Dice Probability For Games Calculator

Work out dice probability for games instantly with clear inputs, formula shown and shareable results.

About Dice Probability For Games Calculator

The distribution of dice totals is built by convolution: start with one way to score zero, then for each die spread every running total across its faces. Dice totals are not uniform, which is why 7 comes up six times more often than 2 on two dice and why board games reward middle numbers.

Formulas

Total outcomes

outcomes = sides ^ number of dice

Probability

probability = combinations giving the target / total outcomes

Worked example

With the default values below, Dice Probability For Games Calculator returns Chance of rolling exactly that total of 16.6667%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of diceaccepts 1–10: 2
Sides per dieaccepts 2–100: 6
Target totalminimum 1: 7

Results

Chance of rolling exactly that total: 16.6667%
Combinations that give the total: 6
Total possible rolls: 36
Chance of that total or higher: 58.3333%

Step by step

1Values used
2Total outcomes
3Probability
4Chance of rolling exactly that total= 16.6667
5Combinations that give the total= 6
6Total possible rolls= 36
7Chance of that total or higher= 58.3333

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Dice Probability For Games figure worked out?

outcomes = sides ^ number of dice. The distribution of dice totals is built by convolution: start with one way to score zero, then for each die spread every running total across its faces.

Why does this matter?

Dice totals are not uniform, which is why 7 comes up six times more often than 2 on two dice and why board games reward middle numbers.

What do I need to enter?

Enter number of dice, sides per die, target total. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.