Dice Roller

A dice roller is only as useful as what it tells you about the roll. This one throws any standard die from d4 to d100, reads full dice notation such as 2d20kh1 or 4d6dl1 + 2, and puts the exact chance of the total you got next to the total itself. Below the tray, the session bars show every total the notation can produce, with your own rolls filling in on top, so you can watch luck even out in real time.

Most pages that rank for this search do the throwing and stop. The questions people actually bring to a virtual dice roller are the ones after the throw: is 15 a good result on 3d6, how much does advantage help, what should I expect from rolling stats, and can I trust the dice at all. This guide answers those with numbers worked out from every possible outcome, not estimates.

Reading dice notation

Dice notation was introduced by Ted Johnstone in 1975 in the fanzine Alarums & Excursions and was picked up by Gary Gygax for Advanced Dungeons & Dragons between 1977 and 1979. The core is NdX: N dice, each with X sides, added together. So 3d6 is three six sided dice summed, and a lone d20 means one twenty sided die. A modifier follows with a plus or minus sign, and it applies once to the total, not to each die: 2d6 + 4 is two dice and then four more, a range of 6 to 16.

Keep and drop letters sit straight after the die. kh keeps the highest dice and kl keeps the lowest; dl drops the lowest and dh drops the highest. The number after the letters says how many, so 4d6dl1 and 4d6kh3 are the same roll written two ways. Groups chain with plus and minus signs, which covers a longsword hit with a sneak attack on top as 1d8 + 3d6 + 4. Percentile dice, written d% or d100, are traditionally two ten sided dice read as tens and units, where 00 and 0 together count as 100 in most games. This roller treats d100 as a single die from 1 to 100, which gives the same odds. Exploding dice and success counting pools use their own extensions and are not part of this tool.

Why dice totals bunch in the middle

One die is flat: every face is equally likely, so a d20 averages 10.5 and a d6 averages 3.5. In general one die averages (X + 1) / 2, and N of them average N times that, plus the modifier. Add dice together and the shape changes. Two d6 have 36 equally likely ordered outcomes, and six of them make 7, so 7 comes up 16.67% of the time. Only one outcome makes 2 and only one makes 12, 2.78% each. That is why 2d6 and 1d12 are not interchangeable even though their ranges look alike: the d12 is flat and can roll a 1, the pair of d6 clusters around 7 and cannot.

Three dice sharpen the curve further. On 3d6 the totals 10 and 11 each turn up 27 times in 216, or 12.5%, while 18 needs three sixes and comes up once in 216, about 0.46%. A total of 15 or more happens 9.26% of the time. More dice always pull the results toward the average, which is why a game designer reaches for 3d6 when they want dependable characters and for 1d20 when they want swingy ones. The bar chart under the roller draws this probability distribution for whatever notation you type, and it handles keep and drop rolls exactly rather than by simulation.

Advantage and disadvantage by the numbers

In the 2024 rules, published for creators as SRD 5.2 under a Creative Commons licence on May 1, 2025, advantage means you roll a second d20 and use the higher one; disadvantage means you use the lower. In notation that is 2d20kh1 and 2d20kl1. A roll never gets more than one extra d20 however many things grant advantage, and if a roll has both advantage and disadvantage they cancel and you roll a single die.

A straight d20 averages 10.5. Advantage lifts the average to 13.825 and disadvantage drops it to 7.175, a shift of 3.325 either way. The average hides where the real effect lands, though. Needing an 11, one die succeeds 50% of the time, advantage makes it 75% and disadvantage 25%, which is worth about a +5 bonus. Needing a 20, advantage only moves you from 5% to 9.75%, so the benefit shrinks toward either end of the die. The table beside the roller lists the chance for each target so you can see the gain before you spend a feature on it. A natural 20 on an attack roll hits whatever the modifier or armour class and counts as a critical hit, and a natural 1 misses. With advantage the chance of at least one 20 is 9.75%, and the chance of a natural 1 falls to 0.25%.

