Devs - what is the chance of a link between any two sockets?

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jawsofhana wrote:

4 link is pretty easy to make.

5 link is not much harder.

6 link is very hard, and -should- be very hard to get.


This is explained elsewhere, but 5 link is only hard to make if you try to do it on a six socket item.

about 50 orbs average is needed to be sure you get 5 sockets linked.

300 for six socket.

Never used more than 8 for a 4 link.

My 6-socket Marohi has eaten 178 fusings without a single 5-link.

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Aelloon wrote:

My 6-socket Marohi has eaten 178 fusings without a single 5-link.

According to the numbers provided by here before, your 178 fusings have had a total of 353% chance to get a 5L ))

sigh.

(0.02*178)-(.98^178)=3.53

Edit: I suck. (0.02*178)-(.998^178)=280% >_> even so. Damnit.

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Alisia261 wrote:

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jawsofhana wrote:

This is explained elsewhere, but 5 link is only hard to make if you try to do it on a six socket item.

You're backwards. Odds to get a 5L on a 6S are better than on a 5S item (1:46 on a 6S, 1:61 on a 5S). A 6S gives you a 2nd chance to roll 5L if it rolls 0 links on the first socket (which is about 30% of the time).

Formulas are as follows:
5S odds = 1 / (5 / 305)
6S odds = 1 / (5 / 306 + (100 / 306 * 5 / 305))

That said, you're way more likely to see a 5L in the wild drop on a 5S item than a 6S item, as 5S items are 5 times more common than 6S items.

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

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prazius wrote:

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Aelloon wrote:

My 6-socket Marohi has eaten 178 fusings without a single 5-link.

According to the numbers provided by here before, your 178 fusings have had a total of 353% chance to get a 5L ))

sigh.

(0.02*178)-(.98^178)=3.53

Edit: I suck. (0.02*178)-(.998^178)=280% >_> even so. Damnit.

my 6s marohi has eaten 396 fusings with 21 5links.

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prazius wrote:

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Aelloon wrote:

My 6-socket Marohi has eaten 178 fusings without a single 5-link.

According to the numbers provided by here before, your 178 fusings have had a total of 353% chance to get a 5L ))

sigh.

(0.02*178)-(.98^178)=3.53

Edit: I suck. (0.02*178)-(.998^178)=280% >_> even so. Damnit.

Your math is like... Really weird, on both figures. What you want is 1-(1-1/46)^178 which will give you about 98%. This is assuming the 1/46 chance figure is correct. Why you've got (0.02*178), rather than 1 out the front I've no idea, that's totally what's messed up your calculation though.

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Sinshlad wrote:

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prazius wrote:

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Aelloon wrote:

My 6-socket Marohi has eaten 178 fusings without a single 5-link.

According to the numbers provided by here before, your 178 fusings have had a total of 353% chance to get a 5L ))

sigh.

(0.02*178)-(.98^178)=3.53

Edit: I suck. (0.02*178)-(.998^178)=280% >_> even so. Damnit.

Your math is like... Really weird, on both figures. What you want is 1-(1-1/46)^178 which will give you about 98%. This is assuming the 1/46 chance figure is correct. Why you've got (0.02*178), rather than 1 out the front I've no idea, that's totally what's messed up your calculation though.

Thanks a bunch, I've been looking for that everywhere. I totally get the formula you've provided, makes absolute sense.

In closed beta, I used a bit above 700 jewelers to get a 6s and then around 350 fusings without any 5/6l
I got a 6L in 13 fusings in open beta so I guess it worked itself out

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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).

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.

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Sinshlad wrote:

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prazius wrote:

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Aelloon wrote:

My 6-socket Marohi has eaten 178 fusings without a single 5-link.

According to the numbers provided by here before, your 178 fusings have had a total of 353% chance to get a 5L ))

sigh.

(0.02*178)-(.98^178)=3.53

Edit: I suck. (0.02*178)-(.998^178)=280% >_> even so. Damnit.

Your math is like... Really weird, on both figures. What you want is 1-(1-1/46)^178 which will give you about 98%. This is assuming the 1/46 chance figure is correct. Why you've got (0.02*178), rather than 1 out the front I've no idea, that's totally what's messed up your calculation though.

If my first guess of numbers is accurate, it's about 1 in 65.7 odds of getting a 5L on a 6S item (1 / ((10 / 881) + ((300 / 881) * (10 / 880)))).

This would make the success rate of 178 fusings ~93.5% (1-(1-1/65.7)^178). That is, assuming 5L is what you consider success.

Um, why do you consider the fusing application events dependent? Unless each item "registers" internally how many jewelers you spent on it and modifies the odds accordingly (sorry, I didn't follow devs comments on the issue), the events of orb application are completely independent, i.e. you roll with the same odds on first, on second, on thrid, etc fusing application.

So your 93.5% on 178 fusings is only if the events are dependent in a way.

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kiorull wrote:

Um, why do you consider the fusing application events dependent? Unless each item "registers" internally how many jewelers you spent on it and modifies the odds accordingly (sorry, I didn't follow devs comments on the issue), the events of orb application are completely independent, i.e. you roll with the same odds on first, on second, on thrid, etc fusing application.

Uh what other approach would you suggest to finding out how many fusings approximately a 5L+ item might cost?

Also, I don't think there were any dev comments so far ] : they keeping the actual data to themselves it seems