Lol, I spend about 40k a day on getting UVs. This week I spent more than usual: 460k and ended up with piercing low for the 5th time. Laylla, I know how you feel.

Well, if you do that way, you won't always get a UV each time you craft. I usually get a UV from crafting every 7-12 times. In either case, getting a UV is pretty frikken annoying and costly.

I roll High/VH quite frequently but it's usually in something useless like Vs Gremlin/Slime/etc. I recommend going to the UV crafting NPC since you're guaranteed a UV. Crafting a million items has low odds for a UV. May as well spend on a sure thing, ya know?

http://steamcommunity.com/id/alanh/screenshot/578956687688760642?tab=public

The torment did not end there.

That crown count? Went down to zero, and only Undead bonus came out of it.

I think the consensus is that the UVs are uniformly distributed, so you have equal odds of getting any of the different UV types (ASI, CTR, Undead Damage, Fiend Damage, etc).

There are 8 different sword UVs, so you have a 1/8 chance of getting ASI. However, if you look at the overall probability of getting ASI in X number of rolls, it would look something like this:

1-(1-1/8)^X = 1-(7/8)^X

Basically, you look at each roll as a success or failure. You have a 7/8 chance of failure and 1/8 chance of success with each roll. If you made X=10 rolls, the probability of an ASI UV occurring in those 10 rolls is:

1-(7/8)^10 = 0.737

So you have a 73.7% chance of landing an ASI UV somewhere in those 10 trials. Whether it is Low, Medium, High, or Very High is a separate matter.

The 50% mark -- the same odds as landing heads in a coin toss -- is between 5 and 6 rolls.

If you want to look at an individual roll, and what the odds of getting a Medium UV or better, you have to look at how the UV levels are distributed. The Wiki says that the levels are roughly distributed as follows:

Very High: 5%
High: 8%
Medium: 21%
Low: 66%

My own data (1600 recorded crafts) suggests these numbers are fairly accurate. So the chance of getting a Medium UV or better is approximately:
(100%-66%)=34%

The odds of landing ASI and Medium+ are independent events, so to calculate the probability of an individual roll landing ASI Medium+, you multiply the two probabilities together:

(1/8)*(0.34) = 0.0425 = 4.25%

That's a very low probability.

To put it into perspective, you would have a 50% chance of getting ASI Medium+ in log(0.5)/log(0.9575) =~ 16 trials. That's 320,000cr and it would still be a coin toss.

TL;DR: Buy a 2-star sword with the desired UV and upgrade it to 5-star.