I'm considering getting into the trade curio game, so I wanted to do some quick cost benefit analysis: how much would I have to spend to start generating them, and how long would it take me to start finishing collections.
My goal is to get a good estimate of how many pieces it would take to finish off either a collection of quest curios, or all of the collections of one type of trade curio. To understand this, I'm going to simulate getting curio pieces using Matlab. Essentially what I do is simulate getting curios and rubbing them, until I finish whatever I'm working on. I run this simulation 1000 times, and then see on average how many curios I needed to receive to finish.
Feedback on this would be useful. If you guys have better numbers, or see where one my assumptions will really throw things off, I'd actually really like to hear it.
1) The probability of a rare is 1/19. I pick this, because it implies each common is twice as likely as the rare.
2) All rares are equally likely, all commons are equally likely.
3) The probability that, when rubbed, a rare turns into another rare of the same type is 3/4. Otherwise, it turns into two commons. This is probably overly optimistic. I'm also ignoring the probability that the rare turns into a rare from another set, but I doubt that changes the results.
4) The probability that, when rubbed, a common turns into another common of the same type is 3/4. Otherwise, it turns into goop.
5) Ignore the possibility that commons rub into rares (anecdotally, this happens extremely rarely).
6) No trading. Instead, if you get a piece you already have, you immediately rub it. Obviously this is too strong. However, I think incorporating trading would be well approximated by increasing the probabilities that curios turn into another curio of the same type (the limit of this is that you can turn a curio into any other type you want, which is essentially the extreme version of trading).
7) Your only goal is to complete all the collections. This is usually false - for instance, with the jewelry curios I suspect people are aiming for particular ones, like braveheart or catsluck. With a bit of work, I could redo the analysis aiming for a subset of the collections. Obviously, this would reduce the total number of pieces you need.
When getting quest curio pieces, you can focus on a single collection at a time. When this is the case, and with the assumptions above, you must receive just over 100 curio pieces on average to finish a quest curio collection, with 10th and 90th percentiles of 62 and 158, respectively. This seems roughly in line with what I've observed farming quest curios, except for the Ice Angel quest which never gives me rares because it hates me
When getting jewelry curio pieces, you are dealing with 6 collections at a time, each of which has 4 sets. When this is the case, it takes on average about 775 curio pieces to finish all of the collections, with 10th and 90th percentiles of 563 and 1030, respectively.
Tailoring Curios - 7 collections: average of 925, 10th and 90th percentiles of 670 and 1207
Not surprisingly, it's the probabilities related to rares which drive the numbers. As the probability that rares rub into commons and commons rub into goop go to 0, the expected curios needed go to about 19 times the number of sets you need (i.e. you just have to get your self four rares). Like I mentioned earlier, I think this is a good approximation of the world in which there were a million other people out there working on curios, and you could trade any rare for any other rare.
If these are correct, the numbers on trade curios seem crazy to me. Even crafting once every hour, 24 hours a day, with the skill transcended and the artifact (10% chance of receiving a curio per hour) it would take you over a year on average to finish everything.