| Position 1 | Position 2 |
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A simplistic definition is that secure(d) territories are ones which the opponent cannot safely invade. But to say that is like to say nothing - its pretty obvious. The question is - what kinds of territories are secure(d) and what kinds are still possibly open to invasion?
I do not think that it is possible to give a comprehensive answer to this question. Why? Because each territory is different, and even if we could look at the collection of all possible territories - we would still don't know for sure! You see - to give a precise answer to the above question we would have not only to know about each possible territory (and thus each possible Go position), but also about the best (i.e. perfect) play in each case. We will run against the same problem during the discussion of the status of groups (see here), with as few concrete conclusions as on this page.
Trust me - it is a very hard nut to crack. An impossible nut! :)
So, how can we tackle the problem, since tackled it must be?
Honestly - I am not really sure.
I thought maybe to give a few examples of really small live groups... and then give some examples or territories which are too small for such groups to be created inside... and then maybe give some examples of territories which are theoretically large enough but in which invasions are still impossible due to territory owner's interventions? Sounds ok? This will nicely circumvent (and lead in) the problem of weak points which is discussed on the next page.
Perfect! So - here we go...
As you can learn here, for a group to be unconditionally alive (this means - it cannot be killed under any circumstances!) it needs two firm eyes. Since a smallest eye is 1 point large, and a group needs two of them, this pretty much puts a lower limit on how small such groups can be.
Below I give a few examples of some of such smallest possible living (two-eyed) groups. Each of the black groups has two firm eyes and is thus unconditionally alive. This should give you some kind of an idea how big a territory has to be to allow such enemy group(s) to be formed inside.
| Position 1 | Position 2 |
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One immediate and unescapable conclusion is that unless a territory is large enough to house such group, it is pretty pointless to invade there! Unless, of course, there are some weak points to exploit, but this will be discussed later. The only exception to this conclusion that I can think about is when the territory being invaded is small enough that by an invasion one can prevent it from making two eyes and thus killing the group which fences-off the territory. But this, again, is in the realms of both the weak points and the status of groups discussions. So let's ignore it for now, ok?
Now, lets look at some examples of territories which are too small and too strong to invade. Lets see what a pointless invasion looks like.
| Position 1 | Position 2 |
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First, lets look at the Position 1 of Figure 2. The kinds of moves you see there (all marked '1') are moves you will typically see complete beginners playing. A beginner usually lacks the experience and the understanding to realize that these moves are pointless. They can actually, depending on rules used (see here), lose points and thus even lose the game! What do such beginners think? Well, I guess they either think "Let me try, maybe something goes here" or "I know I should not play inside my own territory, but I am not sure about passing, so let me play inside my opponent's territory, see what happens". Well, let me tell you - both of these lines of reasoning are wrong! And anything similar you might be thinking, that is wrong as well!
This is exactly where this page comes in. I hope after reading it, and thinking about it, you will not make such moves anymore.
Now, lets look at Position 2 of Figure 2. I did not placed any "invasion" moves there, for a reason! And the reason being that all such moves, from either side, would be as pointless as the moves in previous position. Each of the areas, both black and white, is too small to allow creation of an enemy live group. Convince yourself - try fitting any of the small live shapes from Figure 1 into any of the territories here, and you will see - none would fit! At the same time, the territories (and the groups fencing them off) are solid and strong enough so that there are no weak points to exploit - trust me on that for now.
So, when confronted with a position like the ones in Figure 2, the best possible thing you can do is to pass, let your opponent pass as well, and count the score to see who won the game. And if your thirst for Go is not yet satisfied, play another game. Do not, I repeat - do not! - drag the game on by making pointless moves! It only annoys your opponent, prevents you both from having fun and learning, and wastes valuable time which could have been pleasantly spent on playing another game.
Now, lets look at some territories which, even though theoretically large enough to create a small opposing living group inside, are nonetheless strong and solid enough to make any such invasions futile.
The first example will be build on top of our trusty simplistic position which I have already talked about on the previous page (Supplement #1, Page 04, Figure 1.) Lets assume Black got over-ambitious and attempted an invasion at '1' in Position 1 of Figure 3. This invasion is unreasonable, even though there seems to be enough area around to allow for Black to create a two-eyed group.
| Position 1 | Position 2 | Position 3 |
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| Starting Position | Move Sequence | End Position |
Why is this invasion unreasonable, you may ask. And it is a very good question, indeed. The simple reason is that it is possible for White to foil Black's attempts and thus do not allow him to create a two-eyed group. The recognition of the fact is not a simple matter, and it will come with more play and more experience on your part. For now, to get the process of gaining such experience going, let us look at how exactly White prevents Black from building a live group.
