Dice Laboratory
Roll any configuration and chart the distribution against theory.
Roll virtual dice and watch how the distribution of outcomes takes shape over hundreds or thousands of trials. An educational tool for visualizing probability distributions, expected value, and variance.
No rolls this session yet.
Frequently Asked Questions
What is the probability of rolling a 7 with two dice? ▾
The probability of rolling a sum of 7 with two standard dice is 6/36 = 16.67%. There are 6 ways to make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total combinations, making it the most common outcome.
Are dice rolls truly random? ▾
Physical dice depend on initial conditions, angle, velocity, surface, which are effectively unpredictable, producing outcomes that are statistically random. This simulator uses a cryptographically seeded pseudo-random number generator which passes statistical randomness tests.
What is the expected value of a single die roll? ▾
The expected value of a fair six-sided die is (1+2+3+4+5+6)/6 = 3.5. For two dice, the expected sum is 7. This is why 7 is the most common outcome and the basis for many casino game rules.
What does the distribution chart show? ▾
The bar chart shows how often each sum has appeared in your session versus the theoretical probability. As you roll more dice, the empirical distribution converges toward the theoretical curve, a demonstration of the Law of Large Numbers.