------------------+[/go]

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?

Is White wrong to give Black 8 extra moves?

[shapenaji]

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.

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?

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.