Online dice roller: roll 1 to 12 virtual dice from d4 to d20

How to use this dice roller

1. Choose your dice. The bar at the bottom has all six types: d4, d6, d8, d10, d12 and d20. Tap each one once for every die of that type you want. You can mix types in the same roll, up to 12 dice in total.
2. Roll. Press the Roll button, or touch the tray, drag to shake the dice and release. The speed and direction of your gesture change how they fly out.
3. Read the result. The total appears at the top, with the value of each die and its type alongside. Your previous totals are listed underneath; the list clears if you change the set of dice.

Each die is read by the face pointing upwards, just as on a real table. There are two exceptions worth knowing:

• The d4 has no top face because it is a pyramid: it always lands on a face and leaves a point sticking up. The result is the number next to that top point, which is repeated on all three visible faces.
• The d10 is numbered 0 to 9. Here the 0 counts as 10 in the total, which is how most role-playing games treat a single d10.

If you roll a d20, the page flags a natural 20 and a natural 1, the two results many role-playing games treat as an automatic success or failure. The options button lets you change the dice finish (ruby resin, smoke, sapphire, jade, white, obsidian, bone or brass), change the colour of the felt and turn the sound off. The page remembers your last set of dice and your colours in this browser.

Is a virtual dice roll really random?

Many online dice simply pick a random number and play an animation on top. This one works the other way round: each die is a solid object with its own shape, mass and friction inside a physics engine, and the number comes from the way it lands. No result is decided before the dice stop moving.

The randomness comes in at the throw. Every time you roll, the program gives each die a slightly different starting orientation, speed and spin, using small variations chosen by your browser's random number generator. From then on, collisions with the felt, the walls and the other dice turn a tiny difference at the start into a different face at the end. That is the same reason a physical die is unpredictable: there is nothing magical about it, it is simply that nobody can control a throw that precisely.

Two honest caveats:

• The browser's generator is pseudo-random. It produces sequences that behave like chance for gaming purposes, but it is not designed for cryptography or for draws with legal value. For an official prize draw, or anything involving money, use a method that meets the relevant rules.
• A simulated die has no air bubbles, worn edges or drilled pips that remove more material from one side. In that sense it is more regular than many cheap plastic dice.

If you want to test it yourself, roll a d6 60 or 120 times and note how often each face comes up. Over a few rolls you will see large differences between faces, and that is normal: the spread only evens out as the number of rolls grows.

Polyhedral dice: shapes, faces and what each one is for

The six-sided die is the familiar one, but role-playing and wargames use a full set of other shapes. Gamers name them with a "d" and the number of faces: a d6 has six sides, a d20 has twenty. A standard RPG set contains seven dice: d4, d6, d8, d12, d20 and two d10s, one for units and one for tens, used for percentage rolls.

Why the d4 is read at the top point

A tetrahedron resting on a table leaves no face pointing up, only a point. So each face carries three numbers, one by each corner, and the one that counts is the one at the top: you will see it repeated on all three faces facing you. A less common design puts the numbers along the bottom edges and is read at the base. The d4 barely rolls, and players often say it is tossed rather than rolled.

Why the d10 runs from 0 to 9

The d10 was designed to give single digits. With two d10s you can get any number from 00 to 99: one gives the tens and the other the units. A roll of 00 and 0 is read as 100, which gives you a result from 1 to 100 without a hundred-sided die. When you roll a d10 on its own, the 0 counts as 10, and that is what this roller does when it adds up.

Is there a 100-sided die?

Yes. The Zocchihedron, created by Lou Zocchi, went on sale in 1985. It looks like a ball with a hundred flattened areas and has loose filling inside so that it settles faster. Tests published in gaming magazines found that numbers near the poles come up slightly less often than those around the middle, which is why most players still use two d10s.

Dice probability: what comes up most with one, two and three dice

On a fair die every face is equally likely. What changes a great deal is what happens when you add several dice together, because some totals can be made in more ways than others.

A single die

The average roll is halfway between the lowest and highest number. When you roll several dice, the average of the total is the sum of the averages: two d6 average 7, and a d20 plus a d6 average 14.

The total of two six-sided dice

Two d6 give 36 equally likely combinations. Seven is the most common total because it can be made in six ways (1+6, 2+5, 3+4, 4+3, 5+2 and 6+1). Two and twelve can only be made in one way each.

Rolling a double (both dice the same) has a probability of 6 in 36, or one roll in six. Rolling 8 or more happens 41.67% of the time.

