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Making shapes with two eyes
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Author:  NPW [ Sun Dec 23, 2012 2:23 am ]
Post subject:  Making shapes with two eyes
I understand that if you can make a shape with two eyes your opponent cannot take that shape. What I am not sure about is should you deliberately try and create such shapes as you set out on a game. In the beginners games I have played so far they have rarely if ever featured. What I was wondering is should I have some 2-eyed shapes in mind as I play my matches and should I deliberately try and create them? Any thoughts on this gratefully received!
Author:  Phelan [ Sun Dec 23, 2012 2:42 am ]
Post subject:  Re: Making shapes with two eyes
Basically, yes.
It's very important that all your groups are able to make two eyes at the end of the game, or else they can likely be killed.

However, the concept of life(being able to make two eyes), gets more and more complex as you advance in Go.

To answer you more precisely, could you explain what you mean by two eyed shapes?
Click Here To Show Diagram Code
[go]$$B Two-eye-formation
$$ ---------
$$ | . X . X |
$$ | X X X X |
$$ ---------[/go]
Do you mean something like this?
Author:  EdLee [ Sun Dec 23, 2012 2:44 am ]
Post subject: 
NPW, very good question. Let's look at this (contrived) example:
with every move, Black deliberately tries to make a 2-eye living group as quickly as possible;
after :w10:, Black indeed has succeeded in making one living group, whereas White has ZERO eyes.
However, White has a huge lead overall in this game:
Click Here To Show Diagram Code
[go]$$
$$ -----------------------------------------
$$ | . . . . . . . . . . . . . . . . . 9 . |
$$ | . . . . . . . . . . . . . . . . 5 . 7 |
$$ | . . . . . . . . . . . . . . . . 1 3 . |
$$ | . . . 6 . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 0 . . . . . 8 . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . , . . . . . 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -----------------------------------------[/go]
In the above example, Black's mistake is he focused on making a living group
AT THE EXPENSE of everything else, and he fell far behind globally after :w10:.

Remember that to win a game,
you want to end up with more points than your opponent -- specifically:
- Not (necessarily) more living groups than your opponent
- Not (necessarily) more eye shapes than your opponent
- Not (necessarily) more eyes than your opponent
- Not (necessarily) that you need to make eye-shape on every single move

For example, in a game, you can even give up a 40-stone group
AS LONG AS in the process you gain something more (for example, killing an even bigger group of your opponent's).
Phelan wrote:
It's very important that all your groups are able to make two eyes at the end of the game, or else they can likely be killed.
One counter-example to what Phelan said, which is very common, is if you have 10 groups, you can let 9 of them die,
AS LONG AS with the remaining live group you end up with more points than your opponent, to win the game.

So yes, you need to be aware of the STATUS of ALL your groups and your opponent's (alive, dead, ko, or seki).
And no, you don't need to save every single group -- AS LONG AS you see the global picture,
that is, you want to end up with more points than your opponent.

Of course, if you don't take good care of your groups and your opponent kills ALL of your groups, then you lose. :)
Phelan wrote:
However, the concept of life(being able to make two eyes), gets more and more complex as you advance in Go.
This is true. NPW, if you find that some or most of your groups are constantly being killed by your opponent,
it's because you are not taking care of your groups -- so AT YOUR LEVEL, you want to learn to make eyes...
However, as Phelan said above, as you improve at Go, your understanding of life-and-death will also change,
and you'll learn how to make eyes (or living groups) more efficiently. :)
Author:  NPW [ Sun Dec 23, 2012 3:06 am ]
Post subject:  Re: Making shapes with two eyes
Phelan wrote:
Basically, yes.
It's very important that all your groups are able to make two eyes at the end of the game, or else they can likely be killed.

However, the concept of life(being able to make two eyes), gets more and more complex as you advance in Go.

To answer you more precisely, could you explain what you mean by two eyed shapes?
Click Here To Show Diagram Code
[go]$$B Two-eye-formation
$$ ---------
$$ | . X . X |
$$ | X X X X |
$$ ---------[/go]
Do you mean something like this?