Rolling ability scores with 4d6 drop the lowest

The random method in the current rules is to roll four d6, total the highest three, and repeat until you have six numbers. Every one of the 1,296 possible rolls of four dice was counted to get the exact figures. The average score is 15,869 divided by 1,296, which is 12.24. The single most likely score is 13, which turns up 172 times in 1,296, or 13.27%. An 18 needs three sixes among the kept dice and happens 21 times in 1,296, about 1.62% per score, and across all six scores the chance of at least one 18 is 9.34%. A score of 15 or higher comes up 23.15% of the time. At least one widely read dice page gives the average of this roll as about 8.46; that is not possible, since the lowest three dice alone average more than that.

Six scores rolled this way total 73.47 on average. The standard array of 15, 14, 13, 12, 10 and 8 totals 72, and it costs exactly the 27 points the point buy method gives you, so rolling is a slight upgrade on average with a much wider spread between players. Straight 3d6 averages only 10.5 a score, which is why so few tables still use it. Type 4d6dl1 into the roller and press Roll 100 more a few times to see the bars settle onto the peak at 13.

Damage rolls and critical hits

Damage follows the same arithmetic. A longsword with a +4 modifier, 1d8 + 4, runs from 5 to 12 and averages 8.5. A greatsword, 2d6 + 4, runs from 6 to 16 and averages 11, and because it uses two dice it lands near 11 far more reliably. Fireball, 8d6, spans 8 to 48 with an average of 28. On a critical hit the rules double the dice, not the modifier: a dagger that normally rolls 1d4 rolls 2d4 instead, and any extra damage dice from features are doubled too. The cheat sheet next to the roller has these as one tap rolls.

How this roller picks each face

Every die draws a 32 bit number from crypto.getRandomValues, the browser's cryptographic source, which is seeded from the operating system's entropy. Turning a 32 bit number into a face needs care. There are 4,294,967,296 possible values, and for a d6 that does not divide evenly: 4 values are left over, and a plain remainder would hand those to the low faces. The roller uses rejection sampling instead. Any draw that lands in the leftover slice is thrown away and a fresh one is taken, so every face is backed by exactly the same number of values. The leftover slice is 16 values for a d20 and 96 for a d100, so a retry is rare, but without it the modulo bias would be there by construction.

The value is fixed before the dice start to move. The tumbling cube and the flickering numbers are drawn afterwards and land on the face that was already chosen, so turning the animation off with your device's reduced motion setting changes nothing about the result. If you need numbers in a range, draws without repeats or lottery picks rather than dice, the random number generator handles those and explains its method in more depth.

Checking a physical die

Real dice are rarely perfect. In a 2023 study at Western Kentucky University, only about one in four d20s tested fair over 3,000 rolls each, because of uneven density, air bubbles and moulding marks. The same work found that sums of three dice tested fair even when the individual dice did not, so a bell curve roll like 3d6 hides a bad die much better than a single d20. Casinos go further: their dice are made true to within 0.0005 of an inch, from clear material so nothing can be hidden inside, with pips drilled and filled with paint of the same density, and they are still swapped every four to eight hours.

You can test your own d20 with a chi-square goodness of fit test. Roll it a great many times, count each face, and compare with the expected count. With 20 faces the test has 19 degrees of freedom and the cutoff at the usual 5% level is 30.14; a score above that suggests the die is off. The test needs volume, around 500 rolls per face if you roll 10,000 times, so it is a project for a long evening. A quicker screen is to float the die in salt water, flick it a few dozen times, and see whether the same face keeps coming up. For summary statistics on a list of your results, paste them into the statistics calculator.

What the session bars can and cannot tell you

The outlined bars are the exact odds. The solid bars are the share of your own rolls of that notation in this session. After ten rolls they will look lumpy; after a few hundred they will hug the outline. That convergence is the law of large numbers at work. The dice have no memory, though. A die that has not shown a 20 all night is exactly as likely to show one on the next throw as on the first, and a run of low totals does not make a high one due. The average line under the chart compares your session mean with the expected mean, which is the fairest way to settle an argument about whether the dice have been kind.