Error bounds on the probabilistically optimal problem solving strategy

We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with respect to this optimal strategy on the problem solving effectivity (i.e., the solution candidates examined as well as time spent before solving the problem). Such interchange can happen in the applications with only partial information available. We derive bounds on these errors in general as well as in three special systems in which we impose some restrictions on the solution candidates.