The Adventures Dark & Deep ruleset has no specific rule on how to randomly determine starting distance of an encounter. The one thing it does mention about encounter distance can be found on page 9 of the Game Master's Toolkit.
A group that catches another unawares at a distance of 20' or more may automatically evade, if they so choose, as long as they remain unseen and unheard.
Thus, we refer to the First Edition Advanced Dungeons & Dragons Dungeon Master's Guide for a rule on determining random encounter distance (per the Ur-Text philosophy). The rules for this are found on page 62. The text of the rule has been modified slightly simply for clarity. Note that “units” of distance refer to yards when the encounter is outdoors and feet when the encounter is indoors.
Distance:
When encounters occur, the distance between concerned parties will be 1d6x10+40 units of distance subject to the following modifying factors:
1. Line of Sight: If this is unobstructed and light is involved, the distance possible for determination of another party present is virtually infinite (i.e., a group bearing a light in the dark can be seen from a very long way away by any other group) . It could likewise be sharply restricted due to obstructions (i.e., two groups technically only a few feet apart may still be unaware of each other's presence if they are unable to see each other for some reason).1)
2. Noise: If one party is making considerable noise which is discernible by the other party, the latter will have the options of fleeing or concealment; the former negating the encounter, the latter allowing distance to be 10 - 40 units before discovery by the noisy party.
3. Actual Area: If the encountered party is in a small area, distance between the two can be no greater than the maximum distance possible for discovery of the one by the other, e.g., opening a door into a 20' x 20' room will mean the distance between the two parties can be under 10', 10' or thereabouts, or 20'. In such a case, determine a variety of distance ranges and roll an appropriate die to choose one of those ranges randomly. In the preceding example, one could roll 1d6 where 1 - 2 = under 10', 3 - 4 = 10', 5 - 6 = 20'.
4. Planned or Unplanned Appearance: The sudden precipitation of one party upon the other due to any of a number of factors (teleportation, dimension door spell, other magical means, a chute, etc.) will cause distance similar to that found when actual area is a factor.
5. Surprise: Surprise can only be a factor in close encounter situations. If either or both parties are surprised, the distance must be either 10 - 30 units or it must be less as determined under the actual area modifier. Thus if the actual area were a 40' x 60' room, if surprise exists the distance between parties will be 10' - 30'.2)
6. Light: The illumination factor or visual capability of the concerned parties will affect encounter distance as follows:
A) A light source reliance limits the encounter distance to twice the normal vision radius of the source (2 x radius of the light source).
B) Infravision and/or ultravision operate only to the stated limit of their range and limit encounter distance accordingly.3)