If the research has a cost (and you know this cost), then you actually have three options: original option A, original option B, and research + correct option (

If the research has a cost (and you know this cost), then you actually have three options: original option A, original option B, and research + correct option (or knowledge that both options are the same). If you can at least bound the costs of options A and B, you can make a pretty good guess as to whether the research is worth doing. If it's not, then choosing at random is the optimal choice, and you should not regret it.