When your knowledge is incomplete - meaning that the world will seem to you to have an element of randomness - randomizing your actions doesn't solve the problem

Ants don't agree. Take away their food. They'll go in to random search mode.

As far as that experiment is concerned, it seems that AnneC hits the point: How was it framed? Were the subjects led to believe that they were searching for a pattern? Or were they told the pattern? Wild guess: the former.