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

A neat connection problem

Black has to connect all 3 stones:

http://eidogo.com/#2aruR40

I have found this problem in SmartGo Pro, and it gave me quite a headache. In the end, I couldn't solve it, and felt a bit dumb for it when I saw the solution. ^^'

Have fun!

How I lost against a 14k and won against a 7k

Today I played two games.

The first one was against "cousin", who is a 20k? on KGS, but claimed to be around 13-14 prior to the game.

2012-05-16-Median-cousin.sgf

I didn't like my opening. Up to 6 I'm OK, but with 8 I started goofing up. Luckily, he was nice about it and didn't punish me. 8 and 10 are huge mistakes, as they leave me with no good follow-up in terms of shape. Not to mention that he could atari after 8 which I kind of ignored. That would work out for him much better than the game-play. Lesson learned! I need to spend some time on playing against approaches where I am one step behind.

27 and 29 seemed strange. He probably felt that my upper side was getting too strong. I didn't really cope with the situation well, and that sort of stuck with me up to the end of the match. I feel that 55-59 went hugely in my favor. I wanted to use that momentum to win the game. I made a game-losing mistake with 76. In retrospect, I see that I simply should have played lighter (H9, for example), and that would have been the end of it. I overthought the situation, because I was looking at that K9-H12 connection all the time, and forgot to keep things simple. Lesson learned: always ask yourself: "Is there a simpler way?"

With this in mind, I stepped into the next game. It was against a 7k called "kcang". I don't like handicaps. I really don't. I have nothing against the system per se, and I will always accept it if the other person wants to use handicap, but I rather like to not use a handicap when I am playing against a stronger player and trying to learn. I don't mind being beaten to a pulp.

2012-05-16-kcang-Median.sgf

Lately, I've been playing the first 3 moves as an opening with black quite a lot. I'm starting to dislike it, and move more into an "approach before you enclose" state of mind. So I should have played 5 at Q5 really, but I wanted to give this "passive" attitude a bit more time to settle in my mind. He chose to extend after approaching (6,8) which is gote. That felt strange, but it lifted my hopes. Tiny details, tiny details. When he invaded the upper side, I decided to pincer from the side because I had already enclosed my corner. When he takes his base, I can expand the corner and attack at the same time. He decided to make a wall on the fourth line afterwards. Yay for him. My first instinct was to find a way to neutralize it, and making a thick right side seemed easy as well as profitable. Once I noticed he started to make another wall there, I decided to let him, because his lower left was wiiiide open. I was pretty sure I could live there, so all he would have in the end is the two walls and territory in between. I think his fatal flaw was the attachment at 38. Afterwards he defended his left. I wouldn't. I would hane with 44 on J5 and fight to the bitter end. 48 was another big mistake. It was cuttable, and he could not afford a cut there. 59 was my big mistake. I should have simply turned there. Now he managed to cut me off, and that was baaaad. At 78 he could have killed me. He was ahead in liberties, and he just had to start filling up, and I would have nothing to fight back with. Instead, he tried living on the side for some strange reason, and first chance I got, I played L11 for safety. I don't know if he didn't think of filling up my liberties, or simply didn't see the defense of L11. In any case, this was the big mistake that let me win the game. Well, it would have been very close otherwise... He made a mistake in the lower right probably out of desperation. 128 simply does not work in that situation. I'm pretty sure that the 3-3 stone can live inside even without the support from Q5. I tried living in the lower left, but failed. I think that 187 was the main mistake, and should have been played at C4 for life. Maybe not. One simple response that comes to mind is B2, after which I really don't know what to do.

One thing that struck me about this player was that he was very insecure about shapes. Apparently, reading books on shape, failing at a lot of tesuji, and time spent at www.goproblems.com do pay off. Now I am officially only 1kyu from single-digit! Onward!