Calculate exact probabilities for dice rolls using dynamic programming. Supports any number of dice and sides.
How many dice are being rolled (1-100).
Number of faces on each die (e.g., 6 for standard d6, 20 for d20).
Choose how to compare the sum to your target value.
The target sum value for your condition. For 2d6, the range is 2 to 12.
Results
Dice Configuration
Possible Range
Total Outcomes
Favorable Outcomes
Probability
Percentage
Odds (1 in X)
Expected Sum
Std Dev of Sum
Method
Dynamic programming: build probability table iteratively for each die added.
E(sum) = n × (s+1)/2 Var(sum) = n × (s²−1)/12
References: Dice sum distribution computed via dynamic programming (convolution). E(NdS) = N(S+1)/2. Var(NdS) = N(S²-1)/12. Exact for reasonable N and S.