Dice Probability Calculator

Dice probability uses combinatorics to calculate the exact likelihood of rolling specific sums or outcomes with one or more dice. The distribution of sums follows a discrete probability distribution that becomes approximately bell-shaped (normal) as more dice are added — an illustration of the Central Limit Theorem.

1. 1Total outcomes for d dice with s sides: sᵈ
2. 2Count ways to roll exactly target sum T: dynamic programming (convolution of dice distributions)
3. 3P(sum = T) = ways / total outcomes
4. 4Expected sum for d dice with s sides: d × (s+1)/2
5. 5Variance: d × (s²−1)/12