Vital point method with one point eyes
Here is an attempt for a systematic approach for finding the vital point, if your eye isn't trained to see it on the spot.
![[Diagram]](../../diagrams/18/a272411eee6d2b835b9fd3a1a15cdeee.png)
Reference diagram
This position is taken from Kanazawa Problem 25. White to live. Let's try to make a one-point eye with as few moves as possible.
![[Diagram]](../../diagrams/33/54cb3358159d1edd708633a7622c4ae7.png)
Diagram 1
Adding two stones.
![[Diagram]](../../diagrams/13/6b32e3681df959252773041d4c86a011.png)
Diagram 2
Adding two stones.
![[Diagram]](../../diagrams/14/a2317f1e79b4e1ac31f0c6de69f12663.png)
Diagram 3
Adding three stones.
![[Diagram]](../../diagrams/46/f925d9a4869594360dc72a7bef9dc320.png)
Diagram 4
Adding three stones.
![[Diagram]](../../diagrams/35/985159863f80de3105acb1d6cb8407c7.png)
Reference diagram
Looking back at the reference diagram, points a and b occur in three of the four diagrams. Both are vital points, but a is more valuable than b, because a occurs in both diagrams with two stones. This reasoning can easily be quantified.
Conclusion: a is the vital point.
Dieter Verhofstadt