2 Dice Roller Calculator
Roll two virtual dice with complete probability analysis and statistical insights
Virtual Dice Roller
Die 1
Die 2
Sum
Probability Distribution
Statistics Overview
Dice Rolling Tips
Each roll is independent - past results don't affect future rolls
Middle sums (like 7 for two 6-sided dice) are most probable
Extreme sums (minimum and maximum) are least probable
More sides = more possible outcomes and different probabilities
Understanding Two Dice Probability
Basic Concepts
When rolling two dice, each die is independent, meaning the result of one die doesn't affect the other. With standard 6-sided dice, there are 36 possible outcomes (6 × 6), but only 11 possible sums (2 through 12).
Why Some Sums Are More Likely
The sum of 7 has the highest probability because there are more ways to make it: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). In contrast, there's only one way to make 2: (1,1), and one way to make 12: (6,6).
Probability Distribution
For two standard 6-sided dice:
- • P(sum = 2 or 12) = 1/36 = 2.78%
- • P(sum = 3 or 11) = 2/36 = 5.56%
- • P(sum = 4 or 10) = 3/36 = 8.33%
- • P(sum = 5 or 9) = 4/36 = 11.11%
- • P(sum = 6 or 8) = 5/36 = 13.89%
- • P(sum = 7) = 6/36 = 16.67%
Applications
- •Board games and gambling analysis
- •Educational probability demonstrations
- •Statistical learning and visualization
- •Game design and balancing