A (quasi)rational agent with access to genuine randomness (such as a human)

Whaddaya mean humans are rational agents with access to genuine randomness? That's what we're arguing about in the first place!

A superintelligence could almost perfectly predict the probability distribution over my actions, but by quantum entanglement it would not be able to predict my actual actions.

Perhaps Omega is entangled with your brain such that in all the worlds in which you would choose to one-box, he would predict that you one-box, and all the worlds in which you would choose to two-box, he would predict that you two-box?