Dice Probability Calculator

In short Rolling 7 on two six-sided dice has a probability of 16.6667% — 6 of the 36 possible outcomes. It is the most likely total, and the reason is pure counting: 7 is the only sum that every face can contribute to, from 1+6 through to 6+1. There is exactly one way to roll 2 and one way to roll 12, which is why the extremes are rare and the middle is common. That is where the bell shape comes from, and it appears from nothing but enumeration. This page builds the complete distribution by convolution rather than simulating rolls, so every figure is an exact count of whole outcomes. Two dice give 36 outcomes, three give 216, and ten six-sided dice give over 60 million — all counted exactly, which is why the answers are precise rather than approximate. The important thing this makes visible is that sums are NOT equally likely, even though each individual face is. People reason about the total as though it behaves like a single die, and it does not: on 3d6 the middle totals of 10 and 11 have 27 ways each while 3 and 18 have one apiece, a 27-fold difference. The dice are assumed fair and independent, which is the only assumption on the page.