So... assuming that it is 10% chance per MP level;
And you need 3 keys to have a chance at an organ;
And you need 3 organs to make the ring;
And you can't control which organ you're competing for
Expected Runs to get Organ 1:
Expected Runs to get Organ 2:
1/(MP*0.1)*4*(3/2) ... You only have a 2/3 chance of getting an organ you didn't already have
Expected Runs to get Organ 3:
1/(MP*0.1)*4*3 ... You only have a 1/3 chance of getting an organ you didn't already have
So total expected runs to get a ring is:
MP # Runs
Seem right? Or did I screw something up?
Note that this is expected. Meaning it's the average. Meaning that each person only has around 50% chance to get it in this many runs or less.
Ehh, 10 runs at MP10, or really 9 runs if you make the 9th run in act 1. There is nothing random about spawning portals if you have 3 infernal machines. You just spawn the first one, kill the boss, spawn another in the same game, kill that boss, and spawn the final one, killing that boss; between these boss fights just find one elite pack and replenish your NV buff as needed.