So which do you think will be harder to get

[Iria-1342]

I messed up my calculation in my earlier post, so I will show the work here to avoid mistakes!

@TinneOnnMuin-1187

rather than trying to calculate all the probabilities exactly, which change depending on which affixes roll and the order they roll in since that alters that relative weights of the remaining affixes, and can get complicated, I actually just wrote some functions to generate random items based on an input list of primary and secondary affixes and their weights, then made a million random items and checked to see what came out. Seemed like the easier approach

Monte-Carlo simulations are indeed the easiest approach but I think this one was simple enough that it was still doable via a Markov chain at least for the FoT.

For FoT, you must get correct element, crit chance, crit damage, and a socket. You can only get 3 so that the 4th must be obtained by rerolling the movement speed to it. Since all 4 of those stats have the same weights 1000 out of the total 37500, it’s somewhat easy. The difficulty comes from the fact that only 1 element can roll on the amulet and thus changes the total weights when elemental damage rolls on it.

So to compute the probability, you need to consider 4 cases:

Case 1: Correct element rolls first, then two of: ChC/ChD/Socket
Case 2: One of ChC/ChD/Socket rolls first, then element, then ChC/ChD/Socket (what wasn’t rolled)
Case 3: Two of ChC/ChD/Socket rolls first two, then element last
Case 4: All three ChC/ChD/Socket rolls (no element)

*Note: cases 3 and 4 have the same probability since the total weights are only shifted for rolls that occur after the elemental damage.

The probabilities for each case are:

Case 1 (elem 1st): (1000/37500) * (3000/33500) * (2000/32500) = 1.469575e-4
Case 2 (elem 2nd): (3000/37500) * (1000/36500) * (2000/32500) = 1.348788e-4
Case 3 (elem 3rd): (3000/37500) * (2000/36500) * (1000/35500) = 1.234806e-4
Case 4 (no elem): (3000/37500) * (2000/36500) * (1000/35500) = 1.234806e-4
Total = 1.469575e-4 + 1.348788e-4 + 1.234806e-4 + 1.234806e-4 = 5.287975‬e-4

Which can be approximated as roughly 1 in 1891. To get an ancient on top of that would make it roughly 1 in 18911 which is extremely rare!

Can you try your simulation to see if you get a “good” FoT roughly once every 1890 amulets?