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 ?
Jeweler probability and socket color data
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:
=> 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
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.
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%