Hello Phelan


Yes that was exactly the sort of shape I was thinking about - and larger ones too if you are able to make them.
Author:  RobertJasiek [ Sun Dec 23, 2012 5:18 am ]
Post subject:  Re: Making shapes with two eyes
A group that shall independently live (and protect territory) must have the imagined(!) possibility of living by being transformed into a basic, minimal two-eye-formation. Usually, one does not make superfluous defense plays but protects a territory region on a larger scale; this more often allows one to play elsewhere. Only when the opponent attacks the life of a group and inside defense is the only reasonable option, the defender would transform or start to transform his group into a two-eye-formation.

http://senseis.xmp.net/?TwoEyeFormation
Author:  Mike Novack [ Sun Dec 23, 2012 6:43 am ]
Post subject:  Re: Making shapes with two eyes
I am going to attempt to describe this for beginners.

What you want to do is create shapes whose connectivity and internal space are such that even if the opponent moves first (to place a stone inside) you would be able to respond* in such a way as to to guarantee being able to have two eyes.

In other words, you need to learn for which internal empty spaces this is true and for which it is not.

What I suggest is that you first study the shapes of four or more spaces (up to 7-8) for which this is true (alive) and for which it is not (dead) for fully connected shapes. Then begin again with various defects in the connectivity of the group.

* If you did this before necessary you have wasted a move (in the earlier parts of the game) and in the endgame once all useful moves have been made, wasted a point (if your opponent did make the hopeless attack the stone he or she played and your response cancel out).
Author:  Phelan [ Sun Dec 23, 2012 7:39 am ]
Post subject:  Re: Making shapes with two eyes
As EdLee said, the goal of the game is to get more points than the opponent, so you don't need to save every group, as long as you can surround more spaces/kill more stones than the opponent.
However, one of the first things that help you improve is to learn how to kill opponents' groups, and save your own. Sacrificing groups to get a better result than the opponent is a step after, I think.

NPW wrote:
Phelan wrote:
Basically, yes.
It's very important that all your groups are able to make two eyes at the end of the game, or else they can likely be killed.

However, the concept of life(being able to make two eyes), gets more and more complex as you advance in Go.

To answer you more precisely, could you explain what you mean by two eyed shapes?
Click Here To Show Diagram Code
[go]$$B Two-eye-formation
$$ ---------
$$ | . X . X |
$$ | X X X X |
$$ ---------[/go]
Do you mean something like this?


Hello Phelan


Yes that was exactly the sort of shape I was thinking about - and larger ones too if you are able to make them.

Well, the thing, as EdLee and Mike Novack have pointed out, is that it's a matter of efficiency. If the shape's internal space is large enough, you might not need to divide it into two eyes immediately, as long as you can still divide it into two after the opponent plays inside.
Look at the below example:
Click Here To Show Diagram Code
[go]$$B Larger space
$$ -----------
$$ | . . . . X |
$$ | . . . . X |
$$ | . . . . X |
$$ | X X X X X |
$$ -----------[/go]
Even if white gets to go first, and plays inside, black can still respond and divide the space in two:
Click Here To Show Diagram Code
[go]$$W White tries to kill unsuccessfully
$$ -----------
$$ | . 7 5 6 X |
$$ | . 1 2 . X |
$$ | . 3 4 . X |
$$ | X X X X X |
$$ -----------[/go]
So you wouldn't need to divide it in two before the opponent tries to play inside.

If the space is small enough, however, a white play inside leaves black with no way to divide it in two. For instance, see the below shape:
Click Here To Show Diagram Code
[go]$$B 3 spaces
$$ ---------
$$ | . . . X |
$$ | X X X X |
$$ ---------[/go]
If white gets to go first, he can play as below:
Click Here To Show Diagram Code
[go]$$W White can kill
$$ ---------
$$ | . 1 . X |
$$ | X X X X |
$$ ---------[/go]
Which leaves black with two liberties. If he tries to capture white's stone, he's left with only one liberty:
Click Here To Show Diagram Code
[go]$$W White can kill 2
$$ ---------
$$ | 2 1 . X |
$$ | X X X X |
$$ ---------[/go]
Which leads to White capturing all:
Click Here To Show Diagram Code
[go]$$W White can kill 3
$$ ---------
$$ | . 1 3 . |
$$ | . . . . |
$$ ---------[/go]


