Dice Notation, and What Your Roll Was Actually Worth

Quick Answer

Dice notation packs three facts into one short string. The number before the d counts the dice. The number after it gives the faces. Anything trailing is a flat bonus, added once to the total.

For example, 4d6+2 means roll four six-sided dice, add them, then add two. That pool runs from 6 to 26.

Type the string into the dice roller and it shows every die, the total, and how often a result like that turns up. Input: 2d6+3. Output: a total between 5 and 15, plus the odds of beating it.

What is dice notation?

Dice notation is the shorthand printed in tabletop rulebooks, and it has not changed in fifty years. d20 is one twenty-sided die. The count is optional when it is one, so d20 and 1d20 mean the same thing. A d20 roller is the most common case, therefore it is what the tool starts with.

3d8 means three eight-sided dice, summed. 2d10-1 means two ten-sided dice, summed, then one taken off. Roll a dice or roll a die, both work here.

The modifier applies to the total, not to each die. That is the most common mistake people make reading it. For example, four dice with a plus two bonus is one plus two, so 4d6+2 stops at 26 rather than 32. Avoid adding the bonus per die and your damage numbers stop drifting upward.

How does an online dice roller work?

Each die is one draw from your browser's cryptographic random number generator, the same source behind a password generator.

That source hands back a 32-bit number, which does not divide evenly by six. Taking the remainder would make low faces slightly more likely, so the tool throws away the values in the leftover band and draws again. The bias is gone rather than small. Roll 2d6 here and every one of the thirty six combinations has an equal shot, which is more than a physical die can promise after a year in a dice bag.

Then it sums the faces, applies the modifier, and works out the exact distribution of the pool you asked for. For example, a 14 on 2d6+3 gets reported alongside the share of rolls that reach 14 or better.

Is 2d6 better than 1d12?

Both stop at 12, and there the resemblance ends.

A single twelve-sided die is flat. Every face has a one in twelve chance, so a 12 is exactly as likely as a 7. Unlike that, two six-sided dice have to agree with each other. There are six ways to make a 7 and one single way to make a 12, therefore the totals bunch hard in the middle.

In play the pair is reliable and the lone die is swingy. Roll 2d6 a hundred times and most results land between 5 and 9. Roll 1d12 the same hundred times and the results scatter across the whole range. Neither is better, but they answer different questions, so the difference between them decides the build.

Several small dice beat one big die for consistency, because each extra die drags the total toward the average. That is why old stat lines use 3d6: the method quietly guarantees an ordinary character.

Does a wider range mean a better average?

No, and this is the misconception that costs people damage. Range and average move independently.

For example, 1d12 averages 6.5 and 2d6 averages 7, but the pair reaches 12 far less than the single die does. Swapping to a bigger die raises your ceiling while lowering the number you hit most nights.

A flat bonus behaves differently again. Adding two to 2d6 shifts the entire curve two places, so it is worth far more in the middle than at the ends. Do not judge a bonus by the maximum it reaches. Judge it by how much of the curve it pushes past your target number.

How do I work out the odds of clearing a target?

Most rolls ask a yes or no question rather than asking for a number. On a flat d20 the sum is easy, because every face is equally likely. Needing 15 or better means six faces in twenty, which is 30 percent, and each point of bonus adds another 5 percent.

On a pool it stops being easy, and guesses go badly wrong here. Needing 15 or better on 2d6+3 means needing 12 on 2d6, which is one outcome in thirty six. About 3 percent, instead of the 30 percent the d20 instinct suggests.

The roller prints that share under the result, so comparing two builds takes one roll each.

Are dice due for a high roll?

No. Dice hold no memory, so the next roll carries exactly the distribution the first one did.

What changes is the sample rather than the dice. Over hundreds of rolls the running average settles near the expected value, because later rolls swamp the early ones, and not because bad luck gets repaid. Six low rolls in a row on a d20 happen roughly once in seventy attempts, which is common enough to happen to you on a Tuesday.

Virtual dice attract this suspicion more than physical ones, because nothing tumbles across the table to convince you. Therefore the tool answers with a number: it states how often a result like yours turns up, and you can check that against any probability table you like.

What this roller will not do

There is no drop-lowest, no exploding dice and no advantage keyword. Those are system rules rather than notation, and every game spells them differently.

For advantage, set the roll count to two and take the higher of the pair. The odds line reports the best of the batch, which is the number advantage actually buys you. For a 4d6 drop lowest stat line, roll 4d6 with the breakdown showing and ignore the smallest die yourself.

Instead of a number, you might want a name or a choice. The random choice picker handles named options, and the coin flipper covers the two-outcome case. Nothing you roll is uploaded or stored.