Forum for Vital point method with one point eyes
full example? [#1210]
Would a full example be better? The current page skips a possible one-point eye at e. It also fails to note that one case creates two eyes and lives without further ado.
![[Diagram]](diagrams/48/86ac4a8db2cf5b7ebeb23d259914f46e.png)
Each of the labeled points could be made into a one-point eye. Let's try to make a one-point eye with as few moves as possible.
![[Diagram]](diagrams/5/2b4ab1d0d91e65b5370481b2dcf0ce52.png)
Adding two stones, we get a one-point eye at a but lose the possible eye at c. Yet there remain possible eyes at four points. (1-1-4)
![[Diagram]](diagrams/45/165b17f9d675665c286490e8e4402c4e.png)
Adding two stones, we get a one-point eye at b but lose the possible eyes at c and e. Yet there remain possible eyes at three points. (1-2-3)
![[Diagram]](diagrams/12/0af5d367a0a890ce591f03636e903273.png)
Adding three stones, we get a one-point eye at c but lose the possible eyes at a, b, and f. Yet there remain possible eyes at two points. (1-3-2)
![[Diagram]](diagrams/38/676a9a4dcba66245dba5bf13041d17ca.png)
Adding three stones, we get a one-point eye at d but lose the possible eye at e. Yet there remain possible eyes at four points. (1-1-4)
![[Diagram]](diagrams/48/c17816752c2d376df8e3e795a3261a1d.png)
Adding three stones, we get a one-point eye at e but lose the possible eyes at b and f. Yet there remain possible eyes at two points. (1-2-2)
![[Diagram]](diagrams/3/b9243c5852c0a85a0c5e9dd670159d0e.png)
Adding three stones, we get a one-point eye at f but lose the possible eyes at c and e. Yet there remain possible eyes at two points. (1-2-2)
Note: this is the only case in which we end up with two eyes in the diagram.
![[Diagram]](diagrams/4/5fae12611d1e97c87b6868a737744da2.png)
Perhaps there is only one vital point at the location used three times to make a one-point eye? But that point also destroys the largest number of other possible eyes.
- a used once
- b twice
- c once
- d twice
- e once
- f once
- g twice
- h thrice
- i once
- j once
Can this be applied successfully to larger groups. Does the counting become so unwieldly that its too hard to use? I don't have any conclusions from this one position.
JG The detailed analysis in Dieter's original method led to this tentative conclusion: that the vital point can be seen as the connection between shared liberties of different groups. This new heuristic is an interesting way to approach the kind of broken or incomplete shapes where it is otherwise hard to get started.
Several heuristics for making life are given in ApproachingALifeAndDeathProblemTheRightWay.
The new heuristic applies to cases: with little or no scope to kill some of the opponent's surrounding stones; where it is impossible to connect to a friendly group; and where there is little scope for extending the threatened group's eye-space. The only remaining possibility is to divide the existing eye-space into two or more eyes. The defending player would naturally be reluctant to play on a shared liberty of different groups so a point between two or more such shared liberties is quite likely to be a good point to divide and preserve the available eye-space.
The new heuristic obviously does not offer immediate help if the defending group is already solidly connected. For example, shapes related to the CarpentersSquare or the DoorGroup with one leg. It also does not help with very small shapes such as the TripodGroup, which only has one liberty shared between its
two component groups.
The new heuristic also does not help in the case of problems where the solution involves playing UnderTheStones or forcing the opponent into shortage of liberties.
JG Oops.
There are actually two shared liberties between the component groups of the TripodGroup. But there is no point between those two points. And the between point is only useful if it lies in some sense inside the group to be defended.
In short, Dieter's heuristic is interesting, but it only applies to a small subset of life-and-death situations. Go is indeed a game of pattern-recognition.
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