I would just flip a coin, I guess. I think it would be hard to get better than fifty fifty odds by thinking about it for a really long time.
I'm pretty sure predicting the trajectory of a flipped coin is trivial compared to predicting your future thoughts and actions.
Excuse the horrible terribad pun...
An evil Omega has locked you in a box. Inside, there is a bomb and a button. Omega informs you that in an hour the bomb will explode, unless you do the opposite of what Omega predicted you will do. Namely, press the button if it predicted you won't or vice versa. In that case, the bomb won't explode and the box will open, letting you free.
Your actions?
PS. You have no chance to survive make your time.
PPS. Quick! Omega predicted that in exactly 5 second from now, you will blink. Your actions?
PPPS. Omega vs. Quantum Weather Butterfly. The battle of the Eon!