rsun
2d on KGS, IGS, DGS
Spiral-n opening
![[Diagram]](../../diagrams/18/e2a563a0111956551071056cf696c643.png)
The spiral-3 opening. Spiral-n openings for n=1,2,4,5,6,7,8,9 are labeled by the corresponding alphabets.
Inspired by the Shusaku fuseki, I have invented the spiral-n opening, where n is the smallest number of the coordinates of the black stones. Hence the opening moves of the Shusaku fuseki can be classified as (an incomplete) spiral-3.
However, such an opening will almost never come to completion, as white will almost always play at an empty corner. For the same reason, spiral-4 (d) will also never be realized. It is obvious that spiral-1 and spiral-2 are bad and should be rejected outright. Note that spiral-9 (i) forms a cyclic kosumi (i.e., an eye) and spiral-8 (h) is a cyclic ogeima.
The spiral-9 opening may be discussed in beginner go books. As the saying goes, a ponnuki at tengen is worth 30 points. However, as white gets four corners without sacrificing a stone, this opening is too inefficient for black. Likewise, spiral-8 may be inefficient as well.
Applying Rolle's Theorem to spiral-n
Observe the trend as n increases. For n=1,2, the openings are bad. For n=3,4, the openings become acceptable, but completing it becomes bad, as black blindly attaches into white's corners. For n=8,9, the openings become inefficient. If you believe, as I do, that the strength of the spiral-n opening increases for low n and decreases for high n, then by (improper use of) Rolle's Theorem, there must exist an optimum n where the spiral-n opening is the strongest.
Unfortunately, this optimum n cannot be found analytically. Based on intuition, it seems to me that the spiral-6,7 openings should be the best.
The cyclic daidaigeima opening, as the name suggests, contains 4 daidageimas, forming a relatively solid shape. However, it cannot be classified as a spiral-n opening. It is clear that a spiral-n opening is composed of 2*(9-n)-space extensions. Thus, odd-space extensions cannot be spiral-n.
Strategies
Although spiral-n has a 4-fold rotational symmetry about tengen, mirror symmetry is spontaneously broken. Hence, black's 5th move is greatly influenced by the symmetry of white's first 4 moves.
One must never use the spiral-n opening to defend the tengen territory. That completely misses the point. Instead, one should overplay reasonably (an oxymoron?) at sides and corners to provoke fights, so that the first 4 moves can become effective.
Of course, there is always the possibility that black cannot complete the formation due to an existing white stone. However, black should not feel that s/he is at a disadvantage.