Life In 19x19

Recently I've been making a bad habit of capturing up side territory but allowing my opponents to create such large moyos that they are ahead in points. This results in my having to jump into the middle of their moyos and try to make life or snake out and connect to my stones.

I know that there is a flaw in my play that needs to be corrected, but it led me wonder if there was a certain space in which one could invade and was guaranteed life (i.e. if there is a space that is 10 spaces by 10 spaces then the invading player makes two eyes regardless of what is outside of that area).

All thoughts and ideas are welcomed.

Sounds a bit like this game:

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

Click Here To Show Diagram Code

[go]$$W White to play and live
$$ --------------------------------------
$$ | . B . B . B . B . B . B . B . B . B . |
$$ | B . . . . . . . . . . . . . . . . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . , . . . . . , . . . . . , . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . . . . . . . . . . . . . . . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . . . . . . . . . . . . . . . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . , . . . . . , . . . . . , . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . . . . . . . . . . . . . . . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . . . . . . . . . . . . . . . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . , . . . . . , . . . . . , . . B |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | B . . . . . . . . . . . . . . . . . B |
$$ | . B . B . B . B . B . B . B . B . B . |
$$ --------------------------------------[/go]

If there is such an area it would have to be bigger than 9x9 since obviously if w plays first on a 9x9 board she can make a living group.

Are you sure there is such a thing as "a certain space in which one could invade and was guaranteed life"?
Can you guarantee that a 30k will make life in a space 19x19 in an even game against a dan?

gowan wrote:If there is such an area it would have to be bigger than 9x9 since obviously if w plays first on a 9x9 board she can make a living group.

Outside walls are a lot different than black walls.

Here are the things I considered about this question:

1. On a 5x5 board, with perfect play, black can always kill white. Black takes the center point and then any move white plays is basically a futile invasion of black's board. So a 5x5 area definitely is not large enough. This has been proven and the board-size is declared solved. (Ideal komi then is 24 for territory scoring and 25 for area scoring)
2. A 6x6 board does allow both players to live with optimal play and fair komi is currently set at 4. http://senseis.xmp.net/?6x6 So the area does need to be at least 6x6 for the invader to live assuming we are only dealing with edges of the board on the outside.
3. If you invade on the 3-3 point inside a 4-4 with no other stones in the area then your opponent cannot stop you from making unconditional life (although with the double hane variation they can make it small life). This means that with moves that threaten other things (like making life on a side vs. in the corner) can allow a player to live in a relatively small area. This, of course, assumes that you do so on an edge.

So it seems that edges are a very important factor.

4. Making life in the center is really hard, but seems possible in the Shape Game mentioned earlier (my club plays this where the entire edge is considered to be black stones and everyone still lives in the end). With perfect play perhaps it is not because black would seem to control all ladders, but it also seems that white should be able to double-threaten making an eye at least twice.
5. In professional play, players are able to make life in very small areas, even in the center. However, they are not always successful. It would seem that professional play (pretty much the best thing we have to go on) would imply that making life straight up in the center is possible, but incredibly challenging.
6. Pros almost always live in the center by making double threats against walls or by settling for a ko. Whether you poke at a wall or settle for a ko, this means that the outside of the board absolutely matters.

What is on the outside seems to make a lot of difference.

So, I would argue this:

1. It is easiest to invade a corner because the edges seem to help make life. But could you play and live in a 6x6 corner that looked like this? Probably not. Black can just try to force white into a box-4 corner.

Click Here To Show Diagram Code

[go]Wm1 White to play and live?
$$ -----------------
$$ | . 8 9 . . . X .
$$ | 7 . 3 2 . . X .
$$ | . 5 1 0 . . X .
$$ | 6 4 . , . . X .
$$ | . . . . . . X .
$$ | . . . . . . X .
$$ | X X X X X X X .
$$ | . . . . . . . .[/go]

If white cannot live here then that would imply that at least a 7x7 area is required, and that is just in the corner!

