Custom Dice Roller

How to read dice notation

Tabletop games write dice in a shorthand that reads like a small equation. The form is XdY plus or minus Z, where X is how many dice, Y is how many sides each die has, and Z is a flat number added to the total.

So 2d6+3 means roll two six-sided dice, add the faces together, then add 3. A single die with no count is written d20 or 1d20. A minus sign works the same way: 3d8-2 rolls three eight-sided dice and subtracts 2, which puts the range at 1 through 22.

Three conventions are worth knowing. The letter d is lowercase in most rulebooks but the meaning does not change. A modifier applies once to the total, not once per die, so 2d6+3 is not the same as 2d9. And when a rule says roll with advantage, it means roll twice and keep the higher result, which is a different calculation from adding a bonus.

Some systems use a pool instead of a sum. In a dice pool you count how many dice meet a threshold, so 5d10 with a target of 7 counts the dice showing 7 or more. The calculator on this page sums dice, which covers the notation used by most fantasy and board game systems.

What each notation rolls, in numbers

The table lists the range and the average for common notation. The average matters more than the range for planning, because the extremes are rare and the middle is where most rolls land.

The average of any set of dice follows one rule: dice count times (sides plus one) divided by two, then add the modifier. Two six-sided dice average 7. A d20 averages 10.5, which is why a +1 bonus on a d20 is worth about 5 percentage points of success and a +1 on 2d6 is worth far more in relative terms.

Adding dice changes the shape, not just the size. One d20 is flat: every face has a 5% chance. Two dice summed produce a triangle that peaks in the middle. Three or more dice produce a bell curve that gets narrower relative to its range as you add more dice.

The probability curve of 2d6

Two six-sided dice have 36 equally likely pairs, and the totals are not evenly spread across them. Seven appears six ways, while two and twelve appear one way each.

The last column is the one players need. If a rule says roll 8 or better on 2d6, the chance is 41.7%, not the 5 out of 11 that the range suggests. The middle three totals, 6 through 8, cover 44.4% of all rolls.

The standard deviation is 2.42, which describes how tightly the results cluster around 7. For 3d8-2 the deviation is 3.97 on a range of 22, so that roll is much more spread out in relative terms. Comparing deviations is the fastest way to compare how swingy two options are.

Flat dice, summed dice and the shape of the curve

A single die is uniform. Every face has the same chance, so a d20 gives 5% to each number and the graph is a flat line. That flatness is why a d20 feels random: a 1 and a 20 are equally likely, and a run of low rolls is unremarkable.

Summing dice changes the feel and the math. The total clusters in the middle because there are more ways to reach it. On 3d6 the average is 10.5 and 27 of the 216 outcomes land on 10 or 11, which is 12.5% each. The extremes of 3 and 18 are 0.46% each.

This is why some systems use 3d6 for skill checks and a d20 for attacks. A 3d6 check makes a character with a modest bonus reliable, because the curve punishes extreme results. A d20 attack keeps a 5% chance of a critical hit and a 5% chance of a fumble, which is the drama the system wants.

For a game master building an encounter, the practical version is this: with summed dice, plan around the average and treat the extremes as rare events. With a single die, plan for the full range, because the extremes are as likely as anything else.

Weighted dice versus fair dice

A fair die gives every face the same chance. A weighted die does not, either because the physical die is unbalanced or because a digital roller assigns different weights to different faces. The second kind is common in games, where a loot table or a random event table uses weights instead of equal odds.

Doubling the weight of one face on a d6 raises that face from 16.7% to 28.6% and lifts the average from 3.50 to 3.86. On a d20 the same change moves a face from 5.0% to 9.5%, which nearly doubles the chance of a critical hit without changing the range at all.

Physical weighting is cruder. A die with a lead weight near one face lands on the opposite face more often, and the effect is usually a few percent rather than a doubling. Casino dice are machined to tight tolerances for exactly this reason, and the difference between a casino die and a cheap game die is measurable but small.

Digital weighting is exact because it is arithmetic, not physics. A weighted table lists each outcome with a weight, divides each weight by the total, and rolls against the result. That is how a game can give a rare item a 0.5% drop rate and a common item a 40% rate from the same roll.

Worked example: 2d6+3 and the chance of hitting 10

Say a rule requires a total of 10 or better on 2d6+3. The modifier shifts every total by 3, so a final 10 means the dice themselves must show 7 or more.

Seven or more happens on 21 of the 36 pairs, so the chance is 58.3%. Exactly 10 happens when the dice show exactly 7, which is 6 of 36, or 16.7%. The best possible result, 15, needs a pair of sixes, which is 1 of 36, or 2.8%.

The average total is 10, which sits right on the target. That is a coin flip with a slight edge, and it is why a +3 modifier on 2d6 is a large bonus: without it the same target of 10 would succeed only 16.7% of the time.

Change the target and the odds move in steps, not smoothly. Raising the target from 10 to 11 drops the chance from 58.3% to 41.7%, a fall of 16.6 points. Raising it again to 12 drops it to 27.8%. Each point of target costs roughly one or two of the 36 outcomes, so a small rule change can swing a fight.

Odds that surprise players: advantage and 4d6 drop lowest

Two common mechanics look like small tweaks and are not.

Advantage. Roll two d20 and keep the higher. The chance of a 15 or better rises from 30% to 51%, and the chance of a 20 rises from 5% to 9.75%. Disadvantage does the reverse: a 15 or better falls from 30% to 9%. Advantage is close to a +5 bonus in the middle of the range, which is why it feels so strong at the table.

4d6 drop the lowest. Roll four six-sided dice, discard the lowest, and add the other three. There are 1,296 outcomes and the average is 12.245, not the 12.5 that the naive 3d6 average suggests. The chance of an 18 is 1.62%, and the chance of 16 or better is 13.04%. The method raises the average by about 1.75 over a straight 3d6, which is a meaningful boost for a character stat.

Neither mechanic fits the XdY+Z notation, so a plain dice calculator cannot price them. Run the plain roll for the base odds, then adjust by hand: advantage on a d20 is roughly a +5 bonus for mid-range targets, and 4d6 drop lowest is roughly 3d6 plus 1.75.

Using the roller at the table

Set the dice count, the sides and the modifier, then set the target total you care about. The calculator reports the chance of hitting that target or better, the chance of hitting it exactly, and the full range with the average.

Three habits make it useful in play. First, price the target before you commit to an action, because a 58% chance and a 28% chance feel different at the table and the difference is easy to miss in the moment. Second, use the average to compare options: 2d6+3 averages 10 and 3d8-2 averages 11.5, but the second is far swingier. Third, remember that a run of bad rolls is not evidence of a broken die unless it persists over hundreds of rolls, since a fair d20 produces a 1 every 20 rolls on average.

The roller uses the browser's built in random function, which is fine for games and is not suitable for anything security related. The National Institute of Standards and Technology publishes standards for random number generation used in security work, and the MDN reference for Math.random explains why the browser function is not built for that purpose.

One last note on notation: when a rule says 2d6 and you only have d12s, do not substitute. A d12 is flat and 2d6 is a curve, so the averages match at 6.5 against 7 only by coincidence and the odds of any specific total are completely different.