KMC Forums - Two versions of your favourite character fight each other. Precog vs Timetravel

Power Specifics:

-The person with precognition (P) has a perfect, unlimited ability to see into the future. There are no foggy visions or vague feelings, they know what's about to happen as clearly as if they were currently experiencing it. Assuming infinite alternate/ possible universes, they only see the future of the current universe they are in. This person sees every punch you aim, knows the trajectory of any bullet you shoot, and

-The person with time travel (TT) can move themselves forwards and backwards in time. This is only time travel, not manipulation, so they experience time at exactly the same rate as everyone else. They arrive exactly where they want to, and can initiate the travel as quickly as they can think. When they travel, their body physically moves to that time, so if they move forwards, they appear to disappear for a while and then reappear, and if they move backwards multiple versions of them can exist at once. Paradoxes are not supported, and every instance of time travel creates a new version of the timeline- so if a younger TT dies, any present older TT's die.

Round 1:
P & TT are notified at the same time that they have been hired to assassinate the other. They exist in their world. They have all of their normal resources, including canon allies (who presumably will have to choose sides). Who dies?

Round 2:
P & TT are transported into the battle arena of an unknown alien. They are forced to fight to the death. The arena exists outside the universe so neither power can escape- P doesn't see it coming, and TT can't travel back to before they were abducted. Neither can leave until one of them is dead (so TT can't simply return to before P's birth and prevent their existence or similar tactics). The alien sustains their lives indefinitely so they can live without food, water, sleep, etc, and will die only when the other causes it. They are given any weapons they ask for. Who dies?

Round 3:
Same as round two, but with a time limit of thirty seconds before they are both killed. Can either win before time runs out?
Round 4:

The two team up to fight the most powerful villain in their universe. Can they win?

Ultimate powers round:
TT can now fully manipulate time, including freezing it and slowing it etc. P can now see every potential universe, and has upgraded reflexes that allow them to move and react much faster than is humanly possible. Who kills who?

Not really a round:
If one person won every round of this battle, can you come up with a scenario in which the other is capable of winning?