I saw a proverb that said that a single stone must be surrounded by at least twenty points to live. Is this true and how does it actually work out?

_________________
Thinking like a go player during a game of chess is like bringing a knife to a gun-fight. Thinking like a chess player during a game of go feels like getting knifed while you're holding a gun...

Such a proverb is not useful because neighbouring shapes have a great impact. In order to live, a group must locally build eyes, locally create a seki, move to and reach wide open space with two or more free movement directions or connect to another then live group.

And to learn, do a lot of Life and Death, of course I am also very much in this step.

Oh and lose 100 games. The point of this is to learn to recognize shapes and patterns and get insticts for this.

(I am starting to see patterns in my 9x9 games but far away from it in 19x19)


Is there any more advice from the more learnt.

How much space you need also depends a lot where on the board you are: you need a lot more in the centre than in the corner. Also it depends how strong the surrounding opponent is: if there is a solid wall thats very different to some stones with some weaknesses that give you some free moves in sente which is different to just one stone which is different to open space or the edge of the board. For example this white move is as dead as a dodo even if black passes many times (and it has more than 20 spaces):

Click Here To Show Diagram Code

[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X X X X X X X X . . . . . . |
$$ | . . . . . X . . . . . . X . . . . . . |
$$ | . . . , . X . . 1 , . . X . . , . . . |
$$ | . . . . . X . . . . . . X . . . . . . |
$$ | . . . . . X . . . . . . X . . . . . . |
$$ | . . . . . X X X X X X X X . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]

In fact this white stone is not so easy to live (maybe 50-50 maybe 70-30 for life depending who you ask) and it has almost 300 points to live in:

Click Here To Show Diagram Code

[go]$$W
$$ +---------------------------------------+
$$ | . X X X X X X X X X X X X X X X X X . |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . , . . . . . , . . . . . , . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . , . . . . . 1 . . . . . , . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . , . . . . . , . . . . . , . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | X . . . . . . . . . . . . . . . . . X |
$$ | . X X X X X X X X X X X X X X X X X . |
$$ +---------------------------------------+[/go]

But against this probe of 1, if black chooses the outside with 2 then white 3 has enough space to live in the corner:

Click Here To Show Diagram Code

[go]$$W
$$ --------------+
$$ . . . . . . . |
$$ . . . . 5 . . |
$$ . . X 4 3 . . |
$$ . . . , X 1 . |
$$ . . . . 2 . . |
$$ . . . . . . . |
$$ . . . . . . . |[/go]

Or invading at 3-3 under a lone 4-4 stone lives easily:

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . 1 . . |
$$ . . . . . X . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

But a lone 4-4 with some monstrous walls nearby could kill the 3-3 (in fact black can probably pass and still kill):

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . X . . . . . . |
$$ . . X . . . . . . |
$$ . . X . . . 1 . . |
$$ . . X . . X . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . X X X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

Or if black adds some normal shimari moves he can also kill the invader (but shouldn't pass):

Click Here To Show Diagram Code

[go]$$W
$$ ------------------+
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . X . . 1 . . |
$$ . . . . . X . . . |
$$ . . . . . . X . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

I don't use any proverb like "you need 20 points to make eyes", but knowing many common shapes like the tripod group, L groups, J groups, comb formation, carpenter's square, door groups and notchers gives me an idea of if it's plausible to live in some space. And simply a lot of experience of failed and successful invasions.

How much space is needed to live? Here is the way that I interpret that question: What is the minimum spaced needed to live without capturing a stone that is already on the board and the opponent tries to kill with best play?

Well, we know that in the corner it takes 8 points to make independent, unconditional life, room for 6 stones and 2 eye points. If we assume that the opponent makes 5 replies before we live, that comes to 13 points. However, with correct play it should be easy for the opponent to play on a vital point, so that more points are required. If we add one point for the second eye and three points for the stones to surround it on the edge and three points for the opponent's plays, we get 20 points. Maybe we can make the second eye with only two extra stones, then we get 18 points.

OC, seki is another way to live. Minimal seki on the edge in the corner takes a 5 point eye (3 opposing stones plus 2 dame points) plus 7 surrounding stones. That's 12 points. Add 3 more points for a total of 6 opposing moves, and we get 15 points.

On the side it takes 2 more stones to live than in the corner, so add 4 points to those totals. The minimum is then 17 points for invulnerable life, with 20 or 22 points perhaps more likely, and 19 points for seki.

I suppose that some pro came up with the 20 point heuristic after seeing a lot of amateurs invading regions with fewer than 20 points and expecting to live without capturing one or more of the existing stones. Such invasions are pretty much doomed, as the above numbers indicate. Also, as Uberdude has shown, 20 points may not be enough. (OC, sometimes you invade with the expectation of sacrificing or running out. In that case you do not require so much space. )

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

Visualize whirled peas.

Everything with love. Stay safe.

It sounds like something I've seen Yilun Yang teach as a general practice that 20 point areas or greater are possible and often should be invaded.

maybe this visualization will help (from http://senseis.xmp.net/?SmallestGroupWithTwoEyes )

Click Here To Show Diagram Code

[go]$$B Smallest groups with [two eyes]
$$ ---------------------------------------
$$ | . X O . . . O X X . X O . . . O X X . |
$$ | X X O . . . O X . X X O . . . O X . X |
$$ | . X O . . . O O X X O O . . . O O X X |
$$ | X X O , O O . . O O . . O O . , . O O |
$$ | O O . O X X O O . . . O X X O . . . . |
$$ | . . . O X . X O . . . O X . X O . . . |
$$ | . . . O X X . X O . O X . X X O . O O |
$$ | O O . O O X X X O . O X X X O . O X X |
$$ | X X O . . O O O . . . O O O . . O X . |
$$ | . X O , . . . . . , . . . . . , O X X |
$$ | X . X O . . O O . . . . O O . . O X . |
$$ | X X X O O O X X O . . O X X O . O X X |
$$ | O O O O X X . X O . O X . X X O . O O |
$$ | . . . O X . X X O . O X X . X O . . . |
$$ | . . . O X X O O . . . O X X O O . . . |
$$ | O O O , O O . . O O O O O O . , O O O |
$$ | O X X O . . . . O X X X O . . . O X X |
$$ | X . X O . . . O X X . X O . . O X X . |
$$ | . X X O . . . O X . X O O . . O X . X |
$$ ---------------------------------------[/go]