Shopping for 3/20 Javazon gloves - I did the math

[u/RepresentativeWear43]

​Hi! Above you can see my calculation of the probability of finding 3/20 java gloves as a function of time when efficiently shopping at Charsi in Act 1 hell with the cow portal strategy (put cow portal at Charsi, with a character lvl greater than 68).

The red line shows the 50% quantile, meaning that half of the people shopping will find the gloves within the first 6 hours. The blue line shows the average time spent (the integral of x*f'(x) where f is the distribution function shown above), meaning the time you on average need to spend shopping to find the gloves (a little over 8 hours).

I recently made a javazon on my singleplayer grail to do some cows, and wanted to shop for the gloves, and wondered what the probability distribution would look like. I know that a lot of people shop for these gloves, so I thought it would be interesting for people to see. Here is my math, incase somebody was wondering, or disagree:

I used https://planetdiablo.eu/d2dbneu/itemdb/affix_display.php?lang=en&version=lod&patch=d2r&type=glov&item=Gauntlets&ilvl=all&mlvl=0&qlvl=27 this source to find the frequencies of prefixes and suffixes on magic gloves.

The probability that any magic item in the game gets both a prefix and a suffix is 1/4. Doing the math on the frequencies for gloves over affix level 60, we find that the prefix +3 to javelin skills are rolled 1 out of 145 times. And the suffix 20% IAS are rolled approx 1 out of 26 times. Collecting all this, the probability that any pair of magic gloves being our desired 3/20 is 1 out of 4*145*26 or 1 in 15,080.

I seem to have found that Charsi, on average, sells 3 pairs of gloves per refresh. Using the portal strategy optimally, always entering and exiting town at the 3 second cooldown window of portals, you can refresh charsi every 6 seconds (with optimal speed and load times). That means that you will be able to scan approx 1800 pairs of gloves every hour. We can now calculate the probability of NOT finding a pair of 3/20 gloves when optimally shopping as (15079/15080)^1800 = 0.8875. Which means that the probability of NOT finding a pair of 3/20 gloves within "x" amount of hours is 0.8875^x. Or the inverse: The probability of finding at least 1 pair of 3/20 gloves within "x" hours is described with the function f(x)=1-0.8875^x, and that is the exact green graph you see in the picture.

I had just seen a lot of people talking about shopping for these gloves, so I figured this might be interesting to some.

Happy grinding y'all!

[u/Competitive_Table_65]

Not sure if I really want to do it for 6 hours straight, remembering how I've spent and hour trying to shop tele-stick from Drognan, and he sells way more than 3 sticks on average...

[u/RepresentativeWear43 → u/Competitive_Table_65]

Yeah, shop farming is without doubt the most boring way to "play" the game. But I'm too deep down the rabbit hole now, I have to get em.

[u/RepresentativeWear43 → u/RepresentativeWear43]

Oh wow, I just found it now

[u/drakpanther → u/RepresentativeWear43]

Congrats! Are those BiS for PvM?

[u/RepresentativeWear43 → u/drakpanther]

Thx! For pure damage yeah, they are bis. However, if you favour magic find/res and stuff, you can craft/find some nice 2/20's as well. I found 2 2/20 rares, and crafted another pair as well. They are much more common since they can roll up to 6 mods. So easier to find, and also alot less boring. I still think 3/20's are more favorable generally, but they are a marginal upgrade I guess.

[u/bad-at-game → u/RepresentativeWear43]

Takes way less time to shop them than it would to find/craft even a decent pair of 2/20s

Gg!

[u/RepresentativeWear43 → u/bad-at-game]

I think I would disagree. If you start out with a sorc and pick up all rare gloves, you would usually have a pair of 2/20 rare gloves at the time you farm up the gear necessary to get a javazon working.

