Assuming that Omega is picking at random, it makes sense to me to simply pick a random percentage on the first pull and then swing to 0% or 100% once you see a bead. Update again on the second bead to 0%, 50%, or 100%. Continuing the process should eventually converge on the correct answer.
Picking a random percentage is not a particularly good idea. It will lead you to make absolutely insane bets for no good reason.
Picking a random percentage is not a particularly good idea. It will lead you to make absolutely insane bets for no good reason.