Randomized adaptive test cover

In a general combinatorial search problem with binary tests we are given a set of elements and a hypergraph of possible tests, and the goal is to find an unknown target element using a minimum number of tests. We explore the expected test number of randomized strategies. We obtain several general results on the ratio of the expected and worst-case deterministic test number, as well as complexity results for hypergraphs of small rank, and we state some open problems