RNG is a hot topic in goldmaking with several methods having RNG elements. This is perhaps most pronounced in farming, particularly if you farm for rare items with very low drop chances, alchemy procs and prospecting are other parts that are affected by RNG.
The law of large numbers
In statistics the law of large numbers states that if you do something with a random outcome, but you know the chances of the different outcomes enough time, then your average result will be the same as the actual percentage chances.
If you craft enough rank 3 potions in retail, eventually you will end up with exactly the number of extra potions per craft that the actual rate is. Or if you prospect enough ore, eventually you will get gems according to the chance that you can get them.
The implication
The implication of this is of course that for any activity with a random outcome, you need to do it enough times that the outcome is no longer random. Using the expected long term value for profit calculations also makes it much easier to calculate profit margins for crafting and the gold per hour for farming.
Low drop rate farming clickbait
I’m sure you are familiar with youtube videos with a certain gph in the title based on a single lucky run of farming. If the proc or drop chance is extremely low it can take you much to long to actually get to the required large numbers. A rough rule of thumb is that you need to do it at least 1000 times if the chance is 1%, and even then you will still have variance and can’t be sure. For higher percentages chances you can get away with fewer attempts.
Can you rely on procs?
If you know you will reach the required number then yes. For prospecting and rank 3 alchemy, you should not even enter it unless you plan on going hard enough into it that you reach the required number. If you can’t rely on the procs, then you will not be able to make a profit in these markets.
In farming, it is harder, as farming typically requires way more time invested to reach the required number of kills. If you need to farm 100 hours to reach the average yields of some spot it is probably too RNG-dependent to really be worth it.