The thing is, even if black does not try to immediately capture in this position, and passes(or plays elsewhere in a bigger board), white can still kill the group:
Click Here To Show Diagram Code
[go]$$W White can kill 4
$$ ---------
$$ | . 1 3 X |
$$ | X X X X |
$$ ---------[/go]
Now black only has one liberty, so he needs to capture:
Click Here To Show Diagram Code
[go]$$W White can kill 5
$$ ---------
$$ | 4 . . X |
$$ | X X X X |
$$ ---------[/go]
White can continue playing inside, though:
Click Here To Show Diagram Code
[go]$$W White can kill 6
$$ ---------
$$ | X . 5 X |
$$ | X X X X |
$$ ---------[/go]
Since white again leaves him with only one liberty, he needs to capture again. But if he does:
Click Here To Show Diagram Code
[go]$$W White can kill 7
$$ ---------
$$ | X 6 . X |
$$ | X X X X |
$$ ---------[/go]
He's again left with only one liberty, and white gets the whole group:
Click Here To Show Diagram Code
[go]$$W White can kill 8
$$ ---------
$$ | . . 7 . |
$$ | . . . . |
$$ ---------[/go]


So in that case, dividing it in two is necessary:
Click Here To Show Diagram Code
[go]$$B Necessary to live
$$ ---------
$$ | . 1 . X |
$$ | X X X X |
$$ ---------[/go]


There are a few shapes whose internal spaces can't be divided in two if the opponent plays there first. These are called "Nakade" in Japanese.

I think there is a good introduction to Life and Death at Sensei's Library.

Hope this helps. :)
Author:  Boidhre [ Sun Dec 23, 2012 9:21 am ]
Post subject:  Re: Making shapes with two eyes
I suppose at its simplest it's better to have a group that can unconditionally make two eyes than a group that has made two eyes. One of the signs of becoming stronger is being able to tell when a group can do this rather than the group needing one or more moves to live. When you start out it's really hard to be able to tell if a shape is alive, dead or undecided because you don't know the shapes and can't read very far ahead. With game practice and tsumego the ability to tell improves.
Author:  xed_over [ Sun Dec 23, 2012 11:46 am ]
Post subject:  Re: Making shapes with two eyes
NPW, you ask great questions!
Author:  Bill Spight [ Sun Dec 23, 2012 1:21 pm ]
Post subject:  Re: Making shapes with two eyes
NPW wrote:
I understand that if you can make a shape with two eyes your opponent cannot take that shape. What I am not sure about is should you deliberately try and create such shapes as you set out on a game.


Not at the outset.

Quote:
In the beginners games I have played so far they have rarely if ever featured. What I was wondering is should I have some 2-eyed shapes in mind as I play my matches and should I deliberately try and create them? Any thoughts on this gratefully received!


Life and death is very important. However, to live you should first make large enough territories. Where life and death matters is in close fighting and the endgame. As a rule, it is better to live by capturing the opponent's stones rather than playing safe to make two eyes. (There are many exceptions, of course.) Look to make two eyes when you are on the defensive. For instance, you may invade the opponent's sphere of influence. Then you need to escape, make eyes, or sacrifice. Life and death matters in the endgame because stones get cut off and have to live or because liberties get filled and that can yield threats to kill. For a beginner, in particular, the endgame is a good place to try to kill or capture stones. An inexperienced opponent will give you many chances. By the same token, it is a good place to learn when you need to make two eyes. :)

Good luck!
Author:  Phoenix [ Sun Dec 23, 2012 3:22 pm ]
Post subject:  Re: Making shapes with two eyes
Bill Spight wrote:

Life and death is very important. However, to live you should first make large enough territories. Where life and death matters is in close fighting and the endgame.


