Dice Game Probability Calculator

For a pool of dice, find the chance at least one shows your target number, the expected count, and the odds every die matches. Calculates in your browser.

The number you're hoping to roll on a die (e.g. rolling sixes).

At least one shows it

-

Expected count-
One specific die-
All dice match it-

Show the math

Each die shows the target with probability 1/S. The chance at least one of N dice shows it is one minus the chance every die misses:

P(at least one) = 1 − ((S−1)/S)ᴺ

All math runs locally in your browser.

What this does

A dice game probability calculator finds, for a pool of dice, the chance at least one shows your target, the expected count, and the odds every die matches.

How to use it

  1. Enter the number of dice.
  2. Set the sides per die.
  3. Choose the target number.
  4. Read the probabilities.

How it works

At-least-one is one minus the chance every die misses, so more dice raise the odds quickly. Expected count is dice ÷ sides.

P(at least one) = 1 − (1 − 1/sides)^dice

Understanding your result

The at-least-one odds climb fast as you add dice, because you are really computing one minus the chance that every die misses, not adding up single-die chances. That distinction matters: rolling more dice helps far more than it intuitively seems, while the chance of every die matching your target drops away just as quickly.

Example

Four six-sided dice have about a 52% chance of at least one 6.

Sources & methodology

Last updated .

Frequently asked questions

How is the at-least-one chance found?

It is one minus the chance that every die misses the target, so more dice raise the odds quickly.

What is the expected count?

The average number of dice that will show your target, the pool size divided by the number of sides.

Is my data kept?

No. Everything is computed locally in your browser.