Sarcastic fringehead (fish of the day)

The sarcastic fringehead (Neoclinus blanchardi) is this week's Fish of the Day. Enthusiasts will (or won't) enjoy this puzzler from Mark W. Denny and Steven Gaines's book Chance in biology: using probability to explore nature:

Suppose that a displaced sarcastic fringehead must spend approximately three hours searching for a new shelter. Lets' also assume that each day involves four encounters with invading fringeheads…. How much time will a fringehead waste in a typical day searching for a new shelter?

(Thanks to investigator Lance Gharavi for bringing this to our attention.)