Every three laps unless otherwise decided by the DM
This answer assumes that the only materials you use as reference are PHB, MM, and DMG.
How did I find this answer? (I hear people wondering) The 1st DMG is, as you pointed out in a commentary, organized in a counter-intuitive way.
You will find on page 190 the DMG under City meets the following text.
Check the encounters every three rounds as usual or otherwise as desired.
Where was the "normally" covered? Nowhere, although "once per turn" was "normally" for the original game (see below). Returning to "Keeping track of the weather" & # 39; on page 38, we find:
It is essential to keep an accurate record of the hour so that the deputy minister can determine when to check for stray monsters and to strictly control the duration of certain spells … He may happen that one party wants to hide. a long time maybe at night … that does not exempt them from occasional checks for wandering monsters, although the frequency may be somewhat moderate, according to the conditions …
Disconcertingly, for those looking for a concrete answer, a periodicity was suggested on page 174 …
When a random encounter is indicated by the periodic check …
But there is no hard and fast rule in this section on random monsters, and it also returns you to your own chart / chart in this passage. Which implies that you had better create your own graph and your own periodicity, but it does not require anything.
The 1st DMG AD & D is as usual, not going to give you a hard and fast rule. Do not let this be an obstacle to play. Throughout the 1st DMG AD & D, the author has devoted a significant amount of text to provide the DM the following indications that I will summarize in a simple principle: do what you want, you're the DM.
And it works. (Well, it worked for me for a few years when I ran and played in the AD & D dungeons 1e).
Alternative answer: Once per turn, roll 1d6
Many AD and D have been written with the basic assumptions of playing Original D & D (three little books in a box, 1974) as an integrated hypothesis. In Volume III, Adventures in the Desert and the Underworld, on page 10, we read:
Wandering monsters: At the end of each round, the referee rolls a six-sided die and sees if a wandering monster has been encountered. A score of 6 indicates that a wandering monster has appeared.
In all honesty, during the first five years I played at D & D and AD & D (1975-1981), this was "normal" in many of the dungeon crawls in which I participated .
Use wandering monsters to "get things done"
None of the above precludes the use of a Random Monster Check whenever you feel it is appropriate. With published adventures, some have a guide to random checks of monsters, others not.