Let us assume a repeated game where an agent is presented with a decision between A and B, and Omega observes that the agent chooses A in 80% and B in 20% of the cases.

If Omega now predicts the agent to choose A in the next instance of the game, then the probability of the prediction being correct is 80% - from Omega's perspective as long as the roll hasn't been made, and from the agent's perspective as long as no decision has been made. However, once the decision has been made, the probability of the prediction being correct from the perspective of the agent is either 100% (A) or 0% (B).

If, instead, Omega is a ten-sided die with 8 A-sides and 2 B-sides, then the probability of the prediction being correct is 68% - from Omega's perspective, and from the agent's perspective as long as no decision has been made. However, once the decision has been made, the probability of the prediction being correct from the perspective of the agent is either 80% (A) or 20% (B).

If the agent knows that Omega makes the prediction before the agent makes the decision, then the agent cannot make different decisions without affecting the probability of the prediction being correct, unless Omega's prediction is a coin toss (p=0.5).

The only case where the probability of Omega being correct is unchangeable with p≠0.5 is the case where the agent cannot make different decisions, which I call "no free will".