Dice Probability Calculator
Calculate probabilities for various dice rolling scenarios with polyhedral dice
Configure Dice and Calculation
Select the type of dice (number of faces)
How many dice to roll (1-20)
Value that must appear on the dice (1-6)
Probability Results
All 1 dice show 1
Formula: P = (1/6)^1 = 0.16666667
Common Dice Probability Examples
Rolling a 7 with two 6-sided dice
Ways: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 ways out of 36 total
Probability: 6/36 = 16.67%
Rolling three 6s with three dice
Each die has 1/6 chance of showing 6
Probability: (1/6)³ = 0.46%
Rolling at least one 6 with two dice
Use complement: 1 - P(no 6s) = 1 - (5/6)²
Probability: 1 - 25/36 = 30.56%
Polyhedral Dice Types
Tetrahedron
4 triangular faces
Cube
6 square faces
Octahedron
8 triangular faces
Icosahedron
20 triangular faces
Probability Tips
Each face has equal probability of 1/n
Independent rolls multiply probabilities
Use binomial for "exactly k successes"
Sum probabilities approach normal distribution
Understanding Dice Probability
Basic Principles
Dice probability is based on the fundamental principle that each face of a fair die has an equal chance of appearing. For an n-sided die, each outcome has a probability of 1/n.
Key Formulas
- •Single outcome: P = 1/n
- •Multiple dice, same value: P = (1/n)^k
- •Binomial: P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
- •Complement: P(at least one) = 1 - P(none)
Common Applications
Gaming
Board games, RPGs, and casino games use dice probability to balance gameplay
Statistics
Dice serve as simple models for discrete uniform distributions
Education
Teaching probability concepts through tangible, visual examples