[Unofficial] The complete guide to fusing mechanics

This is a compilation on how fusing work based on my knowldege of the game mechanis as well as these explanation from Chris in these 2 threads

Easier to fuse 5 link than 6 link ?
http://www.pathofexile.com/forum/view-thread/20922

Jeweler probability and socket color data
http://www.pathofexile.com/forum/view-thread/20338

Note: Unless devs provide more information, this infomation is not fact. Numbers are based on jeweler and not actual fusing number.

First let's look at how item sockets are represented in game, let's consider this 6 socket robe:


Here's how the socket looks on the ground



If we number these socket from the left to right as 1-6 we got this



So the link on this item is now simply: 1-2 3-4-5 6

Socket link will be rolled in groups. For this item, there's a group of 2, a group of 3 and a group of 1. In order to get 6 linked, you need to roll a group of 6, at once. Using number for jeweler probability (0.9.6f) we will roll the first group:

1st group:
1:100 (32.68%)
2:90 (29.41%)
3:80 (26.14%)
4:30 (9.80%)
5:5 (1.63%)
6:1 (0.33%)

=> chance of getting a 6 linked item: 0.33%

If you failed to roll a group of 6, subsequent roll doesn't matter. For this first roll, if we get 5 or 6, the item will be 1-2-3-4-5 6 or 1-2-3-4-5-6

If the first roll is 1 we have the following possibility for the next group

2nd group:
1:100 (32.79%)
2:90 (29.51%)
3:80 (26.23%)
4:30 (9.84%)
5:5 (1.64%)

If you failed to roll 5 the 1st time, there is a chance to roll 5 again here, which will get you 1 2-3-4-5-6 instead of 1-2-3-4-5 6

=>Total chance of rolling 5 linked (position doesnt matter): 1.63% + 32.68%*1.64% = 2.17%

For my robe posted above, it will have to roll number 2 the first time around, roll 3 the second time around and done.

This should be enough for those who are curious about the chance to roll a 6 linked. Remember that these number are taken from jeweler probability. Fusing number might be better (since fuse are rarer and you roll more than once with each use). Also this does not take into account the fact that item cannot roll the same link it currently has. This mechanics is unknown and insignificant for links

TL;DR: Here's the probability chart for a 6 sockets item

To have exactly:
6 linked (only 1 position): 0.33%
5 linked (regardless of position): 2.17%
4 linked (regardless of position): 15.96%
3 linked (regardless of position): 42.56%
2 linked (regardless of position): 61.51%
0 linked (only 1 position): 0.70%

This will not add up to 100% since an item can be both 4 linked and 2 linked. Feel free to correct my math if I did some part wrong. For the most part, 5 linked and 6 linked should be correct.
If any of you are interested I can do the math for 5, 4 ,3, 2 socket items.

Edit1: Spelling

Edit2: Chart#2, which is more useful in practice

6 linked or better: 0.33%
5 linked or better: 2.50%
4 linked or better: 18.46%
3 linked or better: 61.01%
2 linked or better: 99.30%
0 linked or better: 100%

For stats purposes:

I spent about 80 fusing on a 6-socket to get 5-linked.

"

perry1986 wrote:

I must be incredibly lucky then, 6 fusing try gave me a 6 linked :)

That is incredibly lucky.

Are the jeweler/fuse probabilities for possible 4S items (helm, gloves, boots, 1H, shield) around the forum anywhere?

"

MorriganGrey wrote:

Are the jeweler/fuse probabilities for possible 4S items (helm, gloves, boots, 1H, shield) around the forum anywhere?

They are the same as a 6S capable item, just without the chance of rolling higher sockets.

6S capable item:
1/2/3/4/5/6 sockets
100:90:80:30:5:1
1 in 306 odds of getting 6 sockets, 1 in 61.2 (5 in 306) of getting 5 sockets, 1:10.2 4S, 1:3.825 3S, 1:3.4 2S, 1:3.06 1S.

4S capable item:
1/2/3/4 sockets
100:90:80:30
1 in 10 (technically 30 in 300 odds of getting 4S, 1:3.75 3S, 1:3.333 2S, 1:3 1S.

3S capabale item:
1/2/3 sockets
100:90:80
1 in 3.375 odds of getting 3 sockets, 1:3 2S, 1:2.7 1S.

Note, the actual odds are better than these posted, the reason being, using a Jeweler's Orb will not result in the same amount of sockets as the item currently has. This means that you are more likely to have 1S and therefore cannot roll another 1S eliminating 100 possibilities. Same thing with 2 sockets and 90 possibilities, etc.

Fusings are very similar odds except for 6 linking. The odds of 6 linking is more like 1 in 1200 instead of 1 in 306, something like (I just quadrupled all the chances except 6L):

6L capable item
0/1/2/3/4/5 links odds on the first roll (socket)
400:360:320:120:20:1

These aren't 100% accurate, but they're close.

Also, if you're interested, I have a Jeweler's orb simulator here which will simulate rolling max sockets 1000 times to give you an accurate read on odds. Also, I have a rather ghetto fusing simulator here, which just simulates the use of 1 fusing orb on an item.