There's truth in these words. Your first concern before the game has reached the middle game is to expand your groups of stones. The first step to making eyes is having space for them, and expanding your base should be your first thought when trying to make groups live. It's also much more efficient than playing inside moves that don't affect your opponent's stones, losing territory and giving your opponent forcing moves or sente. :D

I personally think that life and death are important concepts at every point in the game. In the opening, it's important to determine how strong groups are. If your groups are strong you're likely to get the upper hand, since you can exploit your opponents' weaknesses (again, with knowledge of life & death) to drive the game in a favorable direction.

I feel what while territory is important at every stage (after all, it determines the outcome of the game), it is much less important in the opening than stability and territorial potential. The closer to the end of the game you get, the more important it becomes, until it is all-consuming.

Players tend to fixate on the middle game when they think of life & death. This is probably because the shapes get fixed into what we're used to seeing in tsumego. These issues of shape, strength and flexibility are just as important in the opening and endgame as they are in the middle game. If one of your groups gets chased and your opponent profits, it's because it was weak. If you suddenly lose the upper hand in the opening, it's probably because you played a big point instead of an urgent point. :mrgreen:

I preach a lot, but I'm definitely living proof that old habits die hard... :sad:
Author:  billywoods [ Thu Dec 27, 2012 4:17 pm ]
Post subject:  Re: Making shapes with two eyes
I'm probably not going to say anything new, but perhaps I can say things in a slightly different way:

NPW wrote:
should you deliberately try and create such shapes as you set out on a game

You should deliberately try to create shapes that can't be captured. That does not mean making two eyes immediately - going and playing inside your own territory to split it in half is a last-resort, emergency move. It is a move you play because, if you don't, your opponent's next move will kill you. Moves like this are either desperately urgent (e.g. because you will die if you don't play them) or very bad moves (e.g. because you played them too early). There are many other ways to make sure a group can't be captured, they're just all a little subtler. My thoughts on this are:

  • The groups in most danger are small groups, especially groups containing very few points of territory, groups with few liberties and groups with lots of defects. The ideal group contains lots of territory, has plenty of liberties and has no defects. But this is an ideal situation, and in practice it doesn't always happen...
  • Small groups with little territory inside and few liberties sometimes require emergency moves of the sort I described above - otherwise your opponent can kill them. This is usually (but not always) really big, because dead groups are sort of worth double their own weight: a group of 10 stones surrounding 3 points is worth about 2*(10+3) = 26 points to kill.
  • Groups with lots of defects and cutting points (especially when they're near each other) can sometimes be cut in half by your opponent. Sometimes, both halves can live anyway; sometimes one dies; sometimes both die. If you think your group can be split in half, you should think seriously about whether both halves can live, and (if so) how much profit your opponent can get while forcing you to live both halves. If one or both halves of your group will die, or your opponent will take huge profit while forcing both halves to live, then you have probably made a mistake; if almost all of it will live, and/or you end up with a very favourable position, then it's fine.
  • Groups that are "thin" (e.g. because they are not real, connected groups yet, but rough areas mapped out by a few stones) are sometimes subject to invasions or large reductions - your opponent will play moves that force you to defend in inconvenient places, when you'd rather be attacking, and plonk a live group in the middle of the group you had hoped to establish, or cut it in half. Sometimes, in the process of defending, you won't be able to defend 'fast' enough, and your group will grow defects, and the previous case applies.
  • Groups that are too big and have a few defects may still live, but your opponent may be able to play clever moves to live inside them, considerably reducing your territory.
  • Instead of passively protecting every stone you've put down, it might be more profitable to play 'faster' moves that allow your opponent to take a few stones now, but at a heavy price later.
  • Groups that have few liberties can sometimes be squeezed into weird positions, by what I can only describe as magic. If you're lucky, this magic might leave your group alive in seki. If you're unlucky, it might kill you outright or start a ko for life.

Don't worry about the technicalities of these - you will come across all of them in your own games at some point.

NPW wrote:
What I was wondering is should I have some 2-eyed shapes in mind as I play my matches and should I deliberately try and create them?

Hopefully you'll be able to partly answer this question yourself now - yes, when (and only when) one of the 'emergency' situations above arises, you need to be able to protect your group.

