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

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kiorull wrote:

Um, why do you consider the fusing application events dependent?

They don't. 1-(1-p)^n is the formula for the probability of an event with probability p occurring at least once in n independent trials.

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Xenolith wrote:

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kiorull wrote:

Um, why do you consider the fusing application events dependent?

They don't. 1-(1-p)^n is the formula for the probability of an event with probability p occurring at least once in n independent trials.

this may be my favorite post in the history on the internet.

Using the ratio 300:270:240:60:10:1 and ignoring that you can't get the exact same combination of links (The odds are ever so slightly better without this assumption) , I calculated that:

For a Six Socket Item the probability of:
Getting 5 Sockets Fused First Roll = 0.011351
Getting 6 Sockets Fused First Roll = 0.001135
Getting 1 Socket (Not Fused) and THEN 5 Sockets Fused Second Roll = 0.00387

Thus the probability of getting 5 or more sockets is 0.016355

For a Five Socket Item the probability of:

Getting 5 Sockets Fused First Roll = 0.011364

For comparison I Have produced the following log-log plot:

http://imgur.com/yVcsdyF

As you can see it is always better to roll a 6 socket item.

However the cost benefit becomes statistically insignificant if you are willing to spend more than ~500 orbs to get a 5 links.

The expected number of rolls, or the average number of rolls based on the above ratio is:

5 Socket Item: 1/0.011364 = 88 rolls
6 Socket Item: 1/0.01635 = ~61 rolls

Therefore if you have rolled 178 times and did not receive a 5 link from the PoE Gods, you are unlucky (within the error of my lazy calcs and said assumptions).

tl;dr sucks to your asthma

800+ fuse rolls no 6L handful of 5L guess im unlucky

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deadpplqq wrote:

800+ fuse rolls no 6L handful of 5L guess im unlucky

thats not unlucky ... thats common ^^ ... there is not for fun the 1500 fusion artisan bench recipe for a 6L :)