Problem is that your method is not logical and doesnt allow you to come up with a value greater than 50%. But logic dictates that the worst possible outcome is 50%. Worst case scenerio is that your first two portals are the wrong one and you have to open all three portals in the same game giving you a 50% chance. But that is worst case. You chances of getting a drop get better if you get lucky in the first two portals. That alone should tell you that your logic is wrong if it doesnt allow for higher than a 50% chance.
The problem is that you are confusing the best possible outcome with the worst possible outcome.
You say the worst possible outcome is 50%, but I have already proven a scenario where the possible outcome is just 41 and 2/3 %.
The solution WILL be one single sequence, as you have only 3 machines, and you wish to obtain only one organ.
The challenge remains, because if it is possible to create something from nothing, I would like to know!