How to Read Dice Notation: 2d6+3, d%, Advantage and Everything Between

Open any tabletop rulebook and within a page you will meet a string like 2d6+3, sitting mid-sentence as though everyone already speaks the language. Nobody is born reading it — but it is a genuinely small language, with a grammar you can learn in ten minutes and dialects you can pick up in an afternoon. This guide teaches dice notation from zero: what the letters and numbers mean, how percentile rolls work, what keep, drop, advantage and exploding dice do, and why 2d6 behaves so differently from 1d12 even though their ranges look interchangeable. We also read these expressions from an unusual seat. YSDICE is a dice factory, and every DND dice set we produce started life as a line of notation on a publisher's spec sheet — so we will finish with what "4d6 + 1d20 per box" means when it lands on a factory floor in Dongguan.

1. What dice notation is — and why games invented it

Before the shorthand existed, rules had to spell everything out: "roll two six-sided dice, add the results together, then add three." Accurate, but exhausting — and the moment a game asks for dozens of different rolls, the long form collapses under its own weight. Dice notation compresses the three questions every roll answers into a handful of characters: how many dice, which die, and what arithmetic happens afterwards. That is the whole trick.

Once compressed, the language travels. It appears in rulebooks, on character sheets, in board game forum posts, in wargame army lists, and in the chat bar of virtual tabletops, where typing a roll command is literally typing dice notation and pressing enter. It grew up alongside polyhedral dice in the tabletop boom of the 1970s, not because a committee designed it but because it removes ambiguity: "roll the dice" is a shrug, while "roll 3d6" is an instruction that two strangers on different continents will execute identically. Nobody owns it, every game borrows it, and the core grammar has stayed stable for fifty years — which, for a notation invented by hobbyists, is a remarkable run.

One convention before we start: the "d" is usually written lower-case (2d6), though you will meet capital-D versions (2D6) in older books and European titles. They mean the same thing. Read it aloud as "two dee six."

2. The grammar: what X, d and Y each mean

Every basic expression has the shape XdY. The X before the d is the count — how many dice you pick up. The Y after the d is the die size — how many faces each of those dice has. The d itself simply stands for "dice." So 3d6 means "roll three six-sided dice," and unless the game says otherwise, you add the results together into one total.

When the count is missing, it is 1. A rule that says "roll d20" means 1d20 — one twenty-sided die. The die size, meanwhile, is how dice get their names: a d6 is the familiar cube, while the d4, d8, d10, d12 and d20 are the other polyhedral dice that make up a standard seven-piece DND dice set (the seventh piece is a second d10 with special numbering, which section five explains). Faces are numbered from 1 up to Y, so each die's average roll is easy arithmetic: halfway between the lowest and highest face, or (1 + Y) ÷ 2. A d6 averages 3.5 per roll; a d20 averages 10.5. No single roll can actually land on 3.5, of course — the average describes the long run, not any one throw.

That is the entire core grammar. Count, die, sum. Everything else in dice notation — modifiers, percentile pairs, keep and drop rules — is a bolt-on to XdY, which is why the rest of this article gets easier from here.

3. Modifiers: the +3 in 2d6+3

A trailing +N or −N is a modifier, and it obeys one rule that resolves most beginner confusion: it is applied once, to the final total — never to each die. Read 2d6+3 as "roll two six-siders, add them together, then add three to the result." Roll a 4 and a 5, and the answer is 4 + 5 + 3 = 12.

Modifiers shift the whole range without changing its shape. Plain 2d6 spans 2 to 12 with an average of 7; 2d6+3 spans 5 to 15 with an average of 10. Every possible outcome slides up by exactly three, and the likelihood of each outcome is untouched — the middle totals stay common, the extremes stay rare. In play, that is how games separate the die's randomness from a character's skill or an item's quality: the dice supply the luck, the modifier supplies the competence.

Negative modifiers work the same way in reverse, with one wrinkle: 1d8−1 spans 0 to 7, and games differ on whether a result can actually be zero or gets floored at 1, so the surrounding rules text has the final say. You will also occasionally meet multiplication, usually for currency or distances — an expression like (2d6)×10 means roll 2d6, total it, then multiply the total by ten, giving 20 to 120 in steps of ten. Resolve the dice inside the brackets first, then the arithmetic outside. The order you roll physical dice in never matters; addition does not care.

