hyperactive position

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    Keywords: Ko, Theory

Hyperactive is a combinatorial game theory term coined by Prof. Berlekamp.

A hyperactive position is one whose count depends on who is komaster. Examples: Approach ko, Ten thousand year ko. An example of how who is komaster affects the count of a hyperactive position is given on the komaster page.

An active position is one whose count remains the same no matter who is komaster, but the value of a play differs. (Term coined by Bill Spight.)

A ko whose count does not depend on who is komaster is called placid.

Example

[Diagram]

corner

The count of this position depends on who is komaster. It's allways sente for Black and we know that sente plays don't affect the count so it's not hard to find out what the count is.

[Diagram]

Black komaster

If Black is komaster B1-W6 is sente. So the local count here is +3 counting the marked points

[Diagram]

White komaster

If White is komaster she can block with W2 since if Black cuts, White wins the ko anyway. Now the count is only +1. So who is komaster makes a difference.


Karl Knechtel: Why say "hyperactive position" rather than "hyperactive ko"?
Bill: There are hyperactive positions where a placid ko is threatened.

(Later.) See Endgame Problem 4, where no ko is actually played.


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