Dice Average Calculator
Calculate expected values and statistics for dice rolls
This calculator helps you analyze the statistical properties of dice rolls:
- Enter the number of dice you want to roll
- Specify the number of sides on each die
- The calculator will provide:
- Expected value (theoretical average)
- Minimum and maximum possible rolls
- Standard deviation and variance
- Simulated average from multiple rolls
Key statistical concepts for dice rolls:
- Expected Value:
E = n × (s + 1) / 2
Where n is the number of dice and s is the number of sides
- Variance:
V = n × (s² - 1) / 12
Measures how spread out the possible values are
- Standard Deviation:
SD = √V
Square root of variance, in the same units as the rolls
Understanding dice statistics is useful for:
- Game design and balancing
- Tabletop role-playing games
- Probability education
- Statistical modeling
- Random number generation analysis
- Fair gambling analysis
- Teaching expected value concepts
Why does the simulated average differ from the expected value?
The simulated average is based on random sampling, so it will vary slightly from the theoretical expected value. The more trials we run, the closer it tends to get to the expected value (Law of Large Numbers).
What does the standard deviation tell me?
The standard deviation indicates how spread out the dice rolls are likely to be from the average. About 68% of rolls will fall within one standard deviation of the expected value, and about 95% within two standard deviations.
Can I use this for non-standard dice?
Yes! The calculator works for any number of sides greater than 1. You can use it for standard dice (d4, d6, d8, d10, d12, d20) or custom dice with any number of sides.