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## 11.7 Topology of Half Eyes and False Eyes

A HALF EYE is a pattern where an eye may or may not materialize, depending on who moves first. Here is a half eye for `O`:

 ``` OOXX O.O. OO.X ```

A FALSE EYE is a cave which cannot become an eye. Here are two examples of false eyes for `O`:

 ``` OOX OOX O.O O.OO XOO OOX ```

We describe now the topological algorithm used to find half eyes and false eyes. In this section we ignore the possibility of ko.

False eyes and half eyes can locally be characterized by the status of the diagonal intersections from an eye space. For each diagonal intersection, which is not within the eye space, there are three distinct possibilities:

• occupied by an enemy (`X`) stone, which cannot be captured.
• either empty and `X` can safely play there, or occupied by an `X` stone that can both be attacked and defended.
• occupied by an `O` stone, an `X` stone that can be attacked but not defended, or it's empty and `X` cannot safely play there.

We give the first possibility a value of two, the second a value of one, and the last a value of zero. Summing the values for the diagonal intersections, we have the following criteria:

• sum >= 4: false eye
• sum == 3: half eye
• sum <= 2: proper eye

If the eye space is on the edge, the numbers above should be decreased by 2. An alternative approach is to award diagonal points which are outside the board a value of 1. To obtain an exact equivalence we must however give value 0 to the points diagonally off the corners, i.e. the points with both coordinates out of bounds.

The algorithm to find all topologically false eyes and half eyes is:

For all eye space points with at most one neighbor in the eye space, evaluate the status of the diagonal intersections according to the criteria above and classify the point from the sum of the values.

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