In the late seventies I lived in a roach-ridden old apartment in Fall Church, VA and became grudgingly impressed with the sophistication of some roach behaviors. I know they can't have much brain capacity, really, but they know the concept of line-of-sight and "hiding" really well. If they can see you, you can see them and they know it. They dodge expertly among boxes and cans on a shelf or counter.
I was chasing one about in such a manner and paused, hand in the air, when I realized it was making its break over the edge of the counter. I thought I'd have a clear shot at it as it tried to speed down the side. It anticipated ME and lept straight out into the air and was gone under the side molding in a flash.
Another thing they do when out in the open is freeze when they first see you. They'll let you get only so close and then they take off. That's a pretty good simulation of a rabbit by something with probably 1/500th or less of the neurons.