2. The side is the next easiest to invade, but that would need to be an even larger area. Perhaps as large as 9x9!

Click Here To Show Diagram Code

[go]$$Wm1 White to play and live?
$$ ---------------------------------------
$$ | . . . . X . . . . . . . . . X . . . . |
$$ | . . . . X . 3 7 9 5 4 . . . X . . . . |
$$ | . . . . X . . 6 8 1 . 2 . . X . . . . |
$$ | . . . , X . . . . 0 . . . . X , . . . |
$$ | . . . . X . . . . . . . . . X . . . . |
$$ | . . . . X . . . . . . . . . X . . . . |
$$ | . . . . X . . . . . . . . . X . . . . |
$$ | . . . . X . . . . . . . . . X . . . . |
$$ | . . . . X . . . . . . . . . X . . . . |
$$ | . . . , X X X X X X X X X X X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

This looks hard. Maybe white can later find enough weaknesses in black's position, but I don't think I'd take white in this fight if I had the choice.

3. For living in the center the area must either be very large or you must be able to exploit some type of weakness (be it direct weakness or a ko threat). For that, the Shape Game mentioned earlier would be the thing to analyze. You may need a 17x17 space to make this work unconditionally.

EDIT: I tried this 9x9 living situation and it looks like success may not be possible. I tried myself and failed then had 4 other programs take a crack at it. GnuGo gave up and didn't even try. Pachi tried and quickly failed. MoGo really failed (it couldn't analyze the position correctly). And in two attempts Fuego failed to live (did two with Fuego since MoGo didn't work and Fuego seemed the closest). Here is the SGF of those tries -

gowan wrote:If there is such an area it would have to be bigger than 9x9 since obviously if w plays first on a 9x9 board she can make a living group.

Is that supposed to say you can live in any 9x9 area on the board?
Challenge accepted!

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . X . . |
$$ | . . . 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 . . . . |
$$ | . . . . X X X X X X X X X X X . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . X . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]

White to move. Go ahead. live in the center.

It doesn't make sense to compare 9x9 block of stones to a 9x9 board, because a 9x9 board is not surrounded by stones. The sides and corners have special properties that don't exist when you are trying to live in a walled off area.

tchan001 wrote:Are you sure there is such a thing as "a certain space in which one could invade and was guaranteed life"?
Can you guarantee that a 30k will make life in a space 19x19 in an even game against a dan?

Is there any group that a 30k will always make like with against a dan or sdk or whatever? Surely you're interested in could a 5d live against another 5d here kind of stuff no? Otherwise many, many living shapes are dead because they require some simple tesuji to find life that you can't expect a 30k to be able to find yet.

kaimat wrote:Recently I've been making a bad habit of capturing up side territory but allowing my opponents to create such large moyos that they are ahead in points. This results in my having to jump into the middle of their moyos and try to make life or snake out and connect to my stones.

I know that there is a flaw in my play that needs to be corrected, but it led me wonder if there was a certain space in which one could invade and was guaranteed life (i.e. if there is a space that is 10 spaces by 10 spaces then the invading player makes two eyes regardless of what is outside of that area).

All thoughts and ideas are welcomed.

Kaimat, I've seen professional authors talk about X number of inner spaces on the side, a lack of stones below a certain line within this area and access to the centre (and for you to have somewhere in the centre to run to) as being guaranteeing of life for the invasion (assuming you don't screw up ). One thing that was cautioned was that you need to consider whether there are forcing moves inside this space. If there are then the invader may need less space to live if they are sealed in since they may get free moves that allow them to settle.

I'm pretty sure it's something that's very hard to generalise about unless you are talking about flawless walls surrounding an empty space. As soon as you have cuts and stones related to the wall hanging around inside the area then you can't talk about "a small enough area not to be able to live" anymore much of the time.

