In your opinions, which UV lottery is most economical- single, double, or triple? Triple seems pretty expensive for getting some possibly terrible UVs...
Regarding Punch's UV Lottery
Single UVs are definitely far more economical. There are two reasons for this:
1) Many items benefit greatly only from a small set of possible UVs. Being able to roll more UVs per CR increases the chances of getting one of these UVs. For example, a Divine Avenger would benefit most from ASI, CTR, Undead or Construct. All the other UVs would be considered sub-par for that sword. Bombs are even more restrictive, only CTR is considered useful for Shivermist... and the other UVs possible are not sought after at all.
2) Only UVs with exceptional magnitudes are very noticeable. For weapons, the difference between Low and Very High is pretty extreme. For armor, who wants a "Low Normal?" Max is what people want. Most UV rolls will just be Low. So to ensure anything better than Low UVs one should expect to roll many times.
For the cost of two UVs, you can roll a single 5 times. That is 5 chances to get something you'll cherish vs two UVs that will both likely be unnoticeable. Compared to the cost of three UVs, you can roll 25 times to get something you want.
As a thought experiment, let's say someone has 375k CE to blow on UVs. What would they get for 25 single tickets? They would expect, approximately:
17 Lows
6 Medium
1.5 High
0.5 Very High
Decent chance at High/VH, but maybe they'll land a Medium CTR and decide to stop there if that is a sufficient goal for the weapon.
If they did a triple ticket, 32.5% of the time all three UVs would be Low. Personally, I'd rather have two chances at a High/VH rather than a very likely 3 Lows or 2 Lows and a Medium. There is just a 4.6% chance that one of the UVs will be Very High.
What are the chances of all three UVs being Very High? Approximately 0.00038% chance or 1 in 2632. Yep... almost 1 billion CR is the what one should expect to spend before getting three Very Highs.
(These numbers are based on my set of UV data.)
culture forgot one thing thou~ you could get lucky and we all know, sometimes its better to be lucky than good ;)
2UV rolls are my choice.
Keep in mind that with 2+ UV if you get 1 useless UV the chance of the 2nd being useless has just now decreased.
Ignoring the magnitude of the UV (Low, Medium, etc.) I think it is still optimal to roll single over and over instead of trying a double.
Consider the most generous UV weapon - a DA which has 4 useful UVs out of 8 possibilities so there is a 50% chance of getting a UV that is useful. (Assuming even distribution, but it is probably not actually even.) For the first UV there is a 50% chance to get something useful. Assuming the first is not useful, you now have a 4 in 7 chance of getting a useful UV on the second. Cumulatively there is a 21.4% chance you'll end up with no UVs that are useful.
Compare that to rolling single UV five times, which is the same price. There is only a 3% chance you'll only roll undesirable UVs.
Compare that to crafting, its more or less 3200 to make one item, so one roll costs about 32000, but you get a chance at all 1 2 or 3 uv rolls. and you can sell the results or make 1 uv ticket rolls on them. You are basically trading up your right to get more uvs for time it would take to recover 17k from your 10 items, because we have to agree there will be a point in time no one will want to buy plain weapons because there won't be new players coming every day, forever. Or the cr you would lose by selling to a vendor.
AFAIK it only works when you want to add an uv to your already upgraded weapon you dont want to bother to sell and rework on or for quest items that would be more expensive/a lot more work to roll with crafting by upgrading them.
YMMV depending on rich you are and the item in question to be placed in the UV lottery.