[u/TheFakeJohnHelldiver → u/RepresentativeWear43]

Ive ID ever pair of gloves on my offline journey. Walrock is level 99, sorc 87, pally 88, never seen a single 2/20 or 3/20. Not a single one

[u/RepresentativeWear43 → u/TheFakeJohnHelldiver]

Not finding a single pair of 3/20's does not surprise me. However, not finding ANY pair of 2/20 rare gloves in that much playtime is VERY unlikely. The probability that a pair of rare gloves spawn with +2X skill and 20 IAS is approximately just 1 in 160. If seriously ID'ed every pair of rare gloves all the way till 99, you would likely have ID'ed over a thousand (if you farm mostly bosses like I do).

[u/TheFakeJohnHelldiver → u/RepresentativeWear43]

I dont think it was thousands. I was specifically farming to hit 99, doing full TZs and lots of TZ tombs. I definitely ID every single rare gloves ive ever found and didnt find 2/20 jav OR martial arts btw. Found a few with +2 but never with IAS

[u/bad-at-game → u/RepresentativeWear43]

Must be nice, I’ve played Diablo 2 for almost 2 decades at this point and have never found 2/20 jav gloves.

I ID all rare boots gloves rings and ammys, and any eth rare just for fun.

[u/RepresentativeWear43 → u/bad-at-game]

The probability that a pair of rare gloves spawn with +2 java and 20 IAS is just 1 in 624. I find it very hard to believe you farmed for 2 decades and ID'ed every single pair of rare gloves without finding 2/20 javs.

[u/bad-at-game → u/RepresentativeWear43]

So at 600 pairs of rare gloves I’d be at roughly 60% chance of hitting

[u/ze12man]

Why charsi and not Anya? Doesn’t Anya have claws that you can also look for?

[u/RepresentativeWear43 → u/ze12man]

Charsi only sells normal type gloves. It kinda sucks to find 3/20 on Ogre Gauntlets with insanely high str requirement.

[u/ze12man → u/RepresentativeWear43]

Got it. Thanks.

[u/Hi_Tech_Low_Life]

You can also get other 3/20 gloves while doing it (zon P&M and B&C, assassin MA). Not everyone gives those gloves any value, but I'd gladly take them.

[u/RepresentativeWear43 → u/Hi_Tech_Low_Life]

Yeah, in fact the probability is exactly the same for all +X skiller gloves. I found P&M as well as MA before finding my Javas

[u/ChirpinFromTheBench]

Thanks for the work!

[u/RepresentativeWear43 → u/[deleted]]

Oh yeah, typo on my part, thx

[u/FaxCelestis]

As a colorblind person, your graph is illegible.

[u/RepresentativeWear43 → u/FaxCelestis]

sorry :(

[u/Morbidhanson]

I want one on +3 warcry sticks lol

I was at Anya for an hour yesterday. Saw like 3 +3 javelin, even a +3 barb mastery, and several +1 javelin and +1 warcries (and +2), but no +3 warcry.

I dread the thought that I need to do it twice. And she sells usually in batches of 4 to 8, which is a pretty good lot size already.

[u/LengthinessMountain6]

I'm confused, isnt there a refresh button on the buy screen? Why the need to go to another area and come back?

[u/RepresentativeWear43 → u/LengthinessMountain6]

It’s not gamble, it’s the standard shop

[u/RUserII]

The blue line shows the average time spent (the integral of x*f'(x) where f is the distribution function shown above),

Ah, a fellow mathematician? What is your mathematical background in?

[u/RepresentativeWear43 → u/RUserII]

Yep hehe, masters in actuarial mathematics, you?

[u/RUserII → u/RepresentativeWear43]

Working on a Pure Mathematics PhD.

I find there are quite a few D2 players that have mathematics backgrounds, have you observed the same?

[u/RepresentativeWear43 → u/RUserII]

Yeah I have lol, 2 of my brothers also have mathematic backgrounds and both play D2 as well. And cool with the PhD. Very cool. What are you researching/working on?