The online kernel-search problem is for a mobile robot with 360 degrees degree vision to move from a starting point to the closest kernel point within an unknown star-shaped polygon. Icking and Klein (1991, 1997) presented a simple strategy, called CAB, and showed that CAB is 5.331-competitive. In this paper we show that CAB is (pi + 1)-competitive, which is a tight analysis of it. (C) 1999 Published by Elsevier Science B.V. All rights reserved.