TF2 trade-ups are pretty simple. 10 items of the same grade and quality (unique/decorated or strange/strange-decorated) are inputted, and 1 item of the next higher grade with the same quality is outputted. The most likely method used for this is to pick a number 1-10 to select the item that "upgrades", and then pick a number 1-n from the items in the same collection as the item that was chosen but 1 grade higher. Additionally, a new seed is rolled if the item is a skin or paint. This seed is potentially tied to the upgraded item but I'm not aware of any investigation into this, and if anything it would probably be used to seed the random number itself making it pretty much the same as being random.
So statistically there is 3 layers of randomness:
So with this background information, lets do some math.
The first major question one probably has is 10%, 20%, ... or 100% trade-ups?
This of course, depends on how many items from the collection you have, which translates to how many trade-ups you can do.