4. Reading compound expressions

Real games chain groups together: 1d8+2d6+4 is a perfectly normal expression. The reading strategy is mechanical. Split at every plus and minus sign, identify each XdY group, roll each group, then total everything, constants included. Here that means one eight-sider, plus two six-siders, plus a flat 4 — a range of 7 to 24.

Games mix dice like this because each group usually means something different in the fiction: the d8 might be a weapon, the 2d6 a burst of extra energy, the +4 raw strength. The narrative labels matter at the table, but the arithmetic never changes — everything lands in one pot and gets summed. When an expression looks intimidating, it is almost always just three or four small expressions holding hands.

Two habits make compound reading foolproof. First, find the d's — each d marks one group of actual dice, and whatever carries no d is a constant. Second, work out the minimum and maximum before rolling: add all the dice at their lowest faces plus the constants, then at their highest. If a boss ability reads 2d10+1d6+5, you know instantly the damage lands between 8 and 31, and you know what the worst and best cases look like before any die hits the table. Experienced players do this without noticing; it is the notation equivalent of sight-reading music.

5. Percentile rolls: d% and the two-d10 trick

Some rolls want a result from 1 to 100 — reaction tables, loot tables, anything expressed as a percentage chance. The notation is d% or, equivalently, d100 (occasionally written 1d100). You could roll a single hundred-faced die, and novelty d100s exist — golf-ball-sized spheres of tiny facets — but they roll forever and read badly, so the hobby settled on something cleverer: a pair of ten-siders read together.

Here is how the pair works. One d10 is numbered 0 through 9 and supplies the units digit. Its partner — the seventh die in a standard polyhedral dice set — is numbered 00, 10, 20 … 90 and supplies the tens. Roll both at once and add them: 70 on the tens die plus 7 on the units die is 77. A 40 and a 0 is 40. A 00 and a 3 is 3. The special case is double zero: 00 plus 0 would read as zero, which is not on a 1-to-100 scale, so by near-universal convention that combination reads as 100. That convention is what makes the whole range reachable — every result from 1 to 100, each exactly as likely as any other.

From the factory side, the percentile die is a lovely piece of trivia: the tens die and the units die are the same ten-sided geometry — a pentagonal trapezohedron — with different numerals engraved in the mold. Same shape, same balance behaviour, different artwork. When publishers order custom dice for a percentile-heavy game, they are really ordering one geometry twice with two numbering plates, and a factory that understands dice notation will flag a missing tens die before the order confirms rather than after the boxes are packed.

6. Keep, drop and "roll two, take the higher"

The next layer of dice notation covers rolls where you throw more dice than you use. The generic pattern is "roll N dice, keep the best (or worst) K of them." A famous example, described generically: roll four six-siders and keep the highest three, a method many RPGs use to generate character attributes. Compared with a plain 3d6, dropping the lowest die pushes typical totals upward and makes truly terrible results much rarer — the doomed 3 only happens when all four dice come up 1. Virtual tabletops write this family with a small suffix, along the lines of "kh3" or "kl1" for keep-highest-three or keep-lowest-one, but the wording varies and the idea does not: extra dice in, a chosen subset out.

The simplest member of the family is so common it earned a name. Roll two twenty-siders and use the higher — the mechanic many modern games call rolling with advantage — or use the lower, its pessimistic twin, disadvantage. The effect is bigger than intuition suggests, and one line of arithmetic shows why. A single d20 lands on 11 or better half the time. With two dice keeping the higher, you fail only when both dice land at 10 or under — a half times a half, one chance in four — so you now clear 11 three times out of four. No modifier was added, no die was changed, yet good outcomes jumped from 50% to 75%. Keep-and-drop rules reshape luck itself, which is exactly why designers love them: they change the feel of a roll without touching the maths ceiling.

7. Exploding and rerolled dice

Two more concepts complete a working vocabulary. An exploding die rerolls itself on its maximum face: roll a 6 on an exploding d6 and you roll again and add, and if the new die is also a 6, again — in principle without limit. Hobby shorthand often marks this with an exclamation point after the expression. Explosions make totals open-ended: a single exploding d6 usually behaves like a normal d6, but occasionally delivers a 14 or a 19, and the table erupts accordingly. Chains are self-limiting because each further explosion needs another maximum face — one roll in six continues the chain on a d6, one in thirty-six continues it twice — so the drama stays rare enough to stay dramatic.

