Dice Probability Calculator

Calculate dice probability for a specific total, all dice showing the same value, or at least one target face with exact ratio and percent.

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Dice Probability Formulas

The following formulas are used to calculate different dice probabilities (for fair 6-sided dice).

1. Chance to roll a specific total sum (sum of all dice)
   1. C = N / 6^D
      • Where D is the number of dice
      • Where N is the number of ordered outcomes (rolls) that produce the target sum
2. Chance all dice show a specific value (i.e. 1/1/1 on 3 dice)
   1. C = (1 / 6)^D
      • Where D is the number of dice
3. Chance to roll at least one specific value on a roll of D dice (i.e. at least one 6)
   1. C = 1 – (5 / 6)^D
      • Where D is the number of dice

These formulas are written for 6-sided dice. For s-sided dice, replace 6 with s (so the denominators become s^D). For example: (1/6)^D becomes (1/s)^D, and 1 – (5/6)^D becomes 1 – ((s-1)/s)^D.

Dice Probability Definition

Dice Probability is defined as the chance of an event occurring while rolling 1 or more dice.

Dice Probability Example

How to calculate a dice probability?

First, determine the event or outcome you wish to calculate the probability of. In this example, we are examining the chance to roll 1/1/1 when rolling 3 dice (or the same die 3 times).

Next, choose the formula above that matches the probability event you are calculating and also decide the number of sides on the dice. In this case, the number of sides is 6 and the formula is:

C = (1 / 6)^D

C = (1 / 6)^3

C = 1/216 ≈ 0.00463 = 0.463% chance.

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