I'll be writing a more detailed version, including the numbers that I crunched with, but for now I'll just put something simple up:

Here's the short version:

Your item is 0% of max possibility (Stock, 100% damage), you use midas, your new item rolls for 20%, your old item is tossed away and the new item appears in your inventory.

Your item is 20%, you roll 80%, the 20% gets tossed.

Your item is 80%, you roll 60%, you keep your item and a message appears, nothing appears in your inventory.

Your item is 80%, you roll 90%, the 80% gets tossed. You notice that your Damage actually went down, this is normal because other stats went up (more than likely).

You then try Midas for 50 more times and roll a 95% that raises your damage, but still not as much as the 80% was at. You are now at a stage where you are VERY unlikely to roll a better item, and your damage is (for all intents and purposes) now the best you will get on that item.

I have a max armor chestpiece at 2000, and another max chestpiece armor at 345. The 345 is junk now and I will be tossing it, since using Midas will be wasteful on it.

It is better to upgrade multiple of the same item, rather than a single item over and over, since you will have more "final" versions to choose from.

More info to come.