The odds listed on the Arreat Summit website are incorrect. The game rolls a D6 with any of those four socketing recipes (helm, body armor, shield, weapon).
Let r denote the result of the roll (an integer from the set {1, 2 ... 6}) and let M denote the maximum number of sockets possible (depends on base item and item level).
If r>M then add M sockets, else add r sockets. Hence the odds are as follows:
Code
M S(1) S(2) S(3) S(4) S(5) S(6)
1 6/6
2 1/6 5/6
3 1/6 1/6 4/6
4 1/6 1/6 1/6 3/6
5 1/6 1/6 1/6 1/6 2/6
6 1/6 1/6 1/6 1/6 1/6 1/6
For the case M=2 the chance to get
Socketed (2) is 5/6 (~ 83.3%), and not 3/4 (75%) as stated on the Arreat Summit website.
For the case M=4 the chance to get
Socketed (4) is 3/6 (= 50%).
The four
Horadric Cube socket recipes produce a somewhat random outcome as you can see, and they require a normal quality item without sockets.
Larzuk's reward for the ''Siege on Harrogath'' quest will always add M sockets to a Cracked/Crude/Damaged/Low Quality/normal quality/Superior item without sockets.
This post was edited by Quorra on Nov 7 2018 04:08am