Concept notes

Walls 壁

As Lao Zi taught, what makes a bowl useful is the empty space within it, to hold various things. What makes house useful are the spaces for the doors and windows, to allow all sorts of access. And, by extension, what makes a wall useful in go is the empty space it surrounds, to allow all sorts of strategies.

In go, a wall represents strength. An opponent will want to keep away from enemy strength. It can happen that he keeps away from a wall and the empty space bordered by the wall turns into territory. Good thing, surely? Probably not.

If the opponent deliberately stays away from your wall, he is not necessarily suffering. He is probably getting bigger moves elsewhere, but at the very least he is running the show. You are not likely to win unless at some point you can seize the initiative. The most obvious danger you face is summed up by the proverb "Beware of ippoji" - beware of ending up with one big territory. It is in the nature of such large territories that they occupy much of the centre, which means many stones are required to seal them off. They are not efficiently making free use of the edges of the board as smaller corner and side groups do.

If you have a wall, therefore, you really do need to try to make the opponent inefficiently invest stones in the centre, too. That generally means enticing him inside your sphere of influence. There you attack him - not with the intent of killing him but of letting him live small. The new walls you create as you enclose him within your prison are worth more than your first wall, because by then the board has filled up and they dominate more.

All of this applies, mutatis mutandis, pari passu and with knobs on, to moyos of course. In both cases, a major problem is the enticement. How do you ensure you have a worm big and juicy enough on your hook? One way is to threaten to surround rather more territory than he can compensate for elsewhere. The answer therefore essentially involves counting. That's not easy but there are rules of thumb.

In a moyo, one heuristic is to count six points for each key stone. With a wall, a useful and simple method is Abe Yoshiteru's samurai sword theory. Typically, at the building stage, a wall climbs up one side of an area, while you remain low on the other. Abe symbolises this as a samurai holding a long sword and a short sword. The numerical value of the wall can be defined as the sweep of the long sword, but refined by the strength (or reach) of the short sword.

There are some significant details about how you count the length of a wall (subtracting for enemy stones glued to the inside, for example), how you decide which way a curved wall is facing, how you assess overlap with adjacent walls, etc), which we will omit here in favour of the essence: assuming your long-sword wall is secure and you have a short sword in place, count its height H (you can include any forced future exchanges down to the second line) and then calculate its value as H × (H+1) ÷ 2. The H+1 represents the number of empty lines between your long sword and your short sword.

The (full) method is surprisingly accurate. The main point we want to make here, however, is that the value you come up with by this or any other means is not the value of the territory you can make around the wall. It is the euro-value of the wall.

If you live in the USA and happen to have some yen, they may seem useless as you can't normally spend them there. A short-term solution is to exchange them for dollars. Or you can hold on to the yen in the hope of some future gain - use them on your next trip to Japan and avoid paying exchange commission, or hope the yen grows in strength relative to the dollar, and exchange them for dollars in the future when you need some liquidity within the USA. If you were doing this on a grand scale you would be said to have some euro-yen (the term comes from the days of Eurobonds, not the new european currency).

What you have to learn about walls is that they are worth euro-points. These are an investment. You may be able to convert them into pure territory points, but if you do so at once you probably have to accept some loss. It is usually more investment-savvy to hold on to them and cash them in, here or elsewhere, in the future.

Useful proverbs

• Ippouji wa chiisai - Beware of ippoji (one large territory is too small)
• Walls have ears, not eyes
• Nakaji wo kakou na- Don't surround territory in the centre
• Semenagara co wo tore - Take territory while attacking
• Ou wa keima ni nigeru wa ikken - Chase with knight's moves, escape with one space jumps (a reminder that you normally drive an invader up against your wall with knight's moves)
• Atsumi dake de wa go katenu - Games are not won with thickness alone

© John Fairbairn & T Mark Hall (GoGoD), London 2007.