Quicksaving the game sets the "Dungeon RNG" (The RNG seed used for generating floor layouts) to a fixed value of 1. This means that if you Quicksave at the stairs of a dungeon and then continue, you will get the exact same set of floor layouts each time.
As long as you take the same path each time, all luck-based events will be exactly the same.
Source:
https://www.youtube.com/watch?v=fudOO713qYo
I'm going to leave this as a comment for now as I don't know how to predict where teleport will take you though. I will post a full answer later after doing more research on that.