Rerolls are the gentler cousin: rules along the lines of "reroll results of 1, once, and keep the new roll." A reroll does not extend the range the way an explosion does; it simply makes the worst outcomes less common and nudges the average upward. You will meet both concepts most often in wargames and dice-pool systems, where they interact with big handfuls of dice — and, as the next sections show, big handfuls are precisely where probability starts behaving in ways a single die never would.

8. Why 2d6 clusters at 7 and 1d12 stays flat

Here is the most useful probability idea in all of tabletop, and it needs no formulas. A single die is flat: 1d12 lands on each of its twelve faces equally often, so a 1 is exactly as likely as a 7 or a 12. Add a second die and flatness dies. With 2d6 there are thirty-six equally likely combinations of the two dice, but the totals they build are not equally served. Only one combination makes a 12 (6 and 6), while six different combinations make a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). More roads lead to the middle, so the middle happens more — a 7 turns up six times as often as a 12. Nearly half of all 2d6 rolls (sixteen combinations in thirty-six, about 44%) land on just 6, 7 or 8, three of the eleven possible totals.

Add a third die and the clustering strengthens: 3d6 piles up around 10 and 11 and almost never visits its extremes — the perfect 18 arrives once in 216 rolls. This is why designers treat "one big die" and "several small dice" as different tools even when the ranges look similar. Flat dice make every outcome a live possibility and feel swingy and dramatic; summed dice make results dependable and let a modifier of two or three genuinely matter, because the total rarely strays far from the middle. Neither is better. They are different textures of luck, and reading dice notation well means seeing the texture, not just the range.

9. Board games, RPGs and wargames read it differently

The grammar is shared; the accent changes by table. Board games mostly hide dice notation from players — the rulebook says "roll both dice and move that many spaces" — but it lives openly on the publisher side, where the component list is notation wearing a suit: "2 six-sided dice, 1 twenty-sided die" printed on the back of the box is 2d6 + 1d20 by another name. Designer diaries and playtest forums drop the disguise entirely and argue in raw notation about whether movement should be 1d6 or 2d4.

RPGs speak it natively. Damage lines, attribute generation and tables are printed as expressions, and the classic seven-piece DND dice set exists precisely because one rulebook needs every die from d4 to d20 plus the percentile pair. This is the ecosystem the notation was born in, and it remains the place a new player will first meet 2d6+3 in the wild.

Wargames and dice-pool games add the most important dialect difference in this whole article: in many of them, XdY does not mean "sum the dice" at all. An instruction like "roll 6d6; each 5 or 6 is a hit" asks you to roll six dice and count successes against a target number, ignoring the total entirely. Same notation, different verb. The surrounding rules always tell you which reading applies — but only if you know to ask, which is exactly the kind of trap the next section collects.

10. Common misreadings

Every table sees the same handful of errors, and all of them are cheap to fix once named.

Doubling instead of rolling. 2d6 is not "roll one d6 and multiply by two." Doubling a single die can only produce the six even numbers 2, 4, 6, 8, 10, 12, each equally likely; genuine 2d6 produces eleven different totals with the famous peak at 7. The distinction between XdY and (1dY)×X is the single most consequential misreading in dice notation, because it silently changes a game's probability without changing its range's endpoints.

Adding the modifier per die. As covered earlier, 2d6+3 adds three once. Adding it to each die would quietly turn the expression into 2d6+6.

Misreading the percentile pair. Tens die 00 with units die 7 is 7, not 70 — the tens die is the one with the double digits. And 1d100 is not the same animal as 2d10 summed: the first is flat from 1 to 100, the second spans only 2 to 20 and clusters at 11.

Assuming +2 equals a bigger die. A d6+2 and a d8 both top out at 8, but they are different rolls: d6+2 spans 3 to 8 and averages 5.5, while d8 spans 1 to 8 and averages 4.5. The modifier buys a higher floor and a higher average; the bigger die buys reach and risk.

Summing when you should count. In dice-pool systems, totalling 6d6 when the rule wanted successes counted produces nonsense. Check which verb the game means before the dice leave your hand.

