Dice Notation Explained: What 3d6, 4d6 Drop Lowest and d100 Mean

Open any tabletop rulebook and you'll hit a wall of code: 3d6+2, 4d6 drop lowest, roll with advantage, d100. It looks cryptic, but it's one of the tidiest shorthands in gaming — once you know the pattern, you can read any of it on sight.

This guide decodes dice notation from the ground up, then shows you the probabilities that actually matter at the table: why 7 dominates on 2d6, and why "4d6 drop lowest" quietly hands you a better hero.

Dice Notation: The XdY+Z Pattern

Almost every dice expression follows one template:

X d Y + Z

• X — how many dice. The number before the d. If it's missing, roll one.
• Y — how many sides. The number after the d. A d6 is the cube in your board-game box; a d20 has twenty faces.
• Z — the modifier. A flat number added (+) or subtracted (-) from the total after you roll. It's never multiplied per die — you roll first, sum, then adjust once.

So 3d6+2 is "roll three six-sided dice, add them up, then add 2." That's the entire system. Everything else is a special instruction bolted onto this base.

The Notation Cheat Sheet

The expressions you'll meet most often, and exactly what each one tells you to do:

Notice that a modifier and a die count are different things. d6+3 ranges 4–9 (one die, plus three). 3d6 ranges 3–18 (three dice, no bonus). Mixing those up is the single most common beginner slip.

2d6 Probability: Why 7 Wins

Roll a single die and every face is equally likely — a flat 1-in-6. Roll two dice and add them, and something important changes: the totals stop being equal. This is the fact behind "results tend toward the middle," and here are the actual numbers.

Two d6 produce 6 × 6 = 36 equally likely combinations. But those 36 combinations don't spread evenly across the totals 2–12. There's only one way to roll a 2 (1 and 1), but six different ways to roll a 7 (1-6, 2-5, 3-4, and each reversed). Count the ways for every total and you get this:

The counts form a perfect pyramid — 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1 — and they add up to 36, as they must. Seven is the peak at 16.7%, which is why it's the number Catan robbers love and craps is built around. The extremes, 2 and 12, are six times rarer. Add more dice (3d6, 4d6) and this bell-curve effect sharpens further, clustering results ever more tightly around the average.

Advantage, Disadvantage and Drop-Lowest

The most interesting notation doesn't just add dice — it throws some away. Three mechanics do this, and they all bend the odds in a specific direction.

• Advantage (roll 2d20, keep the higher). A flat d20 averages 10.5. Rolling two and keeping the best pushes the average up to about 13.8 and makes low results scarce — you only whiff if both dice roll low. It's the single biggest swing in D&D 5e without touching a modifier.
• Disadvantage (roll 2d20, keep the lower). The mirror image: your average drops to roughly 7.2, and high rolls almost vanish. Advantage and disadvantage cancel out one-for-one, so having both at once just means you roll a single plain d20.
• 4d6 drop lowest. The classic way to generate a hero's ability scores. Rolling four dice and discarding the worst pulls the average of each score up to about 12.2 — noticeably above the 10.5 you'd expect from 3d6 — which is why characters rolled this way tend to start a cut above average.

The through-line: whenever a rule tells you to roll extra dice and keep only some, it's deliberately shifting your luck. Keeping the highest helps you; keeping the lowest hurts.

Are Digital Dice Actually Random?

A physical die can pick up a real bias — a chipped corner, uneven weighting from the pips drilled into its faces, or a favourite resting spot after years of use. A well-built virtual roller has none of that: it draws from your device's cryptographically secure random generator, so every face of every die is exactly as likely as the maths above promises. That's the same fair-randomness engine behind our coin flip — we unpack how it works, and why it beats a real coin, in the coin toss probability guide.

For tabletop play the practical wins are speed and honesty: no die skitters off the table, no one can accuse anyone of a loaded roll, and rolling ten dice at once takes one tap. When you just need a plain random value rather than a die total, the Random Number Generator lets you set any range you like.

Dice are also the fairest referee your group owns. Deciding turn order, who's the first player, or which team goes first? Let the Who Goes First picker settle it, flip a coin for sides, or browse the rest of our decision tools for whatever the night throws at you.

Frequently Asked Questions

What does 3d6 mean?

Roll three six-sided dice and add them together, for a total of 3 to 18. The number before the d is how many dice; the number after it is how many sides each has. Tack on a modifier — 3d6+2 — and you add that number once, after summing.

How do I roll a d20 online?

A d20 roll is a single random number from 1 to 20 — the core roll of D&D 5e for attacks, saves and checks. Use a virtual roller that supports twenty-sided dice and it generates the result instantly, with no physical die to lose under the couch.

Can I roll multiple dice at once?

Yes — that's what notation like 3d6 or 10d6 is for. Our dice roller rolls up to six dice in one click and shows every face plus the total, covering most board-game and 2d6-style rolls.

What's the most common roll on 2d6?

Seven, at 16.7%. There are six ways to make 7 out of 36 possible combinations — more than any other total — so it lands 1 in 6 rolls. The totals get steadily rarer toward 2 and 12, which have just one combination each.