Dice Roller

A dice roller picks a random face on each die and adds them up. With two six-sided dice (2d6) there are 6 × 6 = 36 equally likely outcomes, and 6 of them make a 7, so 7 is the most likely total at 6/36 ≈ 16.67%. The expected total of 2d6 is 2 × 3.5 = 7.

How to use the dice roller

1. Pick a tab: Pick dice to choose the number and type of dice, Dice notation to type a roll such as 2d6+3, or d20 check for advantage, disadvantage and a target number.
2. Choose 1 to 100 dice: d4, d6, d8, d10, d12, d20, d100, or a custom die with up to 1,000 sides. Add a modifier, or drop the lowest or highest die.
3. Press Roll. You see each die, the total and the sentence behind it, and the roll goes into your history of the last 20 rolls.
4. Read the probability panel below the roll. It shows the chance of every total for the dice you chose, the expected value, and the chance of rolling at least, exactly or at most any number you type.
5. Press Roll 1,000 times to run an experiment and compare what really happened with the theory.
6. To roll the same dice several times at once, set Times (up to 10). The tap 6 × 4d6dl1 rolls a full set of six ability scores and lists every total.
7. For a class or game table, press Big screen: the dice and total fill the screen and stay readable on a projector. Press Escape to go back.

Dice notation explained

Games write rolls in a short code called dice notation. The roller reads all of these forms:

• NdS means N dice with S sides. 3d6 is three six-sided dice; d20 is one twenty-sided die.
• + or − a number is a modifier added to the total. 1d20+5 means roll a d20 and add 5.
• dl1 drops the lowest die and dh1 drops the highest. 4d6dl1 is the same as “4d6 drop lowest” and as 4d6kh3 (keep the highest 3).
• 2d20kh1 is advantage (keep the higher of two d20s) and 2d20kl1 is disadvantage.
• d% is a percentile die, the same as d100.

Probability of dice sums with two dice

Each die has 6 faces, so two dice give 6 × 6 = 36 ordered outcomes, all equally likely. The totals are not equally likely, because some totals can be made in more ways. A 7 can be made 6 ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), but a 2 only one way (1+1).

The ways rise by one up to 7 and then fall by one, which gives the triangle shape you see in the chart. With three or more dice the shape becomes a smooth bell curve. The calculator builds these tables one die at a time: the ways to reach a total with one more die are the ways to reach each of the totals 1 to 6 less before it. Mathematicians call this step convolution.

Expected value of a dice roll

The expected value is the long-run average total. For one fair die with s sides it is the average of the faces, and for several dice you add the averages:

E = n × (s + 1) ÷ 2 + modifier

• n is the number of dice.
• s is the number of sides on each die.
• modifier is the fixed number added or subtracted.

Once a die is dropped there is no shortcut, so you multiply each total by its probability and add. That is how the panel finds 15,869 ÷ 1,296 ≈ 12.24 for 4d6 drop lowest.

Worked dice probability examples

Rolling at least 10 with two dice

From the table, 10 has 3 ways, 11 has 2 and 12 has 1. That is 3 + 2 + 1 = 6 ways out of 36, so P(total ≥ 10) = 6/36 = 1/6 ≈ 16.67%.

A d20 check with advantage

You have a +5 bonus and need 15, so the die must show at least 10. On one d20 that is 11 faces out of 20, or 55%. With advantage you fail only if both dice show 9 or less: (9/20)² = 81/400. So the chance of success is 1 − 81/400 = 319/400 = 79.75%.

Rolling 18 with 4d6 drop lowest

Four dice give 6⁴ = 1,296 outcomes. To keep 6 + 6 + 6 you need at least three sixes: 20 outcomes have exactly three (4 places for the non-six × 5 values) and 1 has four. That is 21/1,296 ≈ 1.62%.

Is an online dice roller fair?

This roller uses the browser’s crypto.getRandomValues, which produces cryptographically strong random numbers. A random 32-bit number has 4,294,967,296 possible values, and that count is not a multiple of 6 (it leaves a remainder of 4). Taking the remainder after dividing by 6 would make the faces 1 to 4 very slightly more likely. To avoid this tiny bias, the roller throws away the top 4 values and draws again, a method called rejection sampling. Every face then has exactly the same chance.

Each roll is independent. The dice have no memory, so a 7 is just as likely after three 7s in a row as after none. If you doubt a roller, run the experiment: over thousands of rolls the observed bars should settle close to the theoretical ones.

Common dice probability mistakes

• Treating all totals as equally likely. On 2d6 a 7 is six times as likely as a 2.
• Thinking 2d6 is the same as 1d12. 1d12 can roll a 1 and gives every total 1/12 ≈ 8.33%; 2d6 starts at 2 and favors the middle.
• Adding chances of separate rolls. The chance of at least one 6 in two rolls is 1 − (5/6)² = 11/36 ≈ 30.56%, not 2/6.
• Expecting a “due” number. Past rolls do not change the next one; this is the gambler’s fallacy.
• Thinking a modifier changes the odds shape. +3 slides every total up by 3; the chances stay the same.

Dice in games and classrooms

Board games lean on the 2d6 shape: in a game where a 6 or 8 pays out, each has 5/36 ≈ 13.89%, while a 2 or 12 has only 1/36. Tabletop role-playing games use the whole set from d4 to d20, plus modifiers, advantage and drop-lowest ability scores. The probability panel tells a player at a glance how likely a check is to succeed.

In a classroom, the roller turns probability into an experiment. Students can predict the chance of a 7, roll 1,000 times, and compare their bars with the theory, then add 1,000 more and watch the gap shrink. That is the law of large numbers in action, and it pairs well with lessons on fractions, percents and expected value. For a quick class game, the Big screen view shows the dice large enough to read from the back of the room.

Dice probability practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is the most common roll with 2 dice?

7. It can be made 6 ways out of 36, which is 1/6 or about 16.67%. The next most likely totals are 6 and 8, at 5/36 each.

What is the probability of rolling a 7 with two dice?

6/36 = 1/6 ≈ 16.67%. On average, a 7 comes up about once every 6 rolls of two dice.

What does 4d6 drop lowest mean?

Roll four six-sided dice, ignore the lowest one and add the other three. Totals run from 3 to 18, the expected total is about 12.24, and 13 is the most likely total at 172/1,296 ≈ 13.27%.

What is the expected value of rolling a die?

For a fair six-sided die it is (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = 3.5. For any die with s sides it is (s + 1) ÷ 2, so a d20 averages 10.5.

What are the odds of a natural 20 with advantage?

You miss a 20 only if neither die shows 20: (19/20)² = 361/400. So the chance is 1 − 361/400 = 39/400 = 9.75%, almost twice the 5% of a single d20.

Sources

• MDN Web Docs: Crypto.getRandomValues() method

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