The phantom d3. Notation happily writes 1d3 even though few dice sets contain one; the standard convention is to roll a d6 and halve the result, rounding up. (Physical d3s do exist — we have made them as custom dice — but the halved d6 is the everyday answer.)

11. Quick reference: frequent expressions

The table below collects the expressions you will meet most often, read generically — individual games may layer their own rules on top, and the rules text always wins. Averages are the long-run arithmetic, not a promise about any single roll of your DND dice.

12. Why a dice factory reads notation

Now the confession of perspective we promised. When a publisher sends us a rules document, our project team reads the dice expressions before anything else — because for a manufacturer, notation is not flavour, it is a bill of materials. A game whose rules ever say "roll 3d6" needs three six-siders in the box, or a printed note telling players to share; a game with a percentile table needs the tens die that casual component lists forget; a game that leans on advantage-style rolls may want a second d20 in every DND dice set it ships. Read every roll the game asks for, and you have effectively read the packing list.

A rulebook's dice expressions are its packing list. Read every roll the game asks for, and you have read the component count before the designer has.— how our project team explains dice notation to first-time publishers

Notation also carries decisions that are invisible at the game table but loud on a production line. Whether the d6s are pipped or numbered changes the engraving plates. Whether two factions each roll "their" dice means colour-splitting the same molds across two Pantone recipes. And one d20 question comes up so often it deserves its own sentence: a rolling d20 and a spindown-style counting d20 are the same twenty-faced geometry with completely different numbering layouts — a standard d20 scatters its numbers so neighbouring faces balance high against low, while a spindown arranges them in sequence so a player can walk a total downward one step at a time. A publisher who writes "1d20 per box" needs to tell the factory which of the two they mean, because the mold's numbering plate, not the shape, is what differs. A factory fluent in dice notation asks that question at the quote stage, not after tooling.

13. From "4d6 + 1d20 per box" to molds and colours

Here is how that fluency plays out concretely at YSDICE — Dongguan Yushun Hardware Co., Ltd., a registered dice manufacturer in Chang'an, Dongguan, running its own production lines since 2018. Suppose your component list reads "4d6 + 1d20 per retail box" across a 5,000-box print run. The first pass is plain multiplication: 20,000 d6 and 5,000 d20, plus overage for quality sampling. The second pass is mold planning: the d6 and the d20 are separate tools, and for volume board game runs we will usually steer you toward injection-moulded acrylic dice, because multi-cavity acrylic molds are what make a per-box cost of five dice sensible at that scale — while a deluxe or collector edition of the same game might move the d20, or the whole dice set, to our metal dice line at a smaller quantity.

The third pass is colour. "4d6" says nothing about whether the four six-siders are identical, colour-matched to the box art, or split across player factions — so we resolve that into a colour plan: which molds run which masterbatch, which Pantone the numeral enamel is matched to, and whether the d20 gets a contrast treatment to read as the hero die of the dice set. The fourth pass is proofing: send the component list through our ordering and design process and you get a free 3D proof of every face within 3 days, then physical samples before anything is mass-produced. Light customisation on proven stock molds starts at just 10 sets; full custom tooling for original geometry is quoted with the mold fee refunded progressively as reorders accumulate; and the whole path — from notation to bagged, boxed polyhedral dice under your own brand — is exactly what our OEM/ODM service exists to run. It is a strange and pleasing fact of this industry that a fifty-year-old hobbyist shorthand is also the cleanest purchase order format we know: Dongguan Yushun Hardware Co., Ltd. has planned entire production quarters around lines no longer than 4d6 + 1d20.

That is dice notation end to end: a grammar of three symbols, a few honest dialects, and a probability texture you can now read at a glance. The next time a rulebook says 2d6+3, you will see the range (5–15), the average (10), the shape (clustered at the middle) — and, if you happen to be publishing the game rather than just playing it, the packing list hiding inside the sentence.

Written by Queenie Founder & English-speaking project manager · Dongguan Yushun Hardware Co., Ltd. (YSDICE)

Queenie has cast, poured and shipped custom dice from Chang'an, Dongguan since 2018 — and still answers every project inquiry herself. Questions about your run? Write to queenie@ysdice.com or message us on WhatsApp.