Two Dice Probability Calculator
Calculate probabilities for rolling two dice with various conditions
Dice Configuration
Probability Results
Favorable Combinations (6)
Sum Distribution
Dice Probability Basics
Single Die
Each face has 1/6 probability
16.67% for any face
Two Dice
Total outcomes: 6²
36 possible combinations
Independence
Each die roll is independent
Multiply probabilities for "and"
Common Examples (6-sided dice)
Quick Actions
Understanding Two Dice Probability
Basic Concepts
When rolling two dice, each die is independent, meaning the outcome of one doesn't affect the other. With standard 6-sided dice, there are 36 possible outcomes (6 × 6), each equally likely to occur.
Probability Formula
n = Favorable outcomes
N = Total possible outcomes
Sum Probabilities
- •Some sums are more likely than others (e.g., sum of 7 has 6 ways)
- •Extreme sums (like 2 or 12) have only one way each
- •The distribution forms a triangular pattern
Different Dice Types
4-sided dice (D4)
16 total outcomes, sums from 2 to 8
6-sided dice (D6)
36 total outcomes, sums from 2 to 12
20-sided dice (D20)
400 total outcomes, sums from 2 to 40
Special Cases
Both dice same: Only N ways (one for each face value)
At least one specific value: Use complement rule: 1 - P(neither)
Specific die value: N ways (other die can be anything)
Applications and Examples
🎲 Board Games
Monopoly: Need doubles to get out of jail
Craps: Sum of 7 or 11 on come-out roll
Backgammon: Specific moves require certain sums
Risk: Battle outcomes depend on dice comparisons
🎯 Tabletop RPGs
D&D: Advantage/disadvantage mechanics
Damage rolls: Multiple dice for weapon damage
Skill checks: Meeting difficulty thresholds
Critical hits: Rolling maximum values
📊 Probability Teaching
Independence: Die rolls don't affect each other
Sample spaces: Listing all possible outcomes
Expected values: Long-run average results
Distributions: How probabilities spread out