Three dice and the puzzle of 9 and 10

Three d6 give 216 combinations. Both 9 and 10 can be written in six different ways using numbers from 1 to 6, so they look equally likely. They are not: once you count the order of the dice, 10 can be made in 27 ways and 9 in only 25. Galileo explained the difference in the early 17th century in a short piece on dice, and it is a good example of why probability means counting ordered outcomes. With three dice, 10 and 11 are the most common totals (12.5% each), and 3 and 18 the rarest (0.46%).

How long does it take to roll a 6?

Although a 6 comes up once in six rolls on average, six rolls do not guarantee one: there is a 33.49% chance of seeing none at all. Dice have no memory, and a long run without a 6 does not make the next roll any more likely to be one.

Why opposite faces add up to 7

On a standard six-sided die, opposite faces always add up to 7: 1 is opposite 6, 2 opposite 5 and 3 opposite 4. As a result, the 1, 2 and 3 meet at one corner. The same idea applies to almost all polyhedral dice, where opposite faces usually add up to the number of faces plus one: 9 on a d8, 13 on a d12 and 21 on a d20. On a d10 numbered 0 to 9, they add up to 9.

It has not always been this way. A study from the University of California, Davis looked at 110 carefully dated cubic dice found in the Netherlands, from Roman times to the early modern period. Roman dice mostly followed the sevens rule but were often lopsided and irregular. The dice that reappear from around 1100 follow a different pattern, with 1 opposite 2, 3 opposite 4 and 5 opposite 6. From around 1450 the sevens rule returns and dice become far more uniform in shape and size. The authors link this to a change in thinking: players began to see a throw as a matter of chance rather than fate, and to expect regular dice.

The 1-2, 3-4, 5-6 layout also appears on much older dice, including some from the Indus Valley found at Mohenjo-daro and Lothal, while others from the same civilisation already follow the sevens rule.

One more detail few people notice: with 1, 2 and 3 meeting at a corner, they can run clockwise or anticlockwise. Western dice usually have them anticlockwise and Chinese dice the other way round. Asian dice also tend to have the 1 and the 4 painted red.

A short history of dice, from bones to RPG sets

Knucklebones: dice made of bone

Before cubes, people played with astragali, small ankle bones from sheep and goats. They have four sides they can come to rest on, each with a different likelihood, and were used both for games and for fortune-telling. They were hugely popular in ancient Greece and Rome among children and adults alike, and the Romans called them tali. The children's game of knucklebones, or jacks, takes its name from them.

The first cubic dice

Among the oldest known six-sided dice are the terracotta dice from Mohenjo-daro in the Indus Valley civilisation, dated to the third millennium BC. In ancient Egypt, throwing sticks did the job of dice in board games.

Rome and the Middle Ages

In Rome, gambling with dice was banned except during the Saturnalia festival, but people played anyway, and loaded dice from the period survive. Museums also hold twenty-sided dice from Ptolemaic Egypt and the Roman era, including examples at the Metropolitan Museum of Art in New York and the Louvre, although nobody knows for certain whether they were used for games or for other purposes.

Dice and the birth of probability

Games of chance pushed mathematics forward. Besides Galileo's piece on three dice, the 1654 letters between Blaise Pascal and Pierre de Fermat, prompted by a gambling problem put to Pascal by the Chevalier de Méré, are regarded as the starting point of modern probability theory.

Modern polyhedral dice

Until the 1970s, dice in shapes other than cubes were hard to find. In 1972 an American educational supplier sold a set based on the five Platonic solids, and the first players of Dungeons & Dragons, published in 1974, took them up. The game came without dice, so you had to buy them separately. Those early d20s were numbered 0 to 9 twice because cheap moulds could only fit one digit per face, and players coloured in one half to tell them apart. The d10 arrived later, around 1980, and since then the seven-dice set has been the RPG standard.

Loaded dice: how they are made and how to spot them

A loaded die is one that has been altered so that a face comes up more or less often than it should. There are three classic methods:

Even without cheating, an ordinary die is not perfect. Pips are usually holes, and the 6 face loses more material than the 1, which shifts the centre of gravity very slightly. That is why casino dice are made from transparent cellulose acetate, cut to very tight tolerances, with pips filled with paint of the same density as the material, and marked with a serial number and logo so they cannot be swapped. Being transparent also means anything inside is visible.

How to test a die at home

What to use an online dice roller for, and practical tips

A few more tips:

• When you throw by dragging, the dice fly in the direction of your gesture. A short, fast flick makes them bounce more off the walls of the tray.
• With lots of dice at once, choose a finish that contrasts with the felt so they are easier to read, such as white or brass dice on dark felt.
• If a die ends up tilted against another one, the page waits for it to settle before reading it.