Hyperactive position

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

A hyperactive position is one whose count depends on who is komaster.

Typical examples are Approach ko, Ten thousand year ko, or positions were a ko is possible, but whether it is played depends on the ko threat situation.

An example of how who is komaster affects the count of a hyperactive position is given count of an approach ko.

Related terms

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

corner  

The count of this position depends on who is komaster. It's always 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.

Black komaster  

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

White komaster  

If White is komaster she can block with 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.