This post is in response to a question someone asked me privately.
Usually in D&D the likelyhood of a random encounter is stated in terms of a m in n chance every p turns. For example, in B5 - The Horror on the Hill the likelihood of encountering wandering monsters was stated, "Check for wandering monsters on The Hill every three turns when the party is moving and every six turns if they are stationary (camping). If you roll a one on a ld6, one of the following types of monsters is encountered (see table below): roll a ld6 again to determine the exact creature(s)." Most adventures have some similar statement.
For planning purposes, it might be useful to know the expected amount of time between random encounters. It's not complicated, though. In the above statement there's a 1 in 6 chance of a random encounter every 3 or 6 turns. That means that you expect that out of 6 trials you expect one of them to result in a random monster. If there's a trial every 3 to 6 turns you expect a wandering monster to appear every 18 to 36 turns.
That makes wandering monsters pretty rare. A lot has been said about how using wandering monsters forces the players to pick their battles. That's only true, though, if wandering monsters are common enough to be a real nuissance.
In The Keep on the Borderlands the wandering monsters statistics are phrased a little differently. "The passage ways here are very busy, and for every 10’ distance covered by the party there is a 1 in 6 chance that they will encounter a group of goblins (see below). Check every time the the party travels 30’ (a 3 in 6 chance) until wandering goblins are encountered.."
That means that you have 50% chance of encountering the wandering monsters in the first 30', so you will on average encounter them 15' into the dungeon. A party that moves 90' per turn will run into them on average in less than a turn!