I would suggest that we only use Omega as a tool to allow us to have information, both about the world and about the consequences of our actions, that we can fully trust. Omega's puprose is to handwave facts and/or cause and effect into being in such a way as to create an interesting problem. The moment we need to start thinking about how or why Omega does or might do something we're off on a different problem that probably doesn't relate to the problem we're looking to investigate. The bead jar game requires looking inside Omega, and therefore would have been better off with a human.