A little chance. A lot of possibility.
Dice Probability: Totals, Advantage and Streaks
A single die has equally likely faces. A sum of dice does not have equally likely totals. Work through the examples below, then use the calculator on a roller to explore your own settings.
By Virtual Dice Roller · How we write and check our guides
Published · Updated
One die: one chance per face
For a fair die with S sides, a particular face has probability 1/S. A 6 on a D6 has a 1/6 chance (about 16.67%); a 20 on a D20 has a 1/20 chance (5%). A D100 result is 1 to 100 here, and each result has a 1% chance.
For a D20 check that needs at least 15 before modifiers, six faces succeed: 15, 16, 17, 18, 19 and 20. The probability is 6/20 = 30%. If you add +3 and need a total of 15, the raw roll must be at least 12, giving 9/20 = 45%.
Two D6: why seven is more likely than two
Two independent six-sided dice have 6 × 6 = 36 equally likely ordered pairs. The total 2 has only one pair, (1, 1). The total 7 has six: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1). Its chance is 6/36 = 1/6.
A double can be (1, 1) through (6, 6), so any double also has a 6/36 chance. A total of at least 7 has 21 possible pairs, giving 21/36 = about 58.33%. Explore every total in the two-dice probability table.
Expected total is an average, not a forecast
The average of one S-sided die is (S + 1)/2. For N independent dice of that size, the expected sum is N × (S + 1)/2. A fixed modifier is added once. For 3d6+2, the range is 5 to 20 and the expected total is 12.5. A single actual roll is still a whole number.
The probability calculator below each numeric dice roller computes the theoretical distribution by combining each die’s possible results. Enter a target to see the chance of exactly that total, at least it or at most it. It supports ordinary sums and RPG modifiers. Mixed pools and keep/drop selections need a different distribution and are excluded explicitly.
D20 advantage and disadvantage
For a raw D20 target T from 1 to 20, a normal roll succeeds with probability p = (21 − T)/20. Advantage succeeds unless both dice fail, giving 1 − (1 − p)². Disadvantage succeeds only when both dice succeed, giving p².
At a target of 15, normal is 30%, advantage is 51% and disadvantage is 9%. A raw 20 has a 5% chance normally, 9.75% with advantage and 0.25% with disadvantage. These figures describe die outcomes; your game decides whether a natural 20 has a special effect. Try the RPG roller to see both dice and the retained result.
Streaks do not make a result due
For independent rolls, the previous result does not change the next one. Three sixes in three D6 rolls have probability (1/6)³ = 1/216, but after two sixes the next roll still has a 1/6 chance of being six.
A short history is useful for checking what happened, but cannot prove whether a generator is fair. This site uses Web Crypto with rejection sampling to avoid modulo bias. Read our randomness method and the Web Crypto specification.
A classroom experiment
Set the classroom dice roller to two dice. Before rolling, ask which total students expect most often. Make a tally of 30 totals, download the latest 20 rolls when you need a record, and compare the tally with the theoretical table. A small sample can look uneven; discuss why that does not change the probability of the next roll.
