How to read 3d6+2 without guessing

The notation on a character sheet is compressed on purpose. “3d6+2” fits in four characters and carries a whole instruction about rolling, counting and adding. The compression is useful until it is not: the moment a rulebook writes “4d6 drop lowest” or “2d10 − 1”, a reader who learned the shorthand by imitation rather than by rule starts improvising.

This note unpacks the shorthand part by part, then covers the conventions that surround it.

The core form: n d s

The free rules write a die as the letter d followed by its number of sides (d4, d6, d8, d10, d12, d20) and put the number of dice in front, so “3d8 + 5” means roll three eight-sided dice, add them, then add 5 (D&D Beyond — Free Rules: Playing the Game). Written generally, the form is n d s: roll n dice with s sides each and add them.

• n is how many dice you pick up.
• d is the marker that separates the count from the sides.
• s is the number of faces on each die.

So 3d6 is three six-sided dice added together, 1d20 is one twenty-sided die, and 2d8 is two eight-sided dice. The free rules write a single d20 roll as “1d20” in places and as “d20” in others; both mean one die.

The range of the roll follows directly: a roll of n dice with s sides lands between n and n × s. That range is a useful check. If a rule says a weapon deals “2d6 damage” and your result is 13, either the rule has a modifier you missed or the arithmetic is wrong, because 2d6 cannot exceed 12.

The average is the midpoint of the range because the faces are evenly spread: for a single die with s sides the average is (s + 1)/2, and for n dice it is n × (s + 1)/2. This is the expected value, the sum of each outcome times its probability (OpenStax — Mean or Expected Value and Standard Deviation). It lets you sanity-check a system’s numbers without rolling anything.

Modifiers: plus and minus

A constant added to the total is written after the dice: “3d6+4” means roll three six-sided dice, add them, then add four (same pattern as the “3d8 + 5” example in D&D Beyond — Free Rules: Playing the Game). The range shifts with it: 3d6+4 runs from 7 to 22. A constant subtracted works the same way, so 3d6−1 runs from 2 to 17.

One caution: a negative modifier can push a total below zero (1d4−3 can reach −2). Some rulebooks add a floor, such as “the result is never less than 1”, and some do not. Look for that sentence before trusting the arithmetic.

Which dice count

Some rules ask you to count only some of the dice rolled. The free rules for character scores say to roll four six-sided dice and record the total of the three highest (D&D Beyond — Free Rules: Creating a Character). That is the instruction commonly called “4d6 drop lowest”. Shorthand for it varies from book to book and from dice app to dice app, so when a rule is written in symbols, find the sentence in words that explains it.

Notation is not probability

The shorthand tells you how to roll. It does not tell you how likely. Two notations with the same range behave very differently: 1d20 covers every integer from 1 to 20 exactly once, each with 5% probability, while 3d6 covers only 16 of those integers and crowds the middle. A rulebook that swaps one for the other without saying so has changed the game’s feel while keeping its printed range.

That is the trap worth watching for. The notation is compact enough to look interchangeable; the distributions behind it are not.

What to check when a rule is ambiguous

When a rule’s notation could be read two ways, four questions settle it:

1. How many dice, and how many sides — does the count multiply the sides?
2. Is the modifier applied to the total, or to each die?
3. Which dice count: all of them, the lowest dropped, the highest kept?
4. What happens when the result lands outside the plausible range — is there a floor, a cap, or a special result?

A rulebook that answers all four for each notation it uses is a rulebook a reader can trust with a pencil and paper in hand. One that answers none is not wrong, exactly; it is leaving the arithmetic to the table, where it becomes a different game on every night.

Quick reference: range and average

For n dice of s sides: the range runs from n to n × s, and the average is n × (s + 1)/2. A modifier of +k shifts both by k. For example, 3d6+2 runs from 5 to 20 with an average of 12.5, and 2d10−1 runs from 1 to 19 with an average of 10.

Sources

• D&D Beyond — Free Rules: Playing the Game: dice written as d plus the number of sides, with the count in front and a modifier after.
• D&D Beyond — Free Rules: Creating a Character: the wording of the roll-four-keep-the-highest-three method.
• OpenStax — Mean or Expected Value and Standard Deviation: expected value as the probability-weighted average.

Written for: a new reader of rulebooks who has seen the shorthand but never been told the grammar behind it.