6 Sided Dice Roller Calculator
Roll virtual 6-sided dice with complete statistical analysis and visual representation
Roll 6-Sided Dice
Choose between 1 and 20 dice to roll
About 6-Sided Dice (D6)
Shape
Perfect cube with six square faces
Probability
Each side has 16.67% (1/6) chance
Usage
Board games, RPGs, probability experiments
Probability Facts
Single Roll
Each number (1-6) has exactly 1/6 probability
Multiple Dice
Total outcomes = 6^n (where n = number of dice)
Expected Value
Average result per die is 3.5
Dice Rolling Tips
Each roll is independent of previous rolls
Law of large numbers applies over many rolls
Uniform distribution means all outcomes equally likely
Use auto-roll to simulate large number of throws
Understanding 6-Sided Dice Statistics
What is a 6-Sided Die?
A 6-sided die (d6) is a cube with six faces numbered 1 through 6. It's the most common die used in games and probability experiments. Each face has an equal probability of landing face-up when rolled, making it a perfect example of uniform distribution.
Statistical Properties
- •Each outcome has probability 1/6 ≈ 16.67%
- •Expected value (mean) = 3.5
- •Variance = 35/12 ≈ 2.92
- •Standard deviation ≈ 1.71
Multiple Dice Calculations
Two Dice Example
Total outcomes: 6² = 36
Expected sum: 2 × 3.5 = 7
Most likely sum: 7 (6 ways to achieve)
Consecutive Identical Rolls
Probability of rolling same number n times:
P = (1/6)ⁿ
Example: 3 sixes in a row = (1/6)³ ≈ 0.46%
Law of Large Numbers
With many rolls, the average approaches 3.5
Each face appears ~16.67% of the time
Deviations decrease as sample size increases
Random Number Generation
Our calculator uses pseudorandom number generation to simulate dice rolls. While not truly random like physical dice, the algorithms produce statistically uniform distributions suitable for games and educational purposes.