Would you agree that, given that Omega asks you, you are guaranteed by the rules of the problem to not pay him?
If you are inclined to take the (I would say) useless way out and claim it could be a simulation, consider the case where Omega makes sure the Omega in its simulation is also always right - creating an infinite tower of recursion such that the density of Omega being wrong in all simulations is 0.
If you are inclined to take the (I would say) useless way out and claim it could be a simulation,
Leaving open the question of whether Omega must work by simulating the Player, I don't understand why you say this is a 'useless way out'. So for now let's suppose Omega does simulate the Player.
consider the case where Omega makes sure the Omega in its simulation is also always right
Why would Omega choose to, or need to, ensure that in its simulation, the data received by the Player equals Omega's actual output?
There must be an answer to the question of...
This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.
Here's a diagram: