Yes if you're playing a Smithing character this is something you should keep in mind. Smithing characters are much more motivated, in many situations, to fully explore levels than other builds are. Especially for that second forge, I suspect based on my own games that it is nearly always of the "forced" variety, and I'm always aware of the chance I'll get a forced one when I enter a new level.
The chance slides from 0 to 100%, from 2000 to 5000 turns since the last forge was generated. So if I'm within that initial 2000 turns since a forge was generated, I feel much more free to leave levels unexplored, knowing I'm unlikely to be missing a forge.
Edit: Is it a sliding probability? If so it would be nice to know the chances to know when to slow diving & look for a forge & when to grab song of aule on a singer smith.
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