If you substitute Omega with a repeated toin coss, there is no Omega, and there is no concept of Omega being always right. Instead of repeating the problem, you can also run several instances of the simulation with several agents simultaneously, and only counting those instances in which the prediction matches the decision.

For this simulation, it is completely irrelevant whether the multiple agents are actually identical human beings, as long as their decision-making process is identical (and deterministic).