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I'm trying to set up a campaign and I'm not great at math. We play old school 1e AD&D.

The 1e DMG gives two tables on page 47 for chance of an encounter. The base chance of encounter depending on population density, then a matrix of when to check based on terrain type.

For example in a "relatively dense" population the base chance is "1 in 20." In "plains" we are instructed to roll morning, evening, midnight.

Does "1 in 20" mean that if I roll 1d20, there's an encounter every time I roll a 20, or a 1?

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Either is fine.

Assuming your d20 is fair, either a 1 or a 20 will occur 5% of the time, or "1 in 20."

The DMG, one paragraph later, lays out a procedure: "when an encounter check is indicated, roll the appropriate die and, if a 1 results, an encounter takes place."

This, however, is mathematically no different than saying "if the highest value results" or "if a 3 results." You just need to set a convention for yourself and stick to it, so you can free up mental space for all the other things you're dealing with. I suggest declaring for yourself that a 1 will be your result that triggers an encounter, for three reasons:

  • it's in accord with the book's instructions, in case you ever forget,
  • it comports with a general notion that "high rolls are good for the party," and
  • since your different population densities specify different die sizes, choosing 1 means that any 1 you see--no matter the die--triggers an encounter.
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On a roll of a "1"

In the last paragraph on page 47 is this sentence:

When an encounter check is indicated, roll the appropriate die, and if a 1 results, an encounter takes place

Conventionally also, the expression "n in x" is usually read as meaning "on a 1 through n, on an x-sided die". For example, a gnome listening at a door for noises will hear something "4 in 20", meaning on a roll of 1–4 on a d20. (DMG p60)

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