Actually, an example is best:

What I've read is that spaces like the below White should always be able to live if they can find the correct (or one of the correct) points to invade at. Assuming that they can find life in the centre by connecting out if needs be that is.

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . X ? ? ? ? ? ? ? X . . . |
$$ | . . . . . . . . ? ? ? ? ? ? ? X . . . |
$$ | . . . . . . . . ? ? ? ? ? ? ? . . . . |
$$ | . . . . . . . . ? ? ? ? ? ? ? . . . . |
$$ +---------------------------------------+[/go]

Ignore the plausibility of the diagram.

Boidhre wrote:

tchan001 wrote:Are you sure there is such a thing as "a certain space in which one could invade and was guaranteed life"?
Can you guarantee that a 30k will make life in a space 19x19 in an even game against a dan?

Is there any group that a 30k will always make like with against a dan or sdk or whatever? Surely you're interested in could a 5d live against another 5d here kind of stuff no? Otherwise many, many living shapes are dead because they require some simple tesuji to find life that you can't expect a 30k to be able to find yet.

What I'm interested in is the word guarantee. If you guarantee something, it means that it works regardless of the skill of the person involved. So in that regard, I'm saying that there is no such space which can absolutely guarantee life on a 19x19 board.

it works regardless of the skill of the person involved

Wat?
Basically you're saying there is no arbitrarily large area which will give an invader (without extra stones for him around) life in all possible move sequnces. (Because if you allow for arbitrarily stupid people we need to allow every move at every turn.)
Obviously we can always find a move sequence that will not live (and thus might be played by some complete idiot).

Taking skill out of the equation is a good idea, but it should go the other way around: assume perfect play. What size area is "just big enough" for life?

tchan001 wrote:

Boidhre wrote:

tchan001 wrote:Are you sure there is such a thing as "a certain space in which one could invade and was guaranteed life"?
Can you guarantee that a 30k will make life in a space 19x19 in an even game against a dan?

Is there any group that a 30k will always make like with against a dan or sdk or whatever? Surely you're interested in could a 5d live against another 5d here kind of stuff no? Otherwise many, many living shapes are dead because they require some simple tesuji to find life that you can't expect a 30k to be able to find yet.

What I'm interested in is the word guarantee. If you guarantee something, it means that it works regardless of the skill of the person involved. So in that regard, I'm saying that there is no such space which can absolutely guarantee life on a 19x19 board.

Yeah I just think it's not a very useful way of interpreting the word guaranteed if we're not going to assume good play by the invader. I mean, otherwise we're just saying "if you play badly enough then nothing can work" which isn't very interesting. I know a 30k can die doing a naked 3,3 invasion under a lone 4,4 stone. It doesn't really affect my opinion of such invasions either way.

kaimat wrote:Recently I've been making a bad habit of capturing up side territory but allowing my opponents to create such large moyos that they are ahead in points. This results in my having to jump into the middle of their moyos and try to make life or snake out and connect to my stones.

I have the same bad habit, but it's one that often leads to a won game. If your opponent is banking on that moyo and doesn't get enough points with it, you win.

kaimat wrote:I know that there is a flaw in my play that needs to be corrected, but it led me wonder if there was a certain space in which one could invade and was guaranteed life (i.e. if there is a space that is 10 spaces by 10 spaces then the invading player makes two eyes regardless of what is outside of that area).

All thoughts and ideas are welcomed.

This reminds me of the saying that someone doesn't really mean what he says before the "but." Being able to live in tight spaces is a great asset to have in go!

I think you are phrasing your question wrong. You don't get guaranteed life anywhere. However, Yilun Yang has said something to the effect of: a space of 24 points on the edge where the invader has the possibility of threatening to escape to the center is sufficient for making a living group. He might even have said it was 21 pts (3 x 7), but I don't have the book with me atm. In any case, the point is that this space doesn't guarantee you life, but that it's not unreasonable to try to live there, particularly if you play right, making forcing moves to expand your eyespace etc.

Go for it!