The other part of your question: should you have some 2-eyed shapes in mind? As you become stronger, this becomes very important, and is one of the purposes of training yourself to solve tsumego (life-and-death problems). Almost all introductory tsumego are small corner life-and-death situations. I generally don't recommend anything more than the most basic tsumego until you've reached 15 kyu or so, but for many players solving tsumego becomes a very important tool on the way to getting stronger - and not just so that they don't die.
Author:  Phelan [ Thu Dec 27, 2012 10:59 pm ]
Post subject:  Re: Making shapes with two eyes
billywoods wrote:
Small groups with little territory inside and few liberties sometimes require emergency moves of the sort I described above - otherwise your opponent can kill them. This is usually (but not always) really big, because dead groups are sort of worth double their own weight: a group of 10 stones surrounding 3 points is worth about 2*(10+3) = 26 points to kill.
Small correction: A group of 10 stones surrounding 3 points is worth (2*10)+3 to kill = 23 points. If you discount the play you have to make inside to kill it, it would be 22 points.
Author:  Bill Spight [ Thu Dec 27, 2012 11:47 pm ]
Post subject:  Re: Making shapes with two eyes
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . O O O O O O O . . . . . . |
$$ | . . . . . . O X X X X X O . . . . . . |
$$ | . . . . . . O X . 1 . X O . . . . . . |
$$ | . . . , . . O O X X X O O . . , . . . |
$$ | . . . . . . . . O O O . . . . . . . . |
$$ | . . . . . . . O . . . O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


:w1: kills the Black group, for 22 points.

How much does it gain? To answer that question, we need to evaluate the position before :w1:.

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . O O O O O O O . . . . . . |
$$ | . . . . . . O X X X X X O . . . . . . |
$$ | . . . . . . O X . 1 . X O . . . . . . |
$$ | . . . , . . O O X X X O O . . , . . . |
$$ | . . . . . . . . O O O . . . . . . . . |
$$ | . . . . . . . O . . . O . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


:b1: lives, for 2 points.

The original position is worth the average of these two results, or 10 points for White. So each play gains 12 points. That is a couple of points smaller than the original play in the game. :)
Author:  Joaz Banbeck [ Thu Dec 27, 2012 11:49 pm ]
Post subject:  Re: Making shapes with two eyes
Being assured of making eyes is like being assured that your car has brakes. Not having them will be a disaster. But you never try to use them immediately.

You try to accomplish other things, always making sure that you have room to brake. As the traffic gets more crowded, maybe you uses them a little. If something happens, and you find yourself suddenly in great danger, you use them immediately. And if you have planned ahead, you'll be ok.


( As my grandpa used to say, ain't nothin can't be explained with a car analogy. )
Author:  billywoods [ Fri Dec 28, 2012 3:10 am ]
Post subject:  Re: Making shapes with two eyes
Phelan wrote:
Small correction: A group of 10 stones surrounding 3 points is worth (2*10)+3 to kill = 23 points.

I'm not sure I agree. When a black group (initially assumed alive) gets killed, each live black stone dies (and becomes 2 points for white); each dead white stone becomes alive (and becomes -2 points for black); all the black territory turns into white territory (-1 for black and +1 for white). That's a total point swing of 2 points per intersection the group occupies. (Count it in Chinese scoring and it becomes somehow clearer, I think.)

The slight imprecision in this is what you said about the killing stone, of course: I can't just assume a group alive and then suddenly dead. The group will initially be unsettled, and will need an extra black move to live (which is a black move inside black's own territory, so -1 point for black) or an extra white move to kill (which - when the black group is viewed as dead - is a white move inside white's own territory, so -1 point for white). So, in a simple unsettled group which needs one move to live/kill, the point swing is 2*(number of spaces the group occupies - 1).

(This was a deliberate imprecision, firstly because it only seems to be a matter of 2 points, secondly because I didn't want to try to explain it - I see that Bill did that for me, though, and he did it well. :) Moreover, it's the rule of thumb I use in real games. Because nothing is ever a matter of one or two points in 4 kyu games!)
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