Cutting and Connecting

1. Connected and Cut Stones

Often when you observe a game of Go, and listen to the commentary of stronger players, you hear about a "cut" and a "connection". What do these terms mean and why are they so important in Go? As stated before, Go is a game of surrounding, not of cutting or connecting.

Well, actually - the concept of cutting and connecting stones is the second-most fundamental concept of Go - the first being the concept of surrounding. So - lets talk about connections first.

2. Connected Stones

As we already established, stones are considered connected if they are adjacent vertically or horizontally, but not diagonally. In Position 1 of Fig 2-1, the stones marked '1' and '2' are connected, while the stones marked '3' are not connected.

Position 1	Position 2

Fig 2-1. Connected and disconnected stones

The same goes for longer chains of stones - they are connected if a straight line (vertical or horizontal) can be drawn from any one stone in a chain to another stone in the chain. This is shown in Position 2 of Fig 2-1 - where again, the stones marked '1' are all connected to each other (so they form a single group), same as the stones marked '2', while the stones marked '3' are not connected and form two separate groups (separated by the diagonal "chasm").

3. Why are connected stones good?

Ok - so now that we know which stones are connected and which are not, we still have to determine "why" are connected stones better than disconnected ones.

The first reason - connected stones are stronger! Just look at the Position 1 of Fig 3-1: A single stone at (a) has 4 liberties (liberties are explained here). Now, when we add a second stone to it, like in Position 1 (b), the group will have 6 liberties! This is very important, because it means that it takes only 4 moves to capture a single stone (or even less if the stone is on the edge of the board), while it takes 6 moves to capture the connected pair of two stones! If you add another stone to this pair, like in Position 1 (c), the opponent would have to make 8 moves to capture such group!! And this is why connected stones are stronger - it takes more moves to surround them and therefore it is more difficult to kill them!

Position 1	Position 2

Fig 3-1. Connected stones are stronger and more efficient

The second reason why connected stones are better than disconnected one is illustrated in Position 2 of Fig 3-1. Observe the two black groups on the left side of the board (the two 'a's) - each of these groups is composed of 4 stones, and each of them surround 4 points of territory! So together, they surround 8 points! 8 points with 8 moves! Good! Now - look at the 8 stones in the bottom right (the 'b's) - they surround 16 point of territory!!! This is twice as much territory as the two groups on the left - and with the same amount of stones!! This is important, because it means that the stones which are connected are more efficient - because they work together!! This is another one of the fundamental concepts of Go - you have to try to make your stones work together, to support each other and enhance each other's efficiency! This efficiency is illustrated very well in Position 2 of Fig 3-1 - the two separate groups are 8 stones, and the surround 8 points - which makes 1 point per stone/move! The 8 stones on the right, on the other hand, surround 16 points - which makes it 2 points per stone/move - and this is more efficient!

Caution:
Ok - so now you know that you should keep your stones connected and why. However - as with almost everything in Go - you cannot just blindly follow this idea - a certain balance needs to be struck! Balance - this word keeps popping up during these considerations over and over - and this is because it is such an important concept! If you forget about balance, and just concentrate on one side of an issue - you will never achieve much! Like with the idea of connecting stones - if you play in such a way that you place stone next to stone next to stone, making a solid wall, then, even tho you follow the idea of connecting - you show that you completely misunderstand it! Such a way of playing, while it keeps your stones connected - is very slow and the amount of territory you will surround in such way will surely not be enough to win any games! To make an efficient use of your stones, you have to play lightly, making extensions along the side and jumping out to the center. The idea of staying connected should be in the back of your mind all the time, however - it should take more of the appearance of "being hard to cut" than of "being firmly connected". An issue which is somewhat related to this is the problem of extending along the side - and this is discussed here.

4. Cutting stones

Now that we have talked about the importance of connecting stones - it is pretty obvious why the opposite - the cutting - is equally important! If being connected is so good, than it just makes sense that you should strive to prevent your opponent from connecting his stones - and thus you should try to cut him! By the same token, he will try to cut you, and again it only stands to reason that you should try to resist such attempts!

Look at Position 1 of Fig 4-1. It shows two black stones, which are in a diagonal relationship to each other - which means that they are not connected!! Look at the marked black stone - it just has one liberty left, namely at 'a'. If white play there, this black stone will be killed! This is shown in Position 2 - and it illustrates another important issue of cutting and connecting - stones which are not connected, can be killed and attacked separately!! Like in Position 2 - one of the black stones can die, while the other is still ok! Now, lets imagine that, starting from Position 1, it is black's turn to play, and so he can play at 'a', thus connecting his stones (and "saving" the marked one). This can be seen in Position 3. Even though they are some white stones around this group, the black stones are connected, and they have 4 liberties together - so they are in no danger of being killed!

Position 1	Position 2	Position 3

Fig 4-1. Cutting stones

This should reinforce the concept of a group of stones - the stones in a group die together or they live together, but they cannot be separated!

Caution:
Cutting and connecting stones in Go is a very important concept. Yet - as important as it is - it is not the only one! There are other concepts which are equally important - and which seemingly run contrary to the principle of connecting. An example of such concepts is the concept if fast development which urges you to place your stones far apart take control of the largest area (some more about it here). A wise player tries to keep all such concepts and principles in his mind at the same time, and weights them out against each other carefully before each move - attempting to strike the best balance and maximize the efficiency of his stones. And this is part of what Go is all about!