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Exact Dice Sum Probability Calculator
Calculate every attainable sum and exact target probability for identical independent fair dice.
Number of dice (text), Sides per die (text), Target comparison (select), Target sum (text)
Complete exact JSON report
Browser only
Runs locally in your browser. Your files, pasted content and generated output are not uploaded. Reset clears this tool’s working data.
This tool needs JavaScript. If it does not load, refresh the page and try again.
How to use this tool
- Enter Number of dice and Sides per die, then choose Target comparison and Target sum.
- Select Calculate exact distribution.
- Download dice-distribution.json for the complete distribution and exact target probability.
Examples
Two fair six-sided dice have36 outcomes; sum7 has6 outcomes and probability1/6.
Limitations
- 1–20 dice, 2–100 integer faces per die, at most 1,981 attainable sums, 1 MiB complete report and a 30-second processing limit.
- Dice and sides require unsigned decimal integers. Target accepts a signed integer of at most 100 digits and 128 raw units; targets outside the attainable range return exact zero or one probabilities.
- No simulation, omitted tail, custom/loaded/exploding dice or keep-highest rules.
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