Dice probability calculator

Count ordered outcomes

Two six-sided dice have 36 equally likely ordered outcomes. Six produce a total of seven: 1+6, 2+5, 3+4 and their reversals. The probability is 6/36, or about 16.67%.

An average is not a guaranteed roll

A fair six-sided die has an expected value of 3.5, so two dice average seven over repeated trials. A single roll can produce any total from two through twelve.

Match the physical model

Choose the number of identical fair dice and the number of sides on each. A proprietary crypto-dice product may use a different outcome range and house rule, so it is not automatically represented by physical dice.

Dice roll average and three-dice games

For n fair dice with s sides numbered 1 through s, the mean total is n × (s+1)/2. Three six-sided dice average 10.5 and have 6³ = 216 ordered outcomes. For sum conditions, the matching outcome count divided by 216 gives the probability.

For payout and triple-exclusion rules in a three-dice casino game, use the Sic Bo calculator. A continuous or integer crypto-dice roll uses a different model; use the crypto dice calculator with a supplied probability and house edge.

See the full distribution rather than only one total

For combinations with at most 100 as the highest possible total, the result includes an exact table for every possible sum. The counts are computed by convolution of the equal face probabilities; they are not sampled from random rolls.

Two six-sided dice have 36 ordered outcomes. Only one gives two, while six give seven. Larger calculations still return the requested probability without adding a long table. The Sic Bo calculator also applies an entered payout to defined three-dice bets.