^^ I believe that is the correct formula. I once empowered my caster to a modded 14 astral str just to get an extra +3 or so on the roll, w/ max gems
1. if the global you cast is already up, it will compete w/ that one
2. if not, it will compete w/ one of yours that is already up.
3. if you don't have any, i believe it will compete w/ a random one.
4. sometimes it doesn't seem to act according to these rules - the situation has always seemed a bit buggy