Dice Roller

The Mathematics of Dice

When you roll a 6-sided die, the sum follows a discrete probability distribution shaped by convolution. A single die produces a uniform distribution: each face equally likely at 1/6. Adding a second die convolves two uniform distributions into a triangular shape. Each additional die smooths the distribution further toward a bell curve, a consequence of the Central Limit Theorem described by Abraham de Moivre in 1733.

Fairness and Randomness

Every die on this page is powered by crypto.getRandomValues(), the Web Cryptography API built into your browser. The distribution chart tracks your empirical results against the theoretical probability. Over many rolls, the two converge, demonstrating the law of large numbers in real time.