In Position 1 of Figure 3, Black has played '1' to attempt to create a live group and make the invasion a success. And he would have done it too, if not for the fact that the next move is White's and he can play such as to crap the available space and deny life to Black's stone(s). Lets look.
The sequence given in Position 2 of Figure 3, starting with White '2', is one of the possible continuations after the Black invasion. There are other continuations possible which would prevent Black's stone(s) to survive. It takes some thinking, but even passing thus and allowing Black to have another move there (this would make two Black moves in a row) is possible - White would still be able to deny life to the Black stones! But this is more complex and I certainly do not encourage you to pass when faced with an invasion until you really know what you are doing.
Some of the alternatives to White '2' in Position 2 would be for White to play at '4', or even at '9'. Playing at a point immediately to the left of '8' would also be good. Almost any move in the area would help preventing Black from building two eyes there. The important idea is that the motivation between such "preventive" moves if to try to limit the space in which the opponent can attempt a creation of a group. This is important!
The final position, after the invasion sequence, is shown in Position 3 of Figure 3. I hope you can agree that there is no room now for the Black to make two eyes. Which means that White's territory is safe and that the invasion was a failure.
Now, lets look at a more real-life example.
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The position in Figure 4 might look familiar to you. This is the end position of the example game I presented at the end of the Go Rules discussion (see here.) It is the position in which, in the actual game, both players passed and the scoring process begun (given here and here.) One of the unanswered question in this game remained - "Why did they pass?" The time has now come to try to answer this question.
First, let me state that the only territory left which is theoretically large enough to allow creation of an enemy live group inside the Black area in the upper right corner. Next, lt us try to visualize some of the possible outcomes on a theoretical invasion White might hope for in that area.
| Position 1 | Position 2 | Position 3 |
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| Hypothetical goal #1 | Hypothetical goal #2 | Hypothetical goal #3 |
Each of the White triangle groups in each of the respective position in Figure 5 constitutes a live group - and as such would be a great outcome of any kind of invasion! Lets first consider the kinds of things White has to think about before invading, and then we will see how easily Black can foil any plans in that area.
If White wants to contemplate invading the upper right corner of Black, the first question would be to ask - which of the outcomes shown in Figure 5 is the most achievable. The second question would be - what is the invading move (which is the first move of an invasion) and a possible continuations These two questions are usually closely related, and you answer the first by answering the second (or at least having some kind of a plan for a sequence of moves with a likelihood for success.) Any such considerations are also strongly related to the presence of any weak points (discussed on the next page) - such is the case here as well, the weak points being the points marked 'a' in Figure 4. Thus White concludes that the most promising course of action is to go for the outcome depicted in Position 2 of Figure 5. So, here we go...
| Position 1 | Position 2 | Position 3 |
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| Using weaknesses '4' connects right below '2' |
...continuation... | and final failure |
In Position 1 of Figure 6, White plays '1' and '3' to use Black's weakness - and indeed, instead of limiting White's invasion space, Black is forced to answer at '3' and '4' to avoid a big loss (each of White's moves here threatens to capture the four black marked stones, so there is no choice.) So far so good, this Position went exactly as planned. But what next?
Well, next - nothing. No matter how hard White tries, if Black remains vigilant and blocks White's attempts, there is no way White stones can survive there! One possible continuation is shown in Position 2 of Figure 6, and the result of the sequence is shown in Position 3. White's invasion is a failure! You might check it yourself by trying out some other sequences, even some other starting moves by White, but if you remember that all Black has to do is to limit White's space - you will realize that any White invasion in that area is pointless.
And this is why the players in the actual game both passed.
Invading enemy territories is not easy, especially near the end of the game. The key points to foiling such invasions is to try to limit opponent's space. Failing that, the key is to prevent him/her from bringing the invading stones to life by making two eyes (see here for some more info about that.) Another important point in foiling invasions is making your territories secure enough, which means considering any weak points the opponent might use and deciding if they need defending ahead of time.
From the point of the invader - the key point is not as much to have enough room inside enemy territory to create a live group, but much more the question of any existing weak point in the enemy shapes and the ways to use these weaknesses.
I will talk about such weak points on the next page.