The Math of Fusings

"

TehHammer wrote:

"

prazius wrote:

where do these formulas come from? Where did the 305 and 306 come from?

Those were stated odds (100:90:80:30:5:1) by Chris regarding Jeweler's orbs. They never were accurate for fusing orbs, so that was just a guess as to what the odds were. They were not accurate. 4Ls, 5Ls and 6Ls are 2 to 3 times less likely than those odds.

So for Jeweler's, there are 306 total possible outcomes with 100 chances to be 1 socket, 90 chances to be 2 sockets, 80 chances to be 3 sockets, 30 chances to be 4 sockets, 5 chances to be 5 sockets, and 1 chance to be 6 sockets (assuming the item is chest/2H weapon and ilvl 50+). The trick is, you can't roll the same amount of sockets as you currently have, so if your item has 1 socket, you have 1:206 odds of getting a 6S (306 - 100), if your item has 2 sockets, it's 1:216 odds of getting a 6S (306 - 90). (You can simulate rolling Jeweler's orbs on my Jeweler's simulator)

Fusing rolls are done similarly, there are odds for socket grouping. Assume they weighted the fusing odds something like 300:270:240:60:10:1 or 200:180:160:60:10:1, one of those is probably close to the fusing odds, although I doubt a dev will confirm or give us actual numbers. Based on how common it is to see 6L take over 1000 fusing orbs and even over 2000 fusing orbs, I'd guess that my first batch of odds is more accurate (1:881 odds of 6Ling an item).

So basically you roll (based on 1st set of guessed odds) a number between 1 and 881, if you roll a 300 or lower, the first socket is grouped in a 1 socket group (aka, no links). If you roll a 301 to 570, you get a 2 socket group (aka 1 link between 1st and 2nd sockets). If you roll a 571 to 810, you get a 3 socket group (aka 2 links between 1st, 2nd and 3rd sockets). If you roll a 811 to 870, you get a 4 socket group (aka 3 links between 1st, 2nd, 3rd and 4th sockets). If you roll a 871 to 880, you get a 5 socket group (aka, links between 1st, 2nd, 3rd, 4th and 5th sockets). If you roll a 881, you get a 6L item.

The trick with fusings is, it rolls until it can't roll any more. If you roll a 1 socket group on the first socket (~34% of the time based on my guessed odds), you have 5 sockets remaining, which means you can still 5L it, so it will roll again with a number between 1 and 880, removing the 1 chance of becoming 6L because there aren't 6 sockets left to link, only 5. This is exactly why it's more likely to roll a 5L on a 6S item than on a 5S item, you basically get a 2nd chance to roll 5L one-third of the time.

If it rolled a 2L on the first socket, it would remove the odds for 6L and 5L. If it rolled a 3L on the first socket, it would remove the odds for 6L, 5L and 4L. Etc.

Also, a fusing can't leave an identical arrangement of links, so if it does, I believe it starts the entire roll over.