rkdmf (version 2)

Black to play. Not trick question.  

This should be mind numbingly obvious at ddk level, but one strategic experiment I tried was always playing as far away from thickness as possible, and many, many points were thrown away.

Black to play  

This shows up in slightly less obvious form too.

Great success  

According to a 4d, a is correct.

The proverbs say not to use thickness to make territory. I think one of the reasons they say this is that making territory from thickness directly is actually pretty hard, and it takes a lot of moves to draw the box, and your opponent can reduce in the meantime. One rough estimate when counting is that influence is worth around 2 points per outward stone and thickness is worth around 3 points per outward stone. So, if the game situation is such that you can use your thickness to make more than 3 points of territory per stone, then it starts to seem really appealing.

Another related idea is that there are some optimal distances for 2 walls to be spaced apart, and not necessarily "as far as possible". One ideal spacing is "as far as possible without the opponent having room to live" - if the moyo can be successfully invaded, the value suddenly drops to maybe something like half of what it would be were the whole thing cash. Then, once you're too far for that, you want to be even farther, until it's "as far as possible so that one move can still make it impossible for the opponent to live". This way, it's still urgent to invade or reduce, but the amount of potential to turn into territory by attacking is maximized. But, if the walls are really far apart, then the opponent can play a wedge, have essentially miai life, and it's not as good anymore, even if the walls still have value.

Speaking of stones with bases, this also sounds a bit obvious, but well, sometimes the right move is a really awkward looking 1 or 2 space extension from a wall, if it turns out to be the right attacking move to keep a group weak.

2. Use thickness to invade, if the invasion is good. Don't use thickness to invade if the invasion gives the opponent a large number of points or a useful wall.

Black to play  

Here, a is not good because white will get a useful wall to develop the top. The fact that a thick wall is facing an enclosure that's almost complete doesn't make it good. If the invasion is bad, thickness doesn't make it good. (Although thickness can make some invasions live easily that otherwise would just die or give lots of points, which is a different thing entirely.)

The correct answer is b, tenuki, and wait for opportunity.

White to play  

This is from a pro game. According to An Younggil (8p), white's move at d was correct. This is an example both of thickness making an invasion live (white won't make a ko shape but instead connect solidly, then black has to fix the outside cutting point because white is thick outside) and of the invasion being strategically good (black's wall won't be very useful and could even come under attack if black isn't careful).

3. Encourage your opponent into a stupid and pointless fight against your thickness, unless the fight would also be stupid and pointless for you.

Inviting a fight that is good for you and bad for opponent  

White's corner is definitely strong, but black can still easily develop the bottom side thanks to the thickness. If white invades, at a, black can attack at b, and white might be in trouble. Black's one stone is strong thanks to the thickness nearby.

On the other hand, playing extremely loose or greedy stones in the center might initiate a fight where your opponent makes dame out of everything, in what could have been mostly your center.

4. Use thickness to build a moyo, unless moyo is a burden.

A moyo is sort of like a weak group. It doesn't make any cash by itself but you're counting on it not being completely destroyed, which means your opponent can sometimes keep sente by threatening it. If you only play passive defending moves, it's probably not going to die, but it might be really painful to give your opponent free moves. So, much like a weak group, if a moyo is in the wrong place, for example next to another weak group, you might be in trouble. If it's next to your opponent's strength, it might be more trouble than it's worth. But if it's next to your opponent's weakness, then all of a sudden it feels stronger and less like a liability. Oh, and sometimes you have to attach to stones to help it out, when that attachment may or may not be a good exchange.

Moyo is a decision, just like invading or tenuki from a weak group. So it has to fit the situation. If moyo is the wrong decision, and there's nothing else to do with your thickness, then it's simple! Just do case #3, play elsewhere and wait for an opportunity.