Influenced by influence

In Go theory, you will often hear talk about influence and territory.  Commonly, you will place stones on the board with one of these two in mind. Which should you pick, and why? The answer I found most sensible is that you should aim for a balance between these two.

Now let's see what some of the words in the previous paragraph actually mean.

One easy way to understand the difference between influence and territory is to redefine them as "fourth line" and "third line", respectively¹. The 4^th is typically called "the line of power" or "the line of influence", whereas the 3^rd is called "the line of territory" or "the line of profit".

The line of territory

If you look at the 3^rd line, it's easy to understand why it is called thus. A play on the san-san (3-3) point lives in the corner. A two-point jump on the 3rd line is a base for making life (typically, you can follow up with a keima on the second line on at least one side, and that should get you settled; you can also commonly jump out, and two eyes should be forming pretty quickly).

It's good to know that the 2^nd line is known as "the line of defeat". This is because for each stone you place on the 2^nd line, your opponent can place one on the 3^rd line, just above it. You are getting one point for each stone, and he is getting a wall on the outside. We will see what this wall is good for a bit further on, but keep in mind that if this same thing was happening just one line higher, you'd be more comfortable with making life, as well as get twice as many points! Don't crawl on the second line if you can avoid it.

The line of power

So what's this about power? Well, conversely to the 3-3 point, a stone on the 4-4 point doesn't secure the corner at all! There is a simple joseki that involves a 3-3 invasion under the 4-4 stone that lives unconditionally. The 4-4 stone needs at least one more stone to secure the corner. If you make an extension² from the 4-4 stone, then you need at least one more stone to secure the corner.

Similarly, if you play a san-ren sei (three stars in a row) opening, you can expect that your opponent will  perform an invasion on your side, and accomplish something with it. The fourth line is too far away from the edge to keep it safe from harm, and you really shouldn't even try to keep all of the side on which you played the san-ren sei. You will get territory from these stones later on on the game. How? Well, that's kind of the point of this post. I had³ a lot of trouble figuring out exactly how to use influence to my advantage, and writing this is about starting to figure that out.

Linking theory and practice

Here is a game.

2012-05-25-viton-Median.sgf

In it, I won by half a point. Skim over the game, quickly, please. Have a look at the end result. I have two corners, he has one. One corner belongs to no player. I have stakes on three sides, and tiny territory in the middle. The only thing he really has is the vast territory in the middle, and it is an even game! How did he build that? Influence. Probably the vital moves for building this framework were 22 and 36. Once I saw the wall he has built, I wanted to let him expand from it, and see who would come out on top. Walls such as the one on C14-G14 are very valuable. If you want to weigh it more precisely, here is a simple calculation:

Imagine that black is building a wall on the 3rd line, and white is building a wall on the 4th line just above the black stones. What does white need to do with his wall to catch up (in actual territory)? Obviously, he needs a box-like shape that is two lines wide, right? I say two lines, because the black territory can be no bigger than two lines. So, all white needs is a few two-point jumps, right? Right. BUT! If white's wall is long enough, he can afford to make a much longer jump. Why? Because if white has a wall that is 6 stones long, and makes two 5-point jumps on each side of that wall, making a box-like shape, black will have an extremely hard time living inside that framework / killing it. All black can really do now is to try and reduce it. But this shape was so much bigger than what black had in territory, that white can afford a reduction. White was ambitious, and it payed off.

Another example!

2012-05-22-justed-Median.sgf

This game involves a failed fight for life in the middle. The outcome of the game is similar to the last one, though. White won with a 10 point lead, and didn't have a single corner! If you look at white's opening, you can see he was clearly experimenting (should I say - fiddling?) with influence. Looking at the final state of the board sort of invites the following analysis: Imagine that black has a wall on the third line on the bottom of the board, and a wall on the third line on the top of the board. White has walls on both fourth lines. Who has more territory? Four lines are occupied by stones, Black has 4 lines, and white has 11. Obviously, this is a fictional calculation, and the 11x19 area would invite an invasion, but in a real game, if you aim for 4 corners, and linking them up similarly to what I had in this game, you are basically giving away much more than you should.

Let me provide another example.

2012-05-27-Median-Marta.sgf

Here I didn't really think about this concept during the game, but it is still a nice example of the difference between influence and direct profit. Every invasion I made here was on the third line, and thus profit-oriented. My fuseki is also strongly turned towards territory, whereas black is gaining a lot of influence. You can see the outcome - it was very difficult for me to cope in the middle game, because black forces had more support all around. I made a massive reduction of black territory, and still lost the game. That is the power of the fourth line.

Nothing is simple

I'd like to put emphasis on the fact that this territory/power relationship does not come down only to choosing 3^rd or 4^th line. Go is a very complex game, and this is probably the simplest way to understand the difference, but in reality, there are many ways to go about these general ideas. The white fuseki in the second game is a good example.

So, the lessons to take from this post are the following:

• Be aware of what your are playing for - influence or profit.
• When you do pick a strategy, make sure to stick to it, and steer the play towards your strength and the opponent's weakness.
• If your opponent is playing an influence game, make sure you defuse that influence as soon as possible, and preferably, try to get some profit while you're doing it.
• If your opponent is playing a territory game, try and make a strong "power" wall against his "territory" wall, and use it to gain more than him in the long run.
• Do not focus exclusively on profit or exclusively on influence.

Now go and play some games! :) Or write a comment.


¹ "Third" and "fourth" here doesn't limit to any specific side of the board - it is merely the third or fourth line from an edge, whichever edge you may happen to be looking at.
² Typically this would be a keima (knight's move) or a  kosumi (diagonal) on the 3^rd line.
³ Have