Dice Roll Probability Calculator
The exact probability distribution for the sum of any number of dice, computed directly (this one’s cheap, closed-form math, not a lookup) — not just the standard 2d6.
16.67%
Exactly 7
58.33%
At least 7
2d6: possible sums range from 2 to 12.
Why the middle comes up more often: with one die every face is equally likely, but the sum of two or more stops being flat. There’s only one way to roll a 2 on 2d6 (1+1) and only one way to roll a 12 (6+6), but six different combinations add up to 7 — so 7 comes up six times as often as either extreme. Add more dice and the effect compounds: the number of ways to hit a middling sum grows much faster than the number of ways to hit an extreme one, which is why large dice pools cluster tightly around their average and rarely land near the top or bottom of the range. Standard board-game rolls sit at different points on that curve on purpose — 2d6 (Catan, Settlers-style production) is deliberately lumpy so certain numbers matter more, while a single d20 (the common tabletop RPG die) stays perfectly flat since it’s only one die.
Rolls people ask about
The same exact maths, worked through for the targets that come up most — with every way to make them listed.