There is no such thing as "random" in a purely logically driven system. A popular RPG approach is to use the "time" or "steps" as a base for this algorythm, as it will be in a state of constant change. I think ffIV uses this; I am nearly sure VI does.
Since you can save and reset, I would think there is a limited step counter involved; one that counts yoursteps and uses this as a part of the equation. ?
Bipper