Yep, your maths are wrong (at least in the OP⦠I must admit I havenāt read the whole thread in detail).
I will only recalculate this bitā¦
⦠because I donāt know what the probabilities are for different perk or blessing tiers, and they could even depend on weapon base rating which would make things harder (but Iām pretty sure itās not a flat distribution, since tier 4 and 1 seem to appera a lot less often than 3 or 2).
Assuming you are going to upgrade the weapon to Transcendant (orange), you will have 2 perk slots and 2 blessing slots. You will also have an ideal weapon in mind, with 2 preferred perks and 2 preferred blessings. Since you can reroll 1 perk and 1 blessing, all that matters is that in either of the two perk slots you get one of the two ideal perks, and in either of the two blessing slots you get one of the two ideal blessings.
For the perks, then, assuming 20 possible perks for a given weapon, we have two ways to succeed: A) you roll one of the desired perks in the first slot (regardless of the roll on the second slot), which means a 2/20 probability, or B) you donāt roll a desired perk on the first slot (18/20 chance) and you roll a desired perk on the second slot, which is a 2/19 chance (because perks in different slots canāt be the same, so when you make the roll for the second slot there are not 20 possibilities but 19, since you locked one out during the first roll). The total probability of getting one desired perk is then the addition of A+B, so 2/20+18/20*2/19 = 19.5%.

(R1 and R2 are the first and second perk rolls. Green means you get one of the two that you want, red means you donāt, grey means it doesnāt matter.)
A very similar calculation can be done for blessings. If we have a weapon with 13 possible blessings then the chance of getting one of them right is 29.5%.

The general formula to calculate these probabilites, depending on the total number of perks or blessings ānā, can be written as:

If we want the probability to get one perk right and one blessing right, we just need to multiply the two probabilites. So for 20 perks and 13 blessings we get 0.195*0.295 = 5.7%.
In the general case of a weapon with ānā perk and āmā blessing options we get the following table:
I believe most weapons have about 20 perks and 8-10 blessings, so we are looking at percentages on the order of 5% to 15% in most cases. Not as gloomy as it looked at first sight
But again, this doesnāt take into account perk and blessing tier, or base weapon stats.
Similar argument for curios. Assuming the three perk slots share the same options (which I have some doubts about) and that all options have the same chance of appearing, we get this:

Or, in general, for any number of perks ānā (I donāt know if there are 22 or how manyā¦):


And then multiply by 1/4 because there are 4 possible blessings, so on the order of sub-1% to get a curio with the blessing and perk combination you want (again, disregarding tiers).
TLDR: the conclusions are that calculating the exact probabilites of things happening is hard because we are missing some of the facts; that the probabilities of getting a specific combination of blessings and perks are low; and that, even though they are low, they are not as low as low as the chances of winning the lottery (unless, perhaps, you are trying to get a perfect item with everything maxed out).