Dice calculator
Work out dice sums, the chance of at least one six and of five of a kind. The results apply to fair, independent dice.
The dice calculator works out probabilities for fair dice: every side is equally likely and the rolls do not affect each other. You can look at sums of several dice or try simple examples of repeated rolls.
Work out a sum
Choose between one and ten dice and the number of sides: 4, 6, 8, 10, 12 or 20. All dice use the same number of sides and are numbered from 1 up to that number.
"Exactly", "at least" or "at most" sets the condition. With two six-sided dice there are 36 ordered results, all equally likely. Six of them give a sum of at least 10: three make 10, two make 11 and one makes 12. That is 6 / 36, about 16.67 per cent.
The bars show how the sums are distributed; highlighted bars meet your condition. "About once every … rolls" is the reciprocal of the probability. It is not a schedule after which a result is due.
At least one six
This part is about one six-sided die. For n rolls the formula is 1 − (5 / 6)ⁿ. In four rolls the chance of at least one six is about 51.77 per cent. Even so, a run without a six is possible.
Our article on loot box odds uses the same principle. There, too, what matters is independent tries with an unchanged single chance.
What is assumed for five of a kind?
Five of a kind means all five six-sided dice show the same number, the roll known from Yahtzee. On the first roll, six of the 6⁵ = 7,776 equally likely results match. That is 1 in 1,296, or about 0.077 per cent.
For up to three rolls the model keeps the largest group of matching dice after each roll and re-rolls the rest. The calculation covers every possible roll for this strategy and comes to about 4.6 per cent. It does not simulate a full game or decisions made for other scoring categories.
More tools are in the calculators overview. If you would like to solve a number puzzle yourself, start a game of Sudoku.