The empty triangle is bad
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The black group to the left is an empty triangle as there is no stone at a. The white group is not an empty triangle (it is a full triangle), as there's a single black stone next to it.
Why is an empty triangle so bad?
First of all, the empty triangle doesn't maximize its liberties. It has 7 liberties in isolation, wheras the straight three have 8 liberties. Both make a strong connection. The loss of a liberty without any kind of gain is unacceptable. There are many, frequently occurring positions in real games, where this one liberty is vital.[1]
Secondly, two stones in a diagonal are connected, in the sense that they cannot be separated in one move, but they can be sacrificed if desired. Now the empty triangle is connected too, strongly, has a little bit more influence but must be sacrificed as a whole if needed. The one extra stone adds close to no value. It is a wasted stone.
Also, if Black wants to develop to the right, then play the marked stone instead. White cannot cut this formation without help from surrounding stones. Black's stones are securely connected. Closer to the side, farther extensions are virtually connected. This development is much more efficient than the empty triangle.
In contrast, the full triangle is very strong and efficient. In the upper position, Black can be cut. So, below fulfills a very important function: it connects two stones. By doing so, the white stone becomes very weak. The investment is 3-1, whereas in the empty triangle it is 3-0. Black's moves all have purpose.
In this opposing jump position, White can lull herself into thinking the peep serves the double purpose of connecting and threatening to cut. Then, jumps out.
However, she puts herself in a bad position. Black's straight three are strong, while White's zigzag three are weak. Black threatens to cut at
, and White has to connect.
Now she has connected, but forms two empty triangles and serves no purpose whatsoever, while Black's peep
is on the outside and provides support to the attacking stone
.
Enfors: Newbie question: I take it, then, that white should have played her first move at directly, to avoid wasting a move?
fractic: White should just jump out to instead of exchanging
-
. If black later plays
then
is needed. But
right away is way too slow. The one point jump is hard to cut anyway. See don't try to cut the one point jump.
There's a proverb saying 'A beginner gets 2 stones stronger by avoiding the empty triangle.' Here's a page to help you spot the empty triangle and avoid it.
Although no longer triangles, the shapes on the left are all considered bad as well for mostly the same reasons. The shapes on the right fulfill the same functions but more efficiently.
The best way to look at it, is that the upper shape does contain an empty triangle (the three marked stones), and the lower shape even two. The fourth stone is also too close, so one may well say that these shapes are even worse than the empty triangle itself.
The shape on the bottom left is known as the farmer's hat, and is equally bad.
Caveat: the empty triangle is not always bad. See Good Empty Triangle.
[1]
Bill: This comparison does not mean that this shape is good. In fact, I do not believe that you will find this shape, with no opposing stone on any of these neighboring empty points, in a professional game.
I reiterate my objection to discussion of shape without reference to opposing stones.
Dieter: You are absolutely right that we must include real game examples demonstrating the artificial explanations. Yet, three points:
- the liberties argument demonstrates the ET is worse than straight three, not that straight three in isolation is good in itself, but indeed we should point it out
- a structure having more liberties than another in isolation, will be harder to catch; people will understand that solid two are stronger than one single stone, because they have two more liberties, and that the offset is the loss of a move; for ET against ST the offset is much more out of balance
- in a way, the empty triangle is per definition in absence of an enemy stone: your objection is the essence of its inefficiency #:-7
Bill: We are not in disagreement. :-) (Except perhaps for the question of definition. An enemy stone must not be in only one location.)
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