Dice Probability Calculator
Chance of rolling at least one chosen face, the expected total, and the odds of all dice matching.
Results
Probability
51.7747
%
True or expected value
14.000
Probability
0.462963
%
Standard deviation (sample)
3.4157
Combinations
1296
What this tool does
The chance of getting at least one six in four dice is just over half — a fact that famously bankrupted gamblers who assumed it was four times one sixth. Probabilities of independent events multiply rather than add, and the calculation works by asking for the chance of it never happening and subtracting that from one.
Formula
P(at least one) = 1 − ((s−1) ÷ s)^n
Variables
| Symbol | Meaning | Unit |
|---|---|---|
nd | Number of dice | — |
sd | Sides per die | — |
P1 | Probability | % |
EV | True or expected value | — |
PA | Probability | % |
SD | Standard deviation (sample) | — |
CM | Combinations | — |
Worked example
- Number of dice4
- Sides per die6
- Probability51.7747 %
- True or expected value14.000
- Probability0.462963 %
- Standard deviation (sample)3.4157
- Combinations1296
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.