Geo political domination :Sauron without the ring versus Hohenheim of the flask?

Round one: they’re both in amestris at the same founding time- say the fall of the ring happens with the follow of xerxes or whatever. neither of them know about each other both of them are looking to take over for mistress who wins?

Round two: both of them know about each other.

Round three: neither of them know about each other, but it is in middle earth after Gil galad falls

Round four they both know about each other and they’re both in middle earth

Both have canonical powers, but in the event that they do know about the